Site Map | Polytopes | Dynkin Diagrams | Vertex Figures | Incidence Matrices | Index |
Acronyms and some of the names are due to Jonathan Bowers.
Index is also available in alphabetical order. Parts of this index - as far as face vectors are provided - are also available in an (accordingly) further sorted order. Parts of this index - as far as circumradii are explicitly given - are also available in an (accordingly) numerically sorted order.
---- 2D ----
Acronym | Name | Circumradius | Face vector |
... | hyperbolic [10,8,4,6] tiling with tetragonal Coxeter domain | ||
... | complex honeycomb x2-4-o4-3-o4 | ||
... | complex honeycomb x2-4-op-4-o2 , complex honeycomb op-4-x2-4-op | ||
... | 2hexat (?) | ||
... | 2hoha (?) | ||
... | 2srothat (?) | ||
... | 2that (?) | ||
... | 2that+∞{3} (?) | ||
... | 2toxat (?) | ||
... | complex honeycomb x3-3-o3-4-o3 | ||
... | complex honeycomb x3-4-o3-3-o3 | ||
... | hyperbolic [(33,4)4] tiling | ||
... | complex honeycomb x4-3-o4-3-o4 | ||
... | complex honeycomb x4-3-o4-4-o2 , complex honeycomb o4-3-x4-3-o4 | ||
... | hyperbolic [4,6,6,∞] tiling with tetragonal Coxeter domain | 0.707107 i | |
asquat | hyperbolic order ∞ square tiling | 0 i | |
azap | apeirogonal antiprism | ||
azat | hyperbolic order 3 apeirogonal tiling, hyperbolic order 3 horocyclic tiling, hyperbolic truncated order ∞ horocyclic tiling | 0.866025 i | |
azazat | hyperbolic order ∞ apeirogonal tiling, hyperbolic order ∞ horocyclic tiling | 0 i | |
azip | apeirogonal prism | ||
aztrat | hyperbolic order ∞ triangular tiling | 0 i | |
... | c01 of hyperbolic [10,8,4,6] tiling with tetragonal Coxeter domain * | ||
... | c0 of hyperbolic [10,8,4,6] tiling with tetragonal Coxeter domain * | ||
cha | complexihexaapeirogonal tiling | ||
chata | complexitrihexaapeirogonal tiling | ||
chatit | complexitrihexagonal tiling | ||
cosa | complexisquariapeirogonal tiling | ||
dazatrapeat | hyperbolic x∞x3o5*a tiling, diapeirogonal apeirogon-triangle-pentagon tiling, cyclotruncated apeirogon-triangle-pentagon tiling | 0.754758 i | |
depat | hyperbolic order 10 pentagonal tiling | 0.206652 i | |
detrat | hyperbolic order 10 triangular tiling | 0.393076 i | |
ditatha | ditrigonary trigonal hemiapeirogonal tesselation, alternate triangular tiling | ||
ditetetrat | hyperbolic order 4 tritetragonal tiling, hyperbolic ditetragonal tritetratrigonal tiling, hyperbolic alternated order 4 hexagonal tiling | 0.408248 i | |
ditetpeat | ditetratgonal triangle-pentagon-tiling, hyperbolic tripentagonal tiling of family o3o4o5*a | 0.357770 i | |
ditetsquat (old: dittitecat) | hyperbolic order 3 tritetragonal tiling, hyperbolic ditrigonary triangle-square tiling, hyperbolic ditrigonary tritetragonal tiling, hyperbolic alternated octagonal tiling | 0.728238 i | |
ditoot | ditrigonary octaoctagonal tiling, hyperbolic order 3 octagonal-octagrammic tiling | 0.557369 i | |
etrat | elongated triangular tiling | ||
ghaha | great hexahexaapeirogonal tiling | ||
gheat | great heptagonal tiling, hyperbolic order 7/2 heptagon tiling | 0.873057 i | |
ghothat, (inbetween: ghath) | great hexagonal-trigonal-hexagonal tiling | ||
gossa | great squarisquariapeirogonal tiling | ||
... | Gott's snic-based pseudopolyhedron | ||
graht | great rhombihexagonal tiling | ||
grotazt | hyperbolic great rhombitriapeirogonal tiling, hyperbolic omnitruncated trigonal-horocyclic tiling, hyperbolic truncated triapeirogonal tiling | 2.397916 i | |
grotehat | hyperbolic great rhombitetrahexagon tiling, hyperbolic order 6 omnitruncated square tiling, hyperbolic order 4 omnitruncated hexagon tiling | 2.474067 i | |
grotepet (old: opeat) | great rhombitetrapentagonal tiling, omnitruncated pentagonal tiling, hyperbolic omnitruncated tetrapentagonal tiling | 3.121470 i | |
grothat (old: othat) | great rhombitrihexagonal tiling, omnitruncated trihexagonal tiling | ||
grothet (old: othet) | hyperbolic great rhombitruncated triheptagonal tiling, hyperbolic omnitruncated triheptagonal tiling | 4.779184 i | |
grotoct (old: otoct) | hyperbolic great rhombated trioctagonal tiling, hyperbolic omnitruncated trioctagonal tiling | 3.699185 i | |
hatha | hexaapeirogonaltruncated hexaapeirogonal tiling | ||
hazt | hyperbolic hexa-apeirogonal tiling | 0.577350 i | |
heat | hyperbolic order 3 heptagonal tiling | 1.742610 i | |
hetrat | hyperbolic order 7 triangular tiling | 0.873057 i | |
hexat | hexagonal tiling, Voronoi complex of hexagonal lattice A2 | ||
hihexat | hyperbolic order 6 hexagonal tiling | 0.353553 i | |
hipat | hyperbolic order 6 pentagonal tiling | 0.393076 i | |
hisquat | hyperbolic order 6 square tiling | 0.5 i | |
huht | hexahexagonal tiling | ||
... | hyperbolic tetrapentagonal tiling of family o3o4o5*a | 0.438176 i | |
... | hyperbolic tritetragonal tiling of family o3o4o5*a | 0.297397 i | |
... | hyperbolic ditetragonal tiling of family o3o4o5*a | 0.921730 i | |
o4x4oP*a | family of (generally hyperbolic) order 2P square tilings | ||
ocat | hyperbolic order 3 octagonal tiling | 1.345608 i | |
ococat | hyperbolic order 8 octagonal tiling | 0.227545 i | |
osquat | hyperbolic order 8 square tiling | 0.321797 i | |
otrat | hyperbolic order 8 triangular tiling | 0.594604 i | |
... | complex honeycomb xp-4-o2-4-o2 , δp,2 3, complex honeycomb o2-4-xp-4-o2 , complex honeycomb xp-4-o2-4-xp | ||
... | complex honeycomb xp-4-o2-4-op , δp,p 3 | ||
... | complex honeycomb xp-4-o2-4-or , δp,r 3 | ||
... | complex honeycomb xp1 -q1-or1 xp2 -q2-or2 , δp1,r1 2 × δp2,r2 2 | ||
... | partially contracted hyperbolic order 3 tritetragonal tiling | ||
pacrothat | partially contracted rhombitrihexagonal tiling | ||
peat | hyperbolic order 4 pentagonal tiling | 0.899454 i | |
pedecat | hyperbolic order 5 decagonal tiling | 0.154508 i | |
pepat | hyperbolic order 5 pentagonal tiling | 0.528686 i | |
pesquat | hyperbolic order 5 square tiling | 0.747674 i | |
pextrat | partially expanded triangular tiling | ||
phat | hyperbolic pentahexagonal tiling | 0.786151 i | |
qrasquit | quasirhombated square tiling | ||
qrothat | quasirhombitrihexagonal tiling | ||
quitothit | quasitruncated trihexagonal tiling | ||
quitsquat | quasitruncated square tiling | ||
quothat | quasitruncated hexagonal tiling | ||
rarsisresa | rhombiretrosnub squarirhombisquariapeirogonal tiling | ||
rasisquat | retrosnub square tiling | ||
rassersa | rhombisnub squarirhombisquariapeirogonal tiling | ||
... | complex honeycomb o3-3-x3-4-o3 | ||
... | complex honeycomb o4-3-x4-4-o2 | ||
... | complex honeycomb op-4-x2-4-o2 , complex honeycomb x2-4-op-4-x2 | ||
... | complex honeycomb op-4-x2-4-or | ||
rethat | rectified trihexagonal-tiling, variation of small-rhombitrihexagonal-tiling | ||
retrat | retroelongated trangular tiling | ||
... | partially contracted hexagonal tiling, rhombic uBxx3uxBx3xooA3*a&#zx | ||
... | partially expanded tri-hexagonal rhombic tiling, rhombic uBxx3xoAo3xooA3*a&#zx | ||
... | tri-hexagonal rhombic tiling | ||
... | multiform rhombic tiling with {5}, {10/3}, and {∞} | ||
rorisassa | rhombiretrosnub squarisquariapeirogonal tiling | ||
rosassa | rhombisnub squarisquariapeirogonal tiling | ||
... | hyperbolic snub tiling of family o3o3o∞*a | ||
... | hyperbolic snub tiling of family o3o4o5*a | ||
satsa | squariapeirotruncated squariapeirogonal tiling | ||
sazazat | hyperbolic snub di-horocyclic tiling, snub apeirogonal tiling | ||
sha | square hemiapeirogonal tesselation, alternate square tiling | ||
shaha | small hexahexaapeirogonal tiling | ||
sheat | stellated heptagonal tiling, hyperbolic order 7 heptagram tiling | 0.484510 i | |
shexat | hyperbolic order 4 hexagonal tiling | 0.707107 i | |
shothat, (inbetween: shath) | small hexagonal-trigonal-hexagonal tiling | ||
siditetpeat | small ditetragonary tetrapentagonal tiling, hyperbolic x4o4o5/2*a tiling | 0.786151 i | |
sittiteteat | hyperbolic rectified ditetragonary tritetragonal tiling, hyperbolic small tritetratetragonal tiling, hyperbolic cantic order 4 hexagonal tiling | 1.060082 i | |
sittitetrat | hyperbolic shieldotritetragonal tiling, hyperbolic ditrigonary tritetratrigonal tiling, hyperbolic cantic octagonal tiling | 1.446026 i | |
snasquat | snub square tiling | ||
snatazt | hyperbolic snub trigonal-horocyclic tiling, hyperbolic snub triapeirogonal tiling, snub triapeirogonal tiling | ||
snathat | snub trihexagonal tiling | ||
snathet | hyperbolic snub triheptagonal tiling | ||
snatoct | hyperbolic snub trioctagonal tiling | ||
socat | hyperbolic order 4 octagon tiling | 0.594604 i | |
sossa | small squarisquariapeirogonal tiling | ||
sost | squarisquaritiling | ||
spepat | hyperbolic snub pentapentagonal tiling | ||
squat | square tiling, 2D hypercubical honeycomb (δ2), Voronoi complex of square lattice, Delone complex of square lattice | ||
squazat | order 4 apeirogonal tiling, hyperbolic order 4 horocyclic tiling | 0.5 i | |
sraht | small rhombihexagonal tiling | ||
srotazt | hyperbolic (small) rhombi-trigonal-horocyclic tiling | 1.322876 i | |
srotehat | hyperbolic (small) rhombisquarehexagonal tiling | 1.405256 i | |
sroteoct | hyperbolic (small) rhombitetraoctagonal tiling | 1.175154 i | |
srotepet | hyperbolic rhombisquarepentagonal tiling | 1.794231 i | |
srotezt | hyperbolic (small) rhombitetraapeirogonal tiling, hyperbolic rhombisquareapeirogonal tiling | 0.978318 i | |
srothat (old: rothat) | (small) rhombitrihexagonal tiling | ||
srothet (old: sirthet) | small rhombitriheptagonal tiling, hyperbolic rhombitriheptagonal tiling | 2.728895 i | |
srotoct (old: sirtoct) | hyperbolic (small) rhombitrioctagonal tiling | 2.096343 i | |
stepet | hyperbolic snub tetrapentagonal tiling | ||
stititet | hyperbolic snub tritritetragonal tiling, hyperbolic snub tiling of family o3o3o4*a | ||
... | snub of hyperbolic [10,8,4,6] tiling with tetragonal Coxeter domain | ||
tasquat | hyperbolic truncated infinite-order square tiling | 1.098684 i | |
tazat | hyperbolic truncated order 3 horocyclic tiling, hyperbolic truncated order 3 apeirogonal tiling | 1.936492 i | |
tazt | hyperbolic trigonal-horocyclic tiling, hyperbolic triapeirogonal tiling | 1 i | |
taztrat | hyperbolic truncated order ∞ trigonal tiling | 1.414214 i | |
tehat | hyperbolic tetrahexagonal tiling | 1 i | |
teoct | hyperbolic tetraoctagonal tiling | 0.840896 i | |
tepet (old: tepeat) | hyperbolic tetrapentagonal tiling | 1.272020 i | |
tezt | hyperbolic tetragonal-horocyclic tiling, hyperbolic square-apeirogon tiling | 0.707107 i | |
tha | trigonal hemiapeirogonal tesselation | ||
that | trihexagonal tiling, Kagomé tiling | ||
theat | truncated heptagonal tiling, hyperbolic order 3 truncated heptagonal tiling | 3.792295 i | |
thet | hyperbolic triheptagonal tiling | 2.012192 i | |
thetrat | truncated order 7 triangular tiling, hyperbolic order 7 truncated trigonal tiling | 2.976586 i | |
thihexat | hyperbolic truncated order 6 hexagonal tiling | 1.221076 i | |
thisquat | hyperbolic truncated order 6 square tiling | 1.632242 i | |
thotithit | trihexagonaltruncated trihexagonal tiling | ||
... | infinite polyhedron from alternating tic/tut structure | ||
tidect | hyperbolic tri-decagonal tiling | 1.272020 i | |
tocat | hyperbolic order 3 truncated octagonal tiling | 2.947161 i | |
toct | hyperbolic trioctagonal tiling | 1.553774 i | |
topazat | hyperbolic truncated order 5 apeirogonal tiling | 1.130426 i | |
topeat | hyperbolic order 4 truncated pentagonal tiling | 2.246127 i | |
topepat | hyperbolic truncated order 5 pentagonal tiling | 1.548400 i | |
topesquat | truncated order 5 square tiling, hyperbolic order 5 truncated square tiling | 2.113125 i | |
tosquat | truncated square tiling | ||
tosquazat | hyperbolic truncated order 4 horocyclic tiling, hyperbolic truncated order 4 apeirogonal tiling | 1.322876 i | |
totrat | truncated order 8 trigonal tiling, hyperbolic order 8 truncated trigonal tiling | 2.276396 i | |
toxat | truncated hexagonal tiling | ||
trat (subsym.: snitititat) | triangular tiling, Delone complex of hexagonal lattice A2 | ||
... | partially contracted hexagonal tiling | ||
... | uBxx3xoAo3xooA3*a&#zx | ||
... | Wells' "hyperbolic" {4,5} polyhedron | ||
... | Wells' infinite polyhedron from the ike/oct diamond structure | ||
... | hyperbolic order 3 trigonal-horocyclic tiling | 0.433013 i | |
... | hyperbolic dipentagonal tiling of family o3o4o5*a | 0.956676 i | |
... | hyperbolic shieldo-trigonal-horocyclic tiling | 0.829156 i | |
... | hyperbolic shieldotetrapentagonal tiling of family o3o4o5*a, ditrigonal tiling of family o3o4o5*a | 0.874835 i | |
... | hyperbolic omnitruncated tiling of family o3o4o5*a | 1.456608 i | |
x4oPo | family of (generally hyperbolic) order P square tilings | ||
... | hyperbolic quarter order 6 square tiling | ||
... | family of (generally hyperbolic) P-gonal tilings of order P |
Count of actually available polytopes: 173
---- 3D ----
Acronym | Name | Circumradius | Face vector |
... | triangle hecatonicosahedron | 62, 180, 120 | |
... | dodeca-augmented rhombicuboctahedron | 36, 72, 38 | |
... | external blend of 12 raded-1-10-5-5 edge facetings | 260, 480, 192 | |
... | 12S-24R-6O polyhedron within quitco's army | 1.062393 | 48, 96, 42 |
... | t16-r12, Stott contraction of t16-s12-r12-h4 | ... | 22, 48, 28 |
... | t16-s12-r12-h4, Stott expansion of t16-r12 | ... | 42, 84, 44 |
... | complex polygon x2-4-or prism, complex polyhedron x2 x2-4-or | 4r, 2r(r+1), r2+2 | |
... | Shephard's 3-generalised octahedron, complex polyhedron x2-3-o2-4-o3 , β3 3 | 0.707107 | 9, 27, 27 |
... | Shephard's 4-generalised octahedron, complex polyhedron x2-3-o2-4-o4 , β4 3 | 0.707107 | 12, 48, 64 |
... | Shephard's 5-generalised octahedron, complex polyhedron x2-3-o2-4-o5 , β5 3 | 0.707107 | 15, 75, 125 |
... | Shephard's p-generalised octahedron, complex polyhedron x2-3-o2-4-op , βp 3 | 0.707107 | 3p, 3p2, p3 |
... | complex polyhedron x2-4-o3-3-o3 | 1 | 54, 216, 72 |
... | external blend of 20 trippescus | 92, 240, 120 | |
... | 24 face equihedral toroid | 12, 36, 24 | |
... | t24-s6-24r, Stott contraction of t32-s24-r24-o6 | ... | 44, 96, 54 |
... | t24-s6-n8 | 2.431352 | 48, 84, 38 |
... | 2cho (?) | 1 | |
... | 2co (?) | 1 | |
... | 2co+16{3} (?) | 1 | |
... | 2cube (?) | 0.866025 | |
... | 2did (?) | 1 | |
... | 2ditdid+5cube (?) | 0.866025 | |
... | 2doe (?) | 1.401259 | |
... | 2gad (?) | 0.951057 | |
... | 2gad+ike (?) | 0.951057 | |
... | 2geihid (?) | 0.618034 | |
... | 2gid (?) | 0.618034 | |
... | 2gidhei (?) | 1 | |
... | 2gidhid (?) | 0.618034 | |
... | 2gidtid+5cube (?) | 0.866025 | |
... | 2gike (?) | 0.587785 | |
... | 2gike+sissid (?) | 0.587785 | |
... | 2gissid (?) | 0.535233 | |
... | 2id (?) | 1.618034 | |
... | 2id+40{3} (?) | 1.618034 | |
... | 2ike (?) | 0.951057 | |
... | 2ike+4gad (?) | 0.951057 | |
... | 2ike+gad (?) | 0.951057 | |
2n-p | 2n-gonal prism | sqrt[1/4+1/(4 sin2(π/2n))] | 4n, 6n, 2n+2 |
2n/2-p | 2n-gonal prism of winding number 2 | sqrt[1/4+1/(4 sin2(π/n))] | 4n, 6n, 2n+2 |
2n/d-p | 2n/d-prism, 2n-prism with winding number d | sqrt[1/4+1/(4 sin2(π d/2n))] | 4n, 6n, 2n+2 |
... | 2oct (?) | 0.707107 | |
... | 2oct+12{4} (?) | 0.707107 | |
... | 2oct+6{4} (?) | 0.707107 | |
... | 2oct+8{3} (?) | 0.707107 | |
... | blend of 2 pentagonal antiprisms, pair of pentagonal butterfly wedges | 0.951057 | 12, 26, 16 |
... | 2pip (?), decagonal prism with winding number 2 | 0.986715 | |
... | 2quitgissid (?) | 0.657550 | |
... | 2quith (?) | 0.579471 | |
... | 2quitsissid (?) | 0.852911 | |
... | 2raded (?) | 1.322876 | |
... | 2seihid (?) | 1.618034 | |
... | 2sidhei (?) | 1 | |
... | 2sidhid (?) | 1.618034 | |
... | 2sidtid+5cube (?) | 0.866025 | |
... | 2sirco (?) | 1.398966 | |
... | 2sissid (?) | 0.587785 | |
... | 2sissid+4gike (?) | 0.587785 | |
... | 2sissid+gike (?) | 0.587785 | |
... | 2srid (?) | 2.232951 | |
... | 2tet (?) | 0.612372 | |
... | 2thah (?) | 0.707107 | |
... | 2ti (?) | 2.478019 | |
... | 2tic (?) | 1.778824 | |
... | 2tid (?) | 2.969449 | |
... | 2tiggy (?) | 1.053292 | |
... | 2tigid (?) | 1.876844 | |
... | 2trip (?), hexagonal prism with winding number 2 | 0.763763 | |
... | 2tut (?) | 1.172604 | |
... | complex polyhedron x3 x3-3-o3 | 0.912871 | 24, 32, 11 |
... | Hessian polyhedron, complex polyhedron x3-3-o3-3-o3 | 0.816497 | 27, 72, 27 |
... | complex polyhedron x3-3-o3-4-o2 | 1 | 72, 216, 54 |
... | complex polyhedron x3-3-o3 || o3-3-x3 , vertex figure of x3-3-o3-3-o3-3-x3 | 0.790569 | 16, 40, 18 |
... | Shephard's 3-generalised cube, complex polyhedron x3-4-o2-3-o2 , γ3 3 | 1 | 27, 27, 9 |
... | hyperbolic [3,4,3,4,4,4] tiling | ||
... | triaconta-augmented rhombicosidodeahedron | ... | 90, 180, 92 |
... | 32 face equihedral toroid | 16, 48, 32 | |
... | t32-s24-r24-o6, Stott expansion of t24-s6-24r | ... | 84, 168, 86 |
... | triangle triacontahexahedron | 20, 54, 36 | |
... | 3doe (?) | 1.401259 | |
... | 3gidtid (?) | 0.866025 | |
... | 3gissid (?) | 0.535233 | |
... | 3ike+3gad (?), 3cid (?) | 0.951057 | |
... | 3ike+gad (?) | 0.951057 | |
..., 3Q3-S3-2P6-2P3-gyro | parallelly that dissected, elongated rich | ||
..., 3Q3-S3-2P6-2P3-ortho | parallelly that dissected, elongated gyrich | ||
... | 3sidtid (?) | 0.866025 | |
... | 3sissid+gike (?) | 0.587785 | |
... | 3tet (?) | 0.612372 | |
... | Shephard's 4-generalised cube, complex polyhedron x4-4-o2-3-o2 , γ4 3 | 1.224745 | 64, 48, 12 |
... | hyperbolic [4,4,6,6] tiling with tetragonal Coxeter domain | ||
... | 4ike+2gad (?) | 0.951057 | |
... | 4ike+gad (?) | 0.951057 | |
... | 4oct (?) | 0.707107 | |
... | 4sissid+2gike (?) | 0.587785 | |
... | 4tet (?) | 0.612372 | |
... | 4thah (?) | 0.707107 | |
... | Leonardo polyhedron of type {4,5;19} | 144, 360, 180 | |
... | Leonardo polyhedron of type {4,5;31} | 240, 600, 300 | |
... | Shephard's 5-generalised cube, complex polyhedron x5-4-o2-3-o2 , γ5 3 | 1.473370 | 125, 75, 15 |
... | biform compound of 5 dodecahedra | 1.401259 | |
... | 5ike+gad (?) | 0.951057 | |
..., 5Y4-4T-4P4 | elongated 10Y4-8T-0 | ||
..., 5Y4-4T-6P3-sq-para | para-staggered shear-elongated 10Y4-8T-0 | ||
..., 5Y4-4T-6P3-sq-skew | skew-staggered shear-elongated 10Y4-8T-0 | ||
... | Leonardo polyhedron of type {5,4;13} | 120, 240, 96 | |
... | triform blend of 6 pentagonal prisms | 0.986715 | 40, 70, 32 |
... | t60-r60-p12, Stott contraction of t80-s60-r60-d12 | ... | 110, 240, 132 |
... | 6doe (?) | 1.401259 | |
... | 6gissid (?) | 0.535233 | |
... | squippy-teddi-G3 toroid | ... | 158, 408, 230 |
..., 6Q3-2S3-gyro | parallelly that dissected rich | ||
..., 6Q3-2S3-ortho | (un)gyrated 6Q3-2S3-gyro | ||
... | 6tet (?) | 0.612372 | |
... | t80-s60-r60-d12, Stott expansion of t60-r60-p12 | ... | 210, 420, 212 |
... | a3b3c, general variation of truncated octahedron | sqrt[(3a2+4b2+3c2+4ab+2ac+4bc)/8] | 24, 36, 14 |
... | a3b4c, general variation of great rhombicuboctahedron | sqrt[2a2+4b2+3c2+4ab+(2ac+4bc)sqrt(2)]/2 | 48, 72, 26 |
... | a3b5c, general variation of great rhombicosidodecahedron | sqrt[(f+2)a2+4(f+1)ab+2(2f+1)ac+4(f+1)b2+4(2f+1)bc+3(f+1)c2]/2 | 120, 180, 62 |
addasi | altered disnub icosahedron, compound of 20 oct (but not dasi) | 0.707107 | |
ahach | hyperbolic alternated order 6 cubical honeycomb, hyperbolic snub order 6 cubical honeycomb | 0 i | |
ahexah | hyperbolic alternated hexagonal-tiling honeycomb | 0.816497 i | |
... | general tetrahedral-octahedral honeycomb variant ao3bo3oa3ob3*a&#zc (but not ao3bo3ob3oa3*a&#zc) | ||
... | general tetrahedral-octahedral honeycomb variant ao3bo3ob3oa3*a&#zc (but not ao3bo3oa3ob3*a&#zc) | ||
apech | hyperbolic alternated order 5 cubical honeycomb | 0.393076 i | |
aphexah | hyperbolic alternated order 5 hexagonal-tiling honeycomb | 0.220528 i | |
arie | antirhombicosicosahedron, compound of 5 co | 1 | |
ashexah | hyperbolic alternated order 4 hexagonal-tiling honeycomb | 0.408248 i | |
atich | alternatedly truncated cubic honeycomb | ||
aud, J58 | augmented dodecahedron | 21, 35, 16 | |
auhip, J54 | augmented hexagonal prism | 13, 22, 11 | |
aupip, J52 | augmented pentagonal prism | 11, 19, 10 | |
auteddi, J64 | augmented tridiminished icosahedron | 10, 18, 10 | |
autic, J66 | augmented truncated cube | 28, 48, 22 | |
autid, J68 | augmented truncated dodecahedron | 65, 105, 42 | |
autip, J49 | augmented triangular prism | 7, 13, 8 | |
autut, J65 | augmented truncated tetrahedron | 15, 27, 14 | |
auwaco, J87 | augmented sphenocorona | 11, 26, 17 | |
... | Waterman polyhedron number 8 wrt. face-centered cubic lattice A3 centered at a lattice point | 54, 120, 68 | |
bagydrid, J79 | bigyrate diminished rhombicosidodecahedron | 2.232951 | 55, 105, 52 |
bamich | biambocubic honeycomb | ||
batch | bitruncated cubic honeycomb, truncated-octahedral honeycomb, Voronoi complex of body-centered cubic (bcc) lattice | ||
bauco | bi-augmented cuboctahedron, 4fold rhombohedron | ... | 14, 24, 12 |
baupip, J53 | biaugmented pentagonal prism | 12, 23, 13 | |
bautic, J67 | biaugmented truncated cube | 32, 60, 30 | |
bautip, J50 | biaugmented triangular prism | 8, 17, 11 | |
... | cubically-diminished dodecahedron, bi-tetrahedrally-diminished dodecahedron | 1.401259 | 12, 30, 20 |
bilbiro, J91 | bilunabirotunda | 14, 26, 14 | |
bimteth | bimesotruncatotetrahedral honeycomb | ||
bimtich | bimesotruncatocubic honeycomb | ||
bipach | biprismatocubic honeycomb | ||
birachach | hyperbolic birectified alternated order-6 cubic honeycomb, hyperbolic runcic order-6 cubic honeycomb | 1.168771 i | |
birapech | hyperbolic birectified alternated order-5 cubic honeycomb, hyperbolic runcic order-5 cubic honeycomb | 1.507495 i | |
birashexah | hyperbolic birectified alternated order 4 hexagonal-tiling honeycomb | 0.934758 i | |
bisch | bisnub cubic honeycomb | ||
bitapech | hyperbolic bitruncated alternated order-5 cubic honeycomb, runcicantic order-5 cubic honeycomb | 2.850727 i | |
bitdi | chiral Weimholt hexahedron, bitrigonally diminished icosahedron, vertex figure of bidex | 0.951057 | 6, 10, 6 |
bithon | bitetrahedral honeycomb | ||
bobipyr | bowtie bipyramid, crossed-square bipyramid, bowtie (line-)tegum | 0.707107 | 6, 10, 6 |
cabisch | cantic bisnub cubic honeycomb | ||
cadditradid | complex (ditrigonary) rhombidodecadodecahedron | 0.866025 | |
caquitpica | cubatiquasitrunciprismated cubatiapeiratic honeycomb | ||
casch | cantic snub cubic honeycomb | ||
chado | chamfered dodecahedron, icosahedrally truncated rhombic triacontahedron, Goldberg polyhedron GP(2,0) | 80, 120, 42 | |
chat (alt.: patex cube) | chamfered tetrahedron, partially tetrahedrally-expanded cube, tetrahedrally truncated cube, partially tri-expanded tetrahedron | 16, 24, 10 | |
chexah | hyperbolic cubic-hexagonal-tiling honeycomb, bitruncated order 4 hexagonal-tiling honeycomb, bitruncated order 6 cubic honeycomb | 1.870829 i | |
chic | chamfered cube, octahedrally truncated rhombic dodecahedron | 32, 48, 18 | |
chike | chamfered icosahedron, dodecahedrically truncated rhombic triacontahedron | 72, 120, 50 | |
cho | cubohemioctahedron, rhomballelohedron | 1 | 12, 24, 10 |
... | cho+4{6/2} (?) | 1 | |
choct | chamfered octahedron, cubically truncated rhombic dodecahedron | 30, 48, 20 | |
chon | cubic honeycomb, 3D hypercubical honeycomb (δ3), Voronoi complex of primitive cubical lattice, Delone complex of primitive cubical lattice | ||
... | cubically truncated rhombic dodecahedral honeycomb | ||
cid | small complex icosidodecahedron, (as type C:) complex polyhedron x2-3-o2-5-o2 | 0.951057 | |
ciddoh | hyperbolic cubic-dodecahedral honeycomb, hyperbolic bitruncated order 5 cubic honeycomb, hyperbolic bitruncated order 4 dodecahedral honeycomb | 2.443795 i | |
co (alt.: ratet – old: ratit, rotet) | cuboctahedron, (small) rhombitetratetrahedron, rectified cube, rectified octahedron, cantellated tetrahedron, expanded tetrahedron, trigonal gyrobicupola, vertex figure of octet, lattice A3 contact polytope (span of its roots), lattice B3 contact polytope (span of its small roots), equatorial cross-section of tet-first spid, equatorial cross-section of oct-first ico | 1 | 12, 24, 14 |
... | (ico derived) tridpy variant, o3m4o3o cell | 5, 9, 6 | |
... | (tes derived) tridpy variant, o4m3o3o cell | 5, 9, 6 | |
... | (hi derived) tridpy variant, o5m3o3o cell | 5, 9, 6 | |
... | dual of pentagonal prism, (ex derived) pedpy variant, o3m3o5o cell | 7, 15, 10 | |
cohon | hyperbolic x4o3o4o3*a tesselation, cubic-octahedral honeycomb | 0.377964 i | |
cotco | cuboctatruncated cuboctahedron, cubitruncated cuboctahedron | 1.322876 | 48, 72, 20 |
cube (alt: squip) | cube, hexahedron, 3D measure-polytope (γ3), geochor(id), square prism, cantellated square dihedron, triangular antitegum, Voronoi cell of primitive cubical lattice, Delone cell of primitive cubical lattice, terminally chamfered tetrahedron, surtegmated tetrahedron | 0.866025 | 8, 12, 6 |
cutpica | cubatitrunciprismated cubatiapeiratic honeycomb | ||
cytacoh | hyperbolic o3x4x3o4*a tesselation, cyclotruncated cubic-octahedral honeycomb | 0.944355 i | |
cytatoh (old: batatoh) | cyclotruncated tetrahedral-octahedral honeycomb (but not the hyperbolic cyclotruncated octahedral-tetrahedral honeycomb cytoth), bitruncated tetrahedral-octahedral honeycomb, bitruncated alternated-cubic honeycomb, quarter cubic honeycomb | ||
cyticth | hyperbolic x3o3o3x4*a tesselation, cyclotruncated cubic-tetrahedral honeycomb | 1.553774 i | |
cytitch | hyperbolic x3x3o3o4*a tesselation, cyclotruncated tetrahedral-cubic honeycomb | 1.391625 i | |
cytoch | hyperbolic x3x4o3o4*a tesselation, cyclotruncated octahedral-cubic honeycomb | 1 i | |
cytoth (old: cytitoh) | hyperbolic x3x3o4o3*a tesselation, cyclotruncated octahedral-tetrahedral honeycomb (but not the euclidean cyclotruncated tetrahedral-octahedral honeycomb cytatoh) | 1.189207 i | |
... | d3o3x, variation of cuboctahedron | 2.661453 | 12, 24, 14 |
dap, 10-ap | decagonal antiprism | 1.674505 | 20, 40, 22 |
dasi | disnub icosahedron, compound of 20 oct (but not addasi) | 0.707107 | |
daso (old: doso) | disnub octahedron, compound of 8 oct | 0.707107 | |
dawci, J90 | disphenocingulum | 16, 38, 24 | |
degpy, 10/3-pyr | decagrammic pyramid | 0.636010 | 11, 20, 11 |
desided | disnub icosidodecadodecahedron, compound of 2 sided | 1.126898 | |
did | dodecadodecahedron, great dodecadodecahedron | 1 | 30, 60, 24 |
... | did+sidhei+gidhei (?) | 1 | |
diddoh | hyperbolic disdodecahedral honeycomb, hyperbolic bitruncated order 5 dodecahedral honeycomb | 1.798907 i | |
digdom, ike-5-7 | diminished ike-gad morpher, 5-fold pyramidal-symmetric ike faceting with 5 trigs and 7 pigs | 11, 25, 12 | |
dih | hyperbolic bitruncated order 3 icosahedral honeycomb, hyperbolic disicosahedral honeycomb | 2.910693 i | |
dip (old: dep) | decagonal prism | 1.693527 | 20, 30, 12 |
dird | dirhimbidodecahedron, compound of 12 pip | 0.986715 | |
dirid, J76 | diminished rhombicosidodecahedron | 2.232951 | 55, 105, 52 |
dis | disnubihedron, compound of 12 tet | 0.612372 | |
disco | disnub cuboctahedron, compound of 2 snic | ||
disdi-verf | vertex figure of disnub disicositetrachoron | 0.866025 | 17, 51, 24 |
disdid | disnub dodecadodecahedron, compound of 2 siddid | ||
dish | hyperbolic dissquare-tiling honeycomb, hyperbolic bitruncated order-4 square tiling honeycomb | 1.553774 i | |
dissid | disnub icosidodecahedron, compound of 2 snid | ||
dissit | disnub tetrahedron, compound of 4 oct | 0.707107 | |
ditdid | ditrigonal dodecadodecahedron, vertex figure of dittady | 0.866025 | 20, 60, 24 |
... | ditdid+gidtid (?) | 0.866025 | |
ditdih | hyperbolic ditrigonary disicosahedral honeycomb | 0.509376 i | |
ditoh | ditetrahedral-octahedral honeycomb | ||
ditra | ditriangular trapezoprism | sqrt[(a+b)2+c2]/2 | 12, 18, 8 |
ditrah | hyperbolic distriangular-tiling honeycomb | 2.075910 i | |
dittec | ditruncated cube, truncated truncated cube, expanded ambified tic | sqrt[(7+4 sqrt(2))y2+(24+16 sqrt(2))y+(24+16 sqrt(2))]/2 | 72, 108, 38 |
dittet | ditruncated tetrahedron, truncated truncated tetrahedron, expanded ambified tut | sqrt[(11y2+36y+36)/8] | 36, 54, 20 |
ditti | ditrigonal icosahedron, vertex figure of idhi | 1.401259 | 20, 60, 20 |
dittoe | ditruncated octahedron, truncated truncated octahedron, expanded ambified toe | sqrt[(5y2+9y sqrt(2)+9)/2] | 72, 108, 38 |
... | Waterman polyhedron number 8 wrt. primitive cubic lattice C3 centered at a lattice point, Waterman polyhedron number 4 wrt. face-centered cubic lattice A3 centered at a deep hole | 2.121320 | 30, 84, 56 |
doe | dodecahedron, cosmohedron, Goldberg polyhedron GP(1,0) | 1.401259 | 20, 30, 12 |
doehon | hyperbolic order 4 dodecahedral honeycomb | 0.899454 i | |
... | Dohány synagoge polyhedron, Tabakgasse polyhedron | 1.080123 | 16, 28, 14 |
dri | dirhombicosahedron, compound of 20 trip | 0.763763 | |
dritit (old: sipstar) | disrhombitritrihedron, "square-pentagon-pentagram(star)-thingy", vertex figure of retroantiprismatosnub disicositetrachoron, edge faceting sidtid-3-0-6-3-b | 0.866025 | 15, 24, 12 |
dro | dirhombioctahedron, compound of 8 trip | 0.763763 | |
dudsi | small noble triangular hexecontahedron, dual of D-stellation of icosahedron, D-faceting of dodecahedron, vertex figure of paphicki | 0.866025 | 20, 90, 60 |
e | icosiicosahedron, compound of 10 tet | 0.612372 | |
ebauco | elongated bi-augmented cuboctahedron, 4fold elongated rhombohedron, bi-augmented pexco | ... | 18, 28, 12 |
ebot | elongated bowtie tegum | 1 | 10, 16, 8 |
edge-snub square prismatic honeycomb | edge-snub square prismatic honeycomb | ||
editoh | elongated ditetrahedral-octahedral honeycomb | ||
epcu, J20 | elongated pentagonal cupola | 25, 45, 22 | |
epedpy, J16 | elongated pentagonal dipyramid | 12, 25, 15 | |
epeppy, J9 | elongated pentagonal pyramid | 11, 20, 11 | |
epgybro, J43 | elongated pentagonal gyrobirotunda | 40, 80, 42 | |
epgycuro, J41 | elongated pentagonal gyrocupolarotunda | 35, 70, 37 | |
epigybcu, J39 | elongated pentagonal gyrobicupola | 30, 60, 32 | |
epobcu, J38 | elongated pentagonal orthobicupola | 30, 60, 32 | |
epobro, J42 | elongated pentagonal orthobirotunda | 40, 80, 42 | |
epocuro, J40 | elongated pentagonal orthocupolarotunda | 35, 70, 37 | |
epro, J21 | elongated pentagonal rotunda | 30, 55, 27 | |
erad | expanded rhombic dodecahedron | 48, 96, 50 | |
erhote | expanded rhombic triacontahedron | 120, 240, 122 | |
erich | parallelly that elongated rich | ||
esch | edge-snub cubic honeycomb | ||
escu, J19 | elongated square cupola, diminished small rhombicuboctahedron | 1.398966 | 20, 36, 18 |
esquidpy, J15 | elongated square dipyramid | 10, 20, 12 | |
esquigybcu, J37 (alt.: pirco) | elongated square gyrobicupola, pseudorhombicuboctahedron, Miller's solid | 1.398966 | 24, 48, 26 |
esquipy, J8 | elongated square pyramid | 9, 16, 9 | |
etcu, J18 | elongated triangular cupola | 15, 27, 14 | |
etidpy, J14 | elongated trigonal dipyramid | 8, 15, 9 | |
etigybcu, J36 | elongated triangular gyrobicupola | 18, 36, 20 | |
etobcu, J35 | elongated triangular orthobicupola | 18, 36, 20 | |
etoh | elongated tetrahedral-octahedral honeycomb, elongated alternated cubic honeycomb | ||
etoph | elongated-triagonal prismatic honeycomb | ||
... | blend of elongated triangular-tiling prisms | ||
etripy, J7 | elongated triangular pyramid | 7, 12, 7 | |
... | expanded dodeca-augmented great rhombicuboctahedron | ... | 72, 108, 38 |
exrad | expanded rhombic dodecahedron | 48, 96, 50 | |
exrhote | expanded rhombic triacontahedron | 120, 240, 122 | |
extoh | expanded octahedral-tetrahedral honeycomb | ||
... | f v10o, variation of decagonal prism, hull of 10/3-prism | 1.286277 | 20, 30, 12 |
... | f v3o, variation of triangular prism, vertex figure of rectified great grand hecatonicosachoron | 0.884212 | 6, 9, 5 |
... | f v5o, variation of pentagonal prism, vertex figure of righi | 0.964832 | 10, 15, 7 |
... | f x3o, variation of triangular prism, vertex figure of rectified hecatonicosachoron | 0.993902 | 6, 9, 5 |
... | f x4o, variation of cube | 1.074481 | 8, 12, 6 |
... | f x5/2o, variation of 5/2-prism, vertex figure of raghi | 0.964832 | 10, 15, 7 |
... | f x5o, variation of pentagonal prism | 1.173932 | 10, 15, 7 |
... | f3o3x, variation of cuboctahedron | 1.327129 | 12, 24, 14 |
... | f3o4x, variation of small rhombicuboctahedron | 1.789732 | 24, 48, 26 |
... | f3o5x, variation of srid, hull of siid, hull of quit gissid | 2.785428 | 60, 120, 62 |
... | f3v5v, variation of grid, hull of idtid | 3.236068 | 120, 180, 62 |
... | f3x5o, variation of ti, hull of tigid, hull of gaddid | 3.036797 | 60, 90, 32 |
... | f3x5x, variation of great rhombicosidodecahedron, hull of quitdid | 4.341518 | 120, 180, 62 |
... | β2β5o, (mere) alternated pip | 0.986715 | 10, 20, 12 |
gabirch | great birhombatocubic honeycomb | ||
gabreth | great birhombitetrahedral honeycomb | ||
gacid | great complex icosidodecahedron | 0.587785 | |
gacoca | great cubaticubatiapeiratic honeycomb | ||
gacocaddit | hyperbolic x3o3o4o3*a tesselation, grand cuboctahedronary cubic-distetrahedral honeycomb | 0.511081 i | |
gacquitpica | great cubatiquasitrunciprismated cubatiapeiratic honeycomb | ||
gactipeca | great cubatitrunciprismated cubatiapeiratic honeycomb | ||
gad | great dodecahedron, faceted icosahedron, vertex figure of fix | 0.951057 | 12, 30, 12 |
gaddid | great dodekicosidodecahedron | 0.716891 | 60, 120, 44 |
gadsid | great disnub dodecahedron, compound of 12 pap | 0.951057 | |
gadtatdic | hyperbolic grand ditetrahedronary tetrahedral-discubic honeycomb | 0.722778 i | |
... | vertex figure of great antifrustary trishecatonicosachoron | 0.816497 | 8, 12, 6 |
... | cell of gap dual, adjacent bikis doe | 14, 22, 10 | |
gaqrich | great quasirhombated cubic honeycomb | ||
gaquapech | great quasiprismated cubic honeycomb | ||
gaquatid | great quasitruncated icosidodecahedron, stellatruncated icosidodecahedron | 1.020684 | 120, 180, 62 |
gari | great antirhombicosahedron, compound of 5 cho | 1 | |
gassic | (chiral) great snub cube, compound of 3 squap | 0.822664 | |
gassid | great snub dodecahedron, compound of 6 pap | 0.951057 | |
geihid | great icosihemidodecahedron | 0.618034 | 30, 60, 26 |
getdoca (old: gotactictosquath) | great tetradicubatiapeiratic honeycomb, great tetrahedral cubic tomocubic tomosquare tiling honeycomb | ||
getit cadoca | great tritrigonary cubatidicubatiapeiratic honeycomb | ||
... | vertex figure of getut | 0.866025 | 20, 108, 64 |
gibil biro | great bilunabirotunda | 14, 26, 14 | |
gicdatrid | great complex (ditrigonary) rhombicosidodecahedron | 0.866025 | 60, 120, 62 |
gid | great icosidodecahedron | 0.618034 | 30, 60, 32 |
... | gid+geihid+gidhid (?) | 0.618034 | |
gidasid | great invertidisnub dodecahedron, compound of 12 starp | 0.587785 | |
giddasid | great disnub icosidodecahedron, compound of 2 gosid | ||
giddird | great dirhombidodecahedron, compound of 12 stip | 0.725530 | |
gidditdid | great ditrigonary dodekicosidodecahedron, great dodekified icosidodecahedron | 1.134229 | 60, 120, 44 |
giddy | great dodekicosahedron | 1.134229 | 60, 120, 32 |
... | giddy+12{10/2} (?) | 1.134229 | |
... | giddy+20{6/2} | 1.134229 | |
gidhei | great dodecahemicosahedron, small dodecahemiicosahedron (but not sidhei) | 1 | 30, 60, 22 |
gidhid | great dodecahemidodecahedron | 0.618034 | 30, 60, 18 |
gidisdrid | great disnub dirhombicosidodecahedron, Skilling's figure | 0.707107 | 60, 360, 204 |
gidpicdoh | hyperbolic great disprismated cubical-dodecahedral honeycomb, hyperbolic omnitruncated order 5 cubical honeycomb, hyperbolic omnitruncated order 4 dodecahedral honeycomb | 4.248159 i | |
gidrid (subsym.: gidrikid) | great dirhombicosidodecahedron, great snub disicosidisdodecahedron, Miller's monster, (subsym.: great dirhombichiricosadodecahedron) | 0.707107 | 60, 240, 124 |
gidrissid | great diretrosnub icosidodecahedron, compound of 2 girsid | ||
gidsac | great disnub cube, compound of 6 squap | 0.822664 | |
gidsid | great invertidisnub icosidodecahedron, compound of 2 gisid | ||
gidtid | great ditrigonary icosidodecahedron, vertex figure of gidtixhi | 0.866025 | 20, 60, 32 |
gifodib | sidtid faceting sidtid-2-10-20-0 (i.e. with 10(=d) {3}, 20(=i) {4}, and 2(=b) {5/2}) | 0.866025 | 20, 60, 32 |
giid | great icosicosidodecahedron | 1.134229 | 60, 120, 52 |
gike | great icosahedron, retrosnub tetrahedron, retrosnub tetratetrahedron, edgified penta-stellahedron, vertex figure of gax | 0.587785 | 12, 30, 20 |
gikkiv pacoca (old: sic vacpeca) | great skewverted prismatocubaticubatiapeiratic honeycomb, small skewverted cubatiprismated cubatiapeiratic honeycomb | ||
gikkivcadach | great skewverted cubatiapeiroducubatic honeycomb | ||
gikrid | great chirorhombidodecahedron, compound of 6 stip | 0.725530 | |
gipidded | hyperbolic great prismatodisdodecahedral honeycomb, hyperbolic omnitruncated order 5 dodecahedral tesselation | 3.176503 i | |
gipiddih | hyperbolic great prismatodisicosahedral honeycomb, hyperbolic omnitruncated order 3 icosahedral honeycomb | 4.308399 i | |
gippich (old: otch) | great prismated cubic honeycomb, omnitruncated cubic honeycomb | ||
girco | great rhombicuboctahedron (but not querco), truncated cuboctahedron, omnitruncated octahedron, omnitruncated cube | 2.317611 | 48, 72, 26 |
gird | great rhombidodecahedron | 0.716891 | 60, 120, 42 |
... | gird+12{10/4} (?) | 0.716891 | |
... | gird+20{6/2} (?) | 0.716891 | |
... | vertex figure of great retrofrustary trishecatonicosachoron | 0.816497 | 8, 12, 6 |
girsid | great (inverted) retrosnub icosidodecahedron, azathoth | 60, 150, 92 | |
gisdid | great snub dodekicosidodecahedron, shub-niggurath | 0.707107 | 60, 180, 104 |
giship | tristrophic heptagrammic prism, heptagrammic prism of winding number 3, great heptagrammic prism, great stellated heptagonal prism | 0.716257 | 14, 21, 9 |
gisid | great inverted snub icosidodecahedron, great vertisnub icosidodecahedron, cthulhu | 60, 150, 92 | |
gissed | great invertisnub dodecahedron, compound of 6 starp | 0.587785 | |
gissi | great snub icosahedron, compound of 10 oct (but not si) | 0.707107 | |
gissid | great stellated dodecahedron, tri-stellahedron | 0.535233 | 20, 30, 12 |
githawro | great triangular hebesphenorotunda | 18, 36, 20 | |
gobath | great biambotetrahedral honeycomb | ||
gocco | great cubicuboctahedron | 0.736813 | 24, 48, 20 |
gosid | great snub icosidodecahedron, tsathoggua | 60, 150, 92 | |
grassid | great rhombisnub dodecahedron, compound of 6 stiddip | 0.794963 | |
gratoh | great rhombated tetrahedral-octahedral honeycomb, cantitruncated alternated cubic honeycomb, cantitruncated tetrahedral-octahedral honeycomb, runcicantic cubic honeycomb | ||
grich | great rhombated cubic honeycomb, cantitruncated cubic honeycomb | ||
grid | great (convex) rhombicosidodecahedron (i.e. not qrid), truncated icosidodecahedron, omnitruncated icosahedron, omnitruncated dodecahedron | 3.802395 | 120, 180, 62 |
griddoh | hyperbolic great rhombated (order 4) dodecahedral honeycomb, hyperbolic cantitruncated order 4 dodecahedral honeycomb | 3.466586 i | |
grih | hyperbolic great rhombated order 3 icosahedral honeycomb, hyperbolic cantitruncated order 3 icosahedral honeycomb | 3.601065 i | |
gripech | hyperbolic great rhombated order 5 cubic honeycomb, hyperbolic cantitruncated order 5 cubic honeycomb | 3.185991 i | |
gripped | hyperbolic great rhombated order 5 dodecahedral honeycomb, hyperbolic cantitruncated order 5 dodecahedral honeycomb | 2.456999 i | |
griso | great rhombisnub octahedron, compound of 4 hip | 1.118034 | |
groh | great rhombihexahedron | 0.736813 | 24, 48, 18 |
... | groh+8{6/2} (?) | 0.736813 | |
grothaph (old: otathaph) | great rhombitrihexagonal prismatic honeycomb, omnitruncated triangular-hexagonal prismatic honeycomb | ||
gybadrid, J82 | gyrate(d) bidiminished rhombicosidodecahedron | 2.232951 | 50, 90, 42 |
gybef, J26 | gyrobifastegium | 8, 14, 8 | |
gyeditoh | gyroelongated ditetrahedral-octahedral honeycomb | ||
gyepabro, J48 | gyroelongated pentagonal birotunda | 40, 90, 52 | |
gyepcu, J24 | gyroelongated pentagonal cupola | 25, 55, 32 | |
gyepcuro, J47 | gyroelongated pentagonal cupolarotunda | 35, 80, 47 | |
gyepibcu, J46 | gyroelongated pentagonal bicupola | 30, 70, 42 | |
gyepip, J11 | gyroelongated pentagonal pyramid, diminished icosahedron | 11, 25, 16 | |
gyepro, J25 | gyroelongated pentagonal rotunda | 30, 65, 37 | |
gyerich | parallelly that elongated gyrich | ||
gyescu, J23 | gyroelongated square cupola | 20, 44, 26 | |
gyesp, J10 | gyroelongated square pyramid | 9, 20, 13 | |
gyesqidpy, J17 | gyroelongated square dipyramid | 10, 24, 16 | |
gyesquibcu, J45 | gyroelongated square bicupola | 24, 56, 34 | |
gyetaph | gyroelongated triangular-prismatic honeycomb | ||
gyetcu, J22 | gyroelongated triangular cupola | 15, 33, 20 | |
gyetibcu, J44 | gyroelongated triangular bicupola | 18, 42, 26 | |
gyetoh | gyroelongated tetrahedral-octahedral honeycomb, gyroelongated alternated cubic honeycomb | ||
gyquerco (alt.: rers quigybcu) | inverto-elongated retrograde square gyrobicupola, gyrated quasirhombicuboctahedron, pseudo great rhombicuboctahedron, retroelongated retrosquare gyrobicupola | 0.736813 | 24, 48, 26 |
gyrich | gyrated rectified cubical honeycomb | ||
gyrid, J72 | gyrated rhombicosidodecahedron | 2.232951 | 60, 120, 62 |
gytoh | gyrated tetrahedral-octahedral honeycomb, gyrated alternated cubic honeycomb | ||
gytoph | gyrated-bifastegium honeycomb | ||
gytoph | gyrated triangular prismatic honeycomb | ||
hachon | hyperbolic order 6 cubical honeycomb | 0 i | |
hap, 6-ap | hexagonal antiprism | 1.087664 | 12, 24, 14 |
hatiph | hemiated triangular-prismatic honeycomb, cell-alternated triangular-prismatic honeycomb | ||
hawmco, J89 | hebesphenomegacorona | 14, 33, 21 | |
heath | hyperbolic o3o3o7x tesselation, heat honeycomb | 1.071823 i | |
hedhon | hyperbolic order 6 dodecahedral honeycomb | 0 i | |
hep | heptagonal prism | 1.256179 | 14, 21, 9 |
hetoh | hyperbolic x3o3o7o tesselation, order 7 tetrahedral honeycomb | 0.376651 | |
hexah | hyperbolic order 3 hexagonal-tiling honeycomb | 1.414214 i | |
... | hexatip blend | ||
hexatip | hexagonal tiling prism | ||
hicu | hexagonal cupola | ∞ i.e. flat in euclidean space | 18, 30, 14 |
hihexah | hyperbolic order 6 hexagonal-tiling honeycomb | 0 i | |
hiktut | hexakis truncated tetrahedron | 1.172604 | 16, 42, 28 |
hip | hexagonal prism, Voronoi cell of unit-stacked hexagonal lattice | 1.118034 | 12, 18, 8 |
hiph | hexagonal prismatic honeycomb, Voronoi complex of unit-stacked hexagonal lattice | ||
hippy, 6pyr | (degenerate) hexagonal pyramid | ∞ i.e. flat in euclidean space | 7, 12, 7 |
hirki | hemirhombichiro-icosahedron, compound of 5 thah | 0.707107 | |
... | ho oh&#q, narrower variant of digonal antiprism | 1.767767 | 4, 6, 4 |
... | ho3oh&#q, narrower variant of trigonal antiprism, hemiation of hip | 1.118034 | 6, 12, 8 |
hog dhidicup verf | vertex figure of hog dhidicup | 0.730749 | 8, 14, 8 |
hoha | hexagonal hemiapeirogonal tesselation | ||
hudsi | great noble triangular hexecontahedron, dual of H-stellation of icosahedron, H-faceting of dodecahedron, vertex figure of paphacki, huitzilopochtli | 0.866025 | 20, 90, 60 |
... | (infinite series of) hyperbolic uniform honeycombs with pyritohedral vertex figure | ||
id | icosidodecahedron, rectified icosahedron, rectified dodecahedron, equatorial cross-section of vertex-first ex | 1.618034 | 30, 60, 32 |
... | id+seihid+sidhid (?) | 1.618034 | |
... | icosidodecahedron faceting | 1.618034 | 30, 120, 62 |
iddei | icosidisicosahedron, compound of 5 oho | 1 | |
ided | icosidodecadodecahedron | 1.322876 | 60, 120, 44 |
idisdid | invertidisnub dodecadodecahedron, compound of 2 isdid | ||
idtid | icosidodecatruncated icosidodecahedron, icositruncated dodecadodecahedron | 2 | 120, 180, 44 |
... | hyperbolic honeycomb by idtid and tidect | 0.485868 i | |
ifbah, ike-6-2 | 2-fold faceted icosahedron ike-6-2, pentagonal butterfly wedge, blend of 2 pentagonal pyramids, half of blend of 2 pentagonal antiprisms | 0.951057 | 8, 14, 8 |
ike (alt.: snit) | icosahedron, snub tetrahedron, snub tetratetrahedron, snub triangle antiprism, hydrohedron, gyroelongated pentagonal bipyramid, vertex figure of ex | 0.951057 | 12, 30, 20 |
... | ike+3gad (?) | 0.951057 | |
ikhon | hyperbolic order 3 icosahedral honeycomb | 0.509376 i | |
isdid | inverted snub dodecadodecahedron, vertisnub dodecadodecahedron, nyarlathotep | 60, 150, 84 | |
ki | chiro-icosahedron, compound of 5 tet | 0.612372 | |
kred (old: red) | chiro-rhombidodecahedron, compound of 6 pip | 0.986715 | |
kri | chirorhombicosahedron, compound of 10 trip | 0.763763 | |
... | lamina-truncate of hyperbolic o8o4x *b3x tesselation | 0.321797 i | |
... | lamina-truncate of hyperbolic x4x3o8o tesselation | 0.594604 i | |
... | dual of uniform triangular prism, triangular dipyramid (but not tridpy), o3m3o3o cell | 5, 9, 6 | |
... | dual of hexagonal prism, hexgonal dipyramid | 8, 18, 12 | |
... | dual of uniform n-gonal prism, n-gonal dipyramid | n+2, 3n, 2n | |
mabaud, J60 | metabiaugmented dodecahedron | 22, 40, 20 | |
mabauhip, J56 | metabiaugmented hexagonal prism | 14, 26, 14 | |
mabautid, J70 | metabiaugmented truncated dodecahedron | 70, 120, 52 | |
mabgyrid, J74 | metabigyrated rhombicosidodecahedron | 2.232951 | 60, 120, 62 |
mabidrid, J81 | metabidiminished rhombicosidodecahedron | 2.232951 | 50, 90, 42 |
mabirch | medial birhombatocubic honeycomb | ||
magydrid, J78 | metagyrate diminished rhombicosidodecahedron | 2.232951 | 55, 105, 52 |
mesdi-verf | vertex figure of medial snub disicositetrachoron | 0.866025 | 15, 42, 21 |
mibdi, J62 | metabidiminished icosahedron | 0.951057 | 10, 20, 12 |
mibkid | metabikis dodecahedron, (subsymmetrically) metabistellated-dodecahedron, dual of mibdi | 12, 20, 10 | |
... | mono lowered small rhombicuboctahedron | ... | 15, 24 ,11 |
... | mono lowered truncated cube | ... | 24, 36, 14 |
n-ap | n-gonal antiprism | sqrt[(3-2 cos(π/n))/(8-8 cos(π/n))] | 2n, 4n, 2n+2 |
n-azedip | n-gonal - apeirogonal duoprism | ||
n-p | n-gonal prism | sqrt[1/4+1/(4 sin2(π/n))] | 2n, 3n, n+2 |
n/2-ap | n/2 antiprism | sqrt[(3-2 cos(2π/n))/(8-8 cos(2π/n))] | 2n, 4n, 2n+2 |
n/d-ap | n/d-antiprism, n-antiprism with winding number d (for d>n/2 also: n/(n-d)-retroprism, retrograde n/(n-d)-antiprism) | sqrt[(3-2 cos(π d/n))/(8-8 cos(π d/n))] | 2n, 4n, 2n+2 |
n/d-cu | n/d-gonal cupola | sqrt[(7+4 cos(π d/n)-4 cos2(π d/n))/(12-16 cos2(π d/n))] | 3n, 5n, 2n+2 |
n/d-p | n/d-prism, n-prism with winding number d | sqrt[1/4+1/(4 sin2(π d/n))] | 2n, 3n, n+2 |
n/d-py | n/d-gonal pyramid | 1/sqrt[4-1/sin2(πd/n)] | n+1, 2n, n+1 |
... | noble {9,3} modwrap within srid, Crennell number 4 stellation of the icosahedron | 2.232951 | 60, 90, 20 |
... | hyperbolic o3o3o4s4*a tesselation | ||
... | hyperbolic o3o3o4s4*b tesselation | 0.267261 i | |
... | hyperbolic o3o3o4x4*a tesselation | 0.5 i | |
... | hyperbolic o3o3o4x4*b tesselation | 0.377964 i | |
... | hyperbolic o3o4o8x tesselation | 0.400236 i | |
... | hyperbolic o3o4s4o4*a tesselation | ||
... | hyperbolic o3o4x4o4*a tesselation | 0.292893 i | |
... | hyperbolic o3o4x4o4*b tesselation | 0.216606 i | |
... | hyperbolic o3o5o10x tesselation | 0.202376 i | |
... | hyperbolic o3o5x5o5*b tesselation | ||
... | o3q4x, variation of truncated cube | 2.179449 | 24, 36, 14 |
... | o3β4o (?) | 1 | 12, 36, 20 |
... | hyperbolic o3β4β3o5*a tesselation | ||
... | o3β4x (?) | 1.778824 | 24, 60, 32 |
... | Holosnub icosidodecahedron | 1.618034 | 30, 120, 62 |
... | o3β5x (?) | 2.969449 | 60, 150, 62 |
... | hyperbolic cyclotruncated tetrahedral-icosahedral honeycomb | 0.786151 i | |
... | hyperbolic o3x3x4o4*b tesselation | 0.886405 i | |
... | hyperbolic o3x3x4x4*b tesselation | 1.428194 i | |
... | hyperbolic honeycomb o3x4o4o5/2*b | 0.485868 i | |
... | hyperbolic o3x4o6o tesselation | 0.447214 i | |
... | o3x4q, variation of truncated cube, hull of sno | 2.121320 | 24, 36, 14 |
... | o3x4u, variation of truncated cube | 2.613126 | 24, 36, 14 |
... | hyperbolic o3x4x3o5*a tesselation, cyclotruncated cubic-icosahedral honeycomb | ||
... | hyperbolic o3x5x3o5*a tesselation | ||
... | hyperbolic o3x:s3s4s honeycomb, hyperbolic rectified x3o:s3s4s honeycomb | ... i | |
... | hyperbolic o3x:s3s5s honeycomb, hyperbolic rectified x3o:s3s5s honeycomb | ... i | |
... | hyperbolic o3x:s3s6s honeycomb, hyperbolic rectified x3o:s3s6s honeycomb | ... i | |
... | hyperbolic o3x:s3sPs honeycomb, hyperbolic rectified x3o:s3sPs honeycomb | ... i | |
... | hyperbolic o4o3x3x3*b tesselation | 1 i | |
... | family of (generally hypercompact) hyperbolic o4s4o2Qo honeycombs (Q≥2) | ||
... | family of hyperbolic o4s4oPo honeycombs (P≠2) | ||
... | o4x3o5β (?) | ... | |
... | family of (generally hypercompact) hyperbolic o4x4o2Qo honeycombs (Q≥2) | ||
... | family of hyperbolic o4x4oPo honeycombs (P≠2) | ||
... | hyperbolic o4x6o4o tesselation | 0.5 i | |
... | o5/2f5x variation of truncated great dodecahedron | 2.478019 | 60, 90, 24 |
... | o5/2β5o (?) | 1 | 30, 120, 54 |
... | o5/2β5x (?) | ... | 60, 150, 54 |
... | hyperbolic o5x3o3o5/2*b tesselation, rectified ditdih | 0.882265 i | |
... | o5x3o5β (?) | ... | |
... | hyperbolic o6o4x3xØo3*c tesselation | 0.447214 i | |
... | hyperbolic honeycomb o6o5x∞xØx∞*c *b3*e | 0.363271 i | |
... | hyperbolic honeycomb o6o5x∞x3*b | 0.363271 i | |
... | hyperbolic o8o3x *b4xØx tesselation | 0.321797 i | |
... | hyperbolic o8o4x *b3x tesselation | 0.321797 i | |
... | hyperbolic o8o4x *b3xØx3*b tesselation | 0.321797 i | |
oap, 8-ap | octagonal antiprism | 1.375549 | 16, 32, 18 |
... | (hi derived) truncated tridpy variant, o2o3o symmetric co relative | ... | 9, 18, 11 |
... | (ico derived) truncated tridpy variant, o2o3o symmetric co relative | ... | 9, 18, 11 |
... | (tes derived) truncated tridpy variant, o2o3o symmetric co relative | ... | 9, 18, 11 |
oct (alt.: trap, tatet) | octahedron, rectified tetrahedron, tricross (β3), tetratetrahedron, aerochor(id), trigonal antiprism, snubbed triangular dihedron, larger Delone cell of face-centered cubic (fcc) lattice, equatorial cross-section of (vertex first) 1/q-tes, vertex figure of hex, Gosset polytope 01,1, lattice C3 contact polytope (span of its small roots), equatorial cross-section of vertex-first hex | 0.707107 | 6, 12, 8 |
... | internal compound of octahedron with 4 gyrated tetrahedra | ||
... | oct+6{4} (?) | 0.707107 | |
octet | alternated cubic honeycomb, tetrahedral-octahedral honeycomb, Delone complex of face-centered cubic (fcc) lattice | ||
... | alternated cubically truncated rhombic dodecahedral honeycomb | ||
octh | hyperbolic order 4 octahedral honeycomb | 0 i | |
... | Waterman polyhedron number 9 wrt. face-centered cubic lattice A3 centered at a lattice point | 3 | 36, 72, 38 |
odsnic | octadiminished snub cube, chiral 4fold dodecahedron-like barrel, vertex figure of octsnich | 1.343713 | 16, 24, 10 |
... | 4fold teddi analog | 1.144123 | 12, 20, 10 |
ogpy, 8/3-pyr | octagrammic pyramid | 0.594604 | 9, 16, 9 |
oho | octahemioctahedron, facetorectified cube, allelotetratetrahedron | 1 | 12, 24, 12 |
... | oho+8{3} | 1 | |
op | octagonal prism, bidiminished small rhombicuboctahedron | 1.398966 | 16, 24, 10 |
... | oq ou&#h squippy variant | 1.224745 | 5, 8, 5 |
... | Waterman polyhedron number 5 wrt. body-centered cubic lattice C3* centered at a lattice point, slightly chamfered cube, octahedrally shallow truncated rhombic dodecahedron | 32, 48, 18 | |
... | oq4oo&#h squippy variant | 1.060660 | 5, 8, 5 |
... | elongated hexagonal dipyramid | 14, 30, 18 | |
... | rectified/ambified n/d-prism, o o-n/d-o symmetric co relative | 1/[sqrt(2) sin(π d/n)] | 3n, 6n, 3n+2 |
... | oqo3ooq&#xt, cubera (cube chimera), (fully) mono-truncated cube | 0.866025 | 7, 12, 7 |
otacoh | hyperbolic x3x4x3x4*a tesselation, omnitruncated cubic-octahderal honeycomb | 2.197368 i | |
otitch | hyperbolic x3x3x3x4*a tesselation, omnitruncated tetrahedral-cubic honeycomb | 2.942253 i | |
otratip | hyperbolic x x3o8o tesselation | 0.321797 i | |
... | Waterman polyhedron number 4 wrt. face-centered cubic lattice A3 centered at a shallow hole | 1.837117 | 16, 42, 28 |
... | vertex figure of thex | 0.948683 | 5, 8, 5 |
... | vertex figure of ope | 0.816497 | 5, 8, 5 |
... | 20 thawroes toroid | 240, 600, 340 | |
... | octagonal Leonardo style "polyhedron of renaissance", vertex figure of lamina-trunc(o8o4xb3x) | 1.847759 | 26, 56, 32 |
... | complex polyhedron xp x2-3-o2 | 3p, 3(p+1), p+3 | |
... | complex polyhedron xp x3-3-o3 | sqrt[2+1/sin2(π/p)] | 8p, 8(p+1), p+8 |
... | complex polyhedron xp xr xt | prt, pr+pt+rt, p+r+t | |
... | complex polyhedron xp xr-4-o2 , complex polyhedron xp xr xr | pr2, 2(p+r)r, p+2r | |
... | complex polyhedron xp xr || op xr | r(p+1), pr+p+r+1, p+r+1 | |
... | Shephard's p-generalised cube, complex polyhedron xp-4-o2-3-o2 , γp 3 | sqrt(3)/(2 sin(π/p)) | p3, 3p2, 3p |
... | p12-h4 | 28, 42, 16 | |
... | pentagonal antidipyramid, pentagonal antitegum, pentagonal kiteohedron, dual of pap, axial bi-kis-doe, deca-truncated sissid | 12, 20, 10 | |
pabaud, J59 | parabiaugmented dodecahedron | 22, 40, 20 | |
pabauhip, J55 | parabiaugmented hexagonal prism | 14, 26, 14 | |
pabautid, J69 | parabiaugmented truncated dodecahedron | 70, 120, 52 | |
pabditoe | parabidiminished truncated octahedron | 1.581139 | 24, 36, 14 |
... | partially bi-expanded hyperbolic order 8 triangular tiling, partially bi-contracted hyperbolic shieldotritetragonal tiling | ||
pabextet | partially bi-expanded tetrahedron | 12, 20, 10 | |
pabextut | partially bi-expanded truncated tetrahedron | 28, 48, 22 | |
pabgyrid, J73 | parabigyrated rhombicosidodecahedron | 2.232951 | 60, 120, 62 |
pabidrid, J80 | parabidiminished rhombicosidodecahedron | 2.232951 | 50, 90, 42 |
pac girco | partially (mono-)contracted great rhombicuboctahedron | ... | 40, 60, 22 |
... | partially contracted hyperbolic shieldotritetragonal tiling | ||
... | partially contracted hyperbolic x4o3x3o3*b tesselation | ||
... | partially contracted hyperbolic x4o3x3x3*b tesselation | ||
pacop | partially Stott contracted octagonal prism | 12, 18, 8 | |
pacprich | partially contracted prismatorhombated cubic honeycomb | ||
pacratoh | partially contracted runcinated tetrahedral-octahedral honeycomb | ||
pacsrich | partially contracted small rhombated cubic honeycomb | ||
pactic | partially (mono-)contracted truncated cube | ... | 20, 32, 14 |
padex snic | partially dodeca-expanded snub cube | 48, 84, 38 | |
pagydrid, J77 | paragyrate diminished rhombicosidodecahedron | 2.232951 | 55, 105, 52 |
pakid | pentakis dodecahedron, apiculated dodecahedron | 32, 90, 60 | |
pap | pentagonal antiprism, para-bidiminished icosahedron | 0.951057 | 10, 20, 12 |
paqrich | prismated quasirhombated cubic honeycomb | ||
... | para bi lowered truncated cube | ... | 24, 36, 14 |
passipsi | pseudosnub pentagrammattic snub (pseudo)icosiicosahedron, compound of 5 sissid | 0.587785 | |
passipsido | pseudosnub pentagrammatic snub (pseudo)disoctahedron, compound of 2 sissid | 0.587785 | |
patex sirco | partially tetrahedrally-expanded small rhombicuboctahedron, tetrahedrally lowered small rhombicuboctahedron, partially tri-expanded truncated tetrahedron | ... | 36, 60, 26 |
pd{3,5,3} | partial diminishing (old: truncation) of hyperbolic order 3 icosahedral tesselation | 0.509376 i | |
peatip | hyperbolic x x5o4o tesselation | 0.747674 i | |
pechon | hyperbolic order 5 cubic honeycomb | 0.555893 i | |
pecu, J5 | pentagonal cupola | 2.232951 | 15, 25, 12 |
pedhon | hyperbolic order 5 dodecahedral honeycomb | 0.427486 i | |
... | vertex figure of pental disnubbachoron, biform twirled compound of 2 vertex-first icosahedra | 0.951057 | |
pedpy (alt.: pet), J13 | pentagonal dipyramid, (line-)pentagon-tegum | 7, 15, 10 | |
pegybcu, J31 | pentagonal gyrobicupola | 20, 40, 22 | |
pegycuro, J33 | pentagonal gyrocupolarotunda | 25, 50, 27 | |
peppy, 5pyr, J2 | pentagonal pyramid | 0.951057 | 6, 10, 6 |
pero, J6 | pentagonal rotunda, half of icosidodecahedron | 1.618034 | 20, 35, 17 |
... | partially extended hyperbolic o4o3x3o3*b tesselation | ||
... | partially extended hyperbolic o4o3x3x3*b tesselation | ||
... | partially expanded hyperbolic order 8 triangular tiling | ||
pexco | partially (mono-)expanded cuboctahedron, 4fold elongated cuboctahedron | ... | 16, 28, 14 |
pexrich | partially expanded rectified cubic honeycomb | ||
pextet | partially (edge-)expanded tetrahedron | 8, 14, 8 | |
pextich | partially expanded truncated cubic honeycomb | ||
pextoe | partially (mono-)expanded truncated octahedron | ... | 32, 48, 18 |
pextoh | partially expanded tetrahedral-octahedral honeycomb | ||
pextut | partially (edge-)expanded truncated tetrahedron | 20, 34, 16 | |
phexah | hyperbolic order 5 hexagonal-tiling honeycomb | 0.381966 i | |
phexdo | partially hexa-expanded dodecahedron | 48, 90, 44 | |
phexid | partially hexa-expanded icosidodecahedron | 54, 96, 44 | |
phexik | partially hexa-expanded icosahedron | 24, 42, 20 | |
pip | pentagonal prism, 5-p, vertex figure of rox | 0.986715 | 10, 15, 7 |
pobcu, J30 | pentagonal orthobicupola | 20, 40, 22 | |
pobro, J34 | pentagonal orthobirotunda | 1.618034 | 30, 60, 32 |
pocuro, J32 | pentagonal orthocupolarotunda | 25, 50, 27 | |
pox snic | partially octa-expanded snub cube | 48, 96, 50 | |
presipsi | pseudoretrosnub pentagonal snub (pseudo)icosiicosahedron, compound of 5 gad | 0.951057 | |
presipsido | pseudoretrosnub pentagonal snub (pseudo)disoctahedron, compound of 2 gad | 0.951057 | |
prich | prismatorhombated cubic honeycomb, runcitruncated cubic honeycomb | ||
priddoh | hyperbolic prismatorhombated (order 4) dodecahedral honeycomb, hyperbolic prismatotruncated order 5 cubical honeycomb, hyperbolic runcitruncated order 5 cubical honeycomb | 2.878623 i | |
prih | hyperbolic prismatorhombated order 3 icosahedral honeycomb, hyperbolic runcitruncated order 3 icosahedral honeycomb | 2.809263 i | |
pripech | hyperbolic prismatorhombated order 5 cubic honeycomb, hyperbolic prismatotruncated order 4 dodecahedral honeycomb, hyperbolic runcicantellated order 5 cubic honeycomb, hyperbolic runcitruncated order 4 dodecahedral honeycomb | 3.081165 i | |
pripped | hyperbolic prismatorhombated order 5 dodecahedral honeycomb, hyperbolic runcitruncated order 5 dodecahedral honeycomb | 2.212971 i | |
pritrah | hyperbolic prismatorhombated triangular-tiling honeycomb | 1.931852 i | |
pysnic | pyritosnub cube, pyritohedral sirco variant, hexadiminished id | 1.618034 | 24, 48, 26 |
pysnic | pyritosnub cube, pyritohedral sirco variant, faceted tigid | 1.876844 | 24, 48, 26 |
pysnic | pyritosnub cube, pyritohedral sirco variant, edge-alternated girco | 2.317611 | 24, 48, 26 |
pystid | pyritohedrally stellated icosidodecahedron | 38, 60, 24 | |
... | q x3o, variation of triangular prism, vertex figure of rectified tesseract | 0.912871 | 6, 9, 5 |
... | q x4o, variation of cube, vertex figure of rectified cubic honeycomb | 1 | 8, 12, 6 |
... | q x5o, variation of pentagonal prism | 1.106168 | 10, 15, 7 |
... | q x6o, variation of hexagonal prism | 1.224745 | 12, 18, 8 |
... | q x8o, variation of octagonal prism | 1.485633 | 16, 24, 10 |
... | q3o3x, variation of cuboctahedron | 1.215958 | 12, 24, 14 |
... | q3o4x, variation of small rhombicuboctahedron, hull of tisso | 1.658312 | 24, 48, 26 |
... | q3o5x, variation of srid | 2.601518 | 60, 120, 62 |
... | q3q4x, Waterman polyhedron number 5 wrt. primitive cubic lattice C3 centered at a hole, variation of girco | 2.958040 | 48, 72, 26 |
... | q3x3o, variation of truncated tetrahedron, triangle-snub small rhombicuboctahedron | 1.398966 | 12, 18, 8 |
... | q3x4x, variation of girco, hull of quitco | 2.564844 | 48, 72, 26 |
... | Qo oq4xx&#zh, variation of squobcu | 16, 32, 18 | |
... | qo oq&#h, longer variant of digonal antiprism, vertex figure of batch | 1 | 4, 6, 4 |
... | qo ou&#h disphenoid | 1.224745 | 4, 6, 4 |
... | Waterman polyhedron number 4 wrt. primitive cubic lattice C3 centered at a hole, cubically expanded rhombic dodecahedron | 2.598076 | 32, 48, 18 |
... | qo3oo&#h, taller variant of trigonal pyramid, vertex figure of tico | 0.981981 | 4, 6, 4 |
... | qo3oo&#x, shallower variant of trigonal pyramid, vertex pyramid of cube | 0.866025 | 4, 6, 4 |
... | Waterman polyhedron number 7 wrt. body-centered cubic lattice C3* centered at a lattice point | 30, 84, 56 | |
... | qo3oq&#x, shallower variant of trigonal antiprism, medial segment of cube | 0.866025 | 6, 12, 8 |
... | Waterman polyhedron number 8 wrt. body-centered cubic lattice C3* centered at a lattice point | 48, 96, 50 | |
qrid | quasi rhombicosidodecahedron, great (non-convex) rhombicosidodecahedron (i.e. not grid) | 0.716891 | 60, 120, 62 |
quequapech | quasiquasiprismated cubic honeycomb | ||
querco | quasirhombicuboctahedron, great rhombicuboctahedron (but not girco) | 0.736813 | 24, 48, 26 |
quipqrich | quasiprismated quasirhombated cubic honeycomb | ||
quiprich | quasiprismatorhombated cubic honeycomb | ||
quishexah | hyperbolic quarter order 4 hexagonal-tiling honeycomb | 0.816497 i | |
quistet | quadratisnub tetratetrahedron, chiral edge faceting sidtid-0-8-12-0-b | 0.866025 | 16, 36, 20 |
quit gissid | quasitruncated great stellated dodecahedron, great stellated truncated dodecahedron, great stellatruncated dodecahedron | 0.657550 | 60, 90, 32 |
quit sissid | quasitruncated small stellated dodecahedron, small stellated truncated dodecahedron, small stellatruncated dodecahedron | 0.852911 | 60, 90, 24 |
quitar (old: quahri) | quasitruncated rhombihedron, quasihyperhombicosicosahedron, compound of 5 quith | 0.579471 | |
quitch | quasitruncated cubic honeycomb | ||
quitco | quasitruncated cuboctahedron, great truncated cuboctahedron, stellatruncated cuboctahedron | 1.062393 | 48, 72, 26 |
quitdid | quasitruncated dodecadodecahedron, stellatruncated dodecadodecahedron | 1.658312 | 120, 180, 54 |
quith | quasitruncated hexahedron, stellated truncated hexahedron, stellatruncated cube | 0.579471 | 24, 36, 14 |
... | rhombic enneacontahedron | 92, 180, 90 | |
racoh | hyperbolic x3o4x3o4*a tesselation, rectified cubic-octahedral honeycomb | 1.045866 i | |
rad (old: rhode) | rhombic dodecahedron, granatahedron, Voronoi cell of face-centered cubic (fcc) lattice, terminally chamfered cube, terminally chamfered octahedron, surtegmated cube, surtegmated octahedron, Waterman polyhedron number 4 wrt. primitive cubic lattice C3 centered at a lattice point, Waterman polyhedron number 2 (and 6) wrt. body-centered cubic lattice C3* centered at a lattice point | 14, 24, 12 | |
raded | rhombidodecadodecahedron | 1.322876 | 60, 120, 54 |
... | edge faceting raded-1-10-5-5 | 1.322876 | 30, 50, 21 |
radh | rhombic dodecahedral honeycomb, Voronoi complex of face-centered cubic (fcc) lattice | ||
rah | rhombihexahedron, compound of 3 cube | 0.866025 | |
raheath | hyperbolic o3o3x7o tesselation, rectified heat honeycomb | 1.312710 i | |
rahet | hyperbolic o3x3o7o tesselation, rectified order 7 tetrahedral honeycomb | 0.657675 i | |
rahrie | rhombihyperhombicosicosahedron, compound of 5 socco | 1.398966 | |
rapescu | retrograde pentagonal cuploid, retrograde pentagonal semicupola | 0.866025 | 10, 20, 11 |
raquahri | rhombiquasihyperhombicosicosahedron, compound of 5 gocco | 0.736813 | |
rasher | rhombisnub hyperhombihedron, compound of 5 sroh | 1.398966 | |
rasquacu | retrograde square cupola, crossed square cupola, 4/3-cupola | 0.736813 | 12, 20, 10 |
rasquahr | rhombisnub quasihyperrhombihedron, compound of 5 groh | 0.736813 | |
rasseri | rhombisnub rhombicosicoahedron, compound of 5 sirco | 1.398966 | |
rassid | rhombisnub dodecahedron, compound of 6 dip | 1.693527 | |
rastacu | retrograde pentagrammic cupola, 5/3-cupola | 0.716891 | 15, 25, 12 |
rath | hyperbolic rectified (order 6) tetrahedral honeycomb | 1 i | |
ratricu | retrograde trigonal cupola, 3/2-cupola | 0.707107 | 9, 15, 8 |
rebatch | rectified bitruncated cubic honeycomb | ||
reco | rectified cuboctahedron, variation of small rhombicuboctahedron, Waterman polyhedron number 6 wrt. primitive cubic lattice C3 centered at a lattice point, Waterman polyhedron number 3 wrt. face-centered cubic lattice A3 centered at a lattice point | 1.732051 | 24, 48, 26 |
... | complex polyhedron o3-3-x3-4-o2 , complex polyhedron x3-3-o3-3-x3 | 216, 432, 126 | |
... | Shephard's 3-generalised cuboctahedron, complex polyhedron o3-4-x2-3-o2 | 27, 81, 36 | |
... | Shephard's 4-generalised cuboctahedron, complex polyhedron o4-4-x2-3-o2 | 48, 192, 76 | |
... | Shephard's 5-generalised cuboctahedron, complex polyhedron o5-4-x2-3-o2 | 75, 375, 140 | |
... | Shephard's p-generalised cuboctahedron, complex polyhedron op-4-x2-3-o2 | 3p2, 3p3, p3+3p | |
... | rectified hyperbolic x4o3o4x4*b tesselation | ... | |
recta | rectangular alterprism, rectangular trapezoprism | sqrt[c2+(a+b)2/2]/2 | 8, 12, 6 |
recytatoh (old: rebtatoh) | rectified cyclotruncated tetrahedral-octahedral honeycomb (rectified bitruncated tetrahedral-octahedral honeycomb) | ||
repip (alt. ampip) | rectified/ambified pip, o2o5o symmetric co relative | 1.203002 | 15, 30, 17 |
rerich | rectified rectified-cubic-honeycomb, variation of small-rhombated-cubic-honeycomb | ||
resirco (alt.: amsirco) | rectified/ambified small-rhombated-cuboctahedron | 2.613126 | 48, 96, 50 |
resrid (alt.: amsrid) | rectified/ambified small-rhombated-icosidodecahedron | 4.352502 | 120, 240, 122 |
reti (alt.: amti) | rectified/ambified truncated icosahedron | 4.854102 | 90, 180, 92 |
retic (alt.: amtic) | rectified/ambified truncated cube | 3.414214 | 36, 72, 38 |
retid (alt.: amtid) | rectified/ambified truncated dodecahedron | 5.854102 | 90, 180, 92 |
retoe (alt.: amtoe) | rectified/ambified truncated octahedron | 2.121320 | 36, 72, 38 |
... | blend of retro-elongated triangular-tiling prisms | ||
retrip (alt.: amtrip) | rectified/ambified trip, kernel of trip and m m3o, o2o3o symmetric co relative | 0.816497 | 9, 18, 11 |
retut (alt.: amtut) | rectified/ambified truncated tetrahedron | 2.121320 | 18, 36, 20 |
rhom | rhombihedron, compound of 5 cube | 0.866025 | |
... | complex polyhedron x3-3-o3-4-x2 | 432, 1080, 342 | |
... | complex polyhedron xp-4-o2-3-x2 | 3p3, 3p2(p+2), p(p2+3p+3) | |
... | complex polyhedron xp-4-o2-4-x2 | ||
... | complex polyhedron xp-4-o2-4-xr | ||
rhote (old: rattic) | rhombic triacontahedron, terminally chamfered dodecahedron, terminally chamfered icosahedron, surtegmated dodecahedron, surtegmated icosahedron | 32, 60, 30 | |
ri | rhombicosahedron | 1.322876 | 60, 120, 50 |
... | ri+12{10/2} (?) | 1.322876 | |
... | ri+12{10/4} (?) | 1.322876 | |
rich | rectified cubic honeycomb | ||
rid | rectified icosidodecahedron, variation of small rhombicosidodecahedron | 3.077684 | 60, 120, 62 |
ridatha | rectified ditetratihemiapeiratic honeycomb | ||
riddoh | hyperbolic rectified order 4 dodecahedral honeycomb | 1.272020 i | |
rigytoh | rectified/ambified gyrated tetrahedral-octahedral honeycomb | ||
rih | hyperbolic rectified order 3 icosahedral honeycomb | 1.427535 i | |
rihach | hyperbolic rectified order 6 cubic honeycomb | 0.707107 i | |
rihexah | hyperbolic rectified (order 3) hexagonal-tiling honeycomb | 1.732051 i | |
rihihexah | hyperbolic rectified order 6 hexagonal-tiling honeycomb | 0.577350 i | |
ripech | hyperbolic rectified order 5 cubic honeycomb | 1.057371 i | |
ripped | hyperbolic rectified order 5 dodecahedral honeycomb | 0.813126 i | |
risdoh | rhombisnub dishexahedron, compound of 6 cube, Skilling's compound | 0.866025 | |
rishexah | hyperbolic rectified order 4 hexagonal-tiling honeycomb | 1 i | |
risquah | hyperbolic rectified square-tiling honeycomb | 1.224745 i | |
ritch | hyperbolic x3o3x3o4*a tesselation, rectified tetrahedral-cubic honeycomb | 1.429970 i | |
ritrah | hyperbolic rectified triangular-tiling honeycomb | 1 i | |
ro | (chiral) rhombioctahedron, compound of 4 trip | 0.763763 | |
rosaqri (old: rasquahpri) | rhombisnub quasirhombicosicosahedron, rhombisnub quasihyperpseudorhombicosicosahedron, compound of 5 querco | 0.736813 | |
rosi | rhombisnub icosahedron, compound of 10 hip | 1.118034 | |
rusch | runcicantic snub cubic honeycomb | ||
... | β3/2o3β (?) | ... | 12, 36, 20 |
... | β3/2β3x3*a (?) | ... | 24, 60, 28 |
... | β3o4β (?) | 1.398966 | 24, 60, 32 |
... | β3o5β (?) | 2.232951 | 60, 180, 92 |
... | hyperbolic s3s4o4o tesselation | ... | |
... | hyperbolic s3s4o4x tesselation | ... | |
... | β3x3o | 1.172604 | |
... | β3x4β (?) | 2.317611 | 48, 96, 44 |
... | β3x5β (?) | 3.802395 | 120, 240, 92 |
... | hyperbolic alternated small prismated order-4 square tiling honeycomb | 0.594604 i | |
... | hyperbolic s4o4o4s + x4x4o4o4*a blend tesselation | 0.594604 i | |
... | hyperbolic o3o4s4o tesselation | 0.866025 i | |
... | family of (generally hyperbolic) s4oPo4s tesselation | ||
... | β5/2o5β (?) | ... | 60, 180, 84 |
... | β5/2x5β (?) | ... | 120, 240, 84 |
... | hyperbolic s5s3s5s honeycomb, alternated hyperbolic great prismatodisdodecahedral honeycomb | ||
... | s60-r60-p12-h30 | 200, 360, 162 | |
sabirch | small birhombatocubic honeycomb | ||
saddid | small dodekicosidodecahedron | 2.232951 | 60, 120, 44 |
sadsid | small disnub dodecahedron, compound of 12 stap | 0.656431 | |
... | vertex figure of small antifrustary trishecatonicosachoron | 0.816497 | 8, 12, 6 |
sapisseri | (chiral) snub pseudosnub rhombicosahedron, compound of 20 thah | 0.707107 | |
sassid | (chiral) small snub dodecahedron, compound of 6 stap | 0.656431 | |
sassiph | snub square prismatic honeycomb | ||
scuffi, ike-7-3 | semicupolaically faceted icosahedron | 0.951057 | 9, 18, 10 |
scufgi, sissid-3-7 | semicupolaically faceted great icosahedron | 0.587785 | 9, 18, 10 |
se | small icosiicosahedron, compound of 5 oct | 0.707107 | |
... | hyperbolic honeycomb with seed point at face of right-angled octahedron domain | ||
seihid | small icosihemidodecahedron | 1.618034 | 30, 60, 26 |
serch | snub rectified cubic honeycomb | ||
seside | small snub icosicosidodecahedron, snub disicosidodecahedron, holosnub icosahedron, hastur | 1.458190 | 60, 180, 112 |
... | vertex figure of setut | 0.866025 | 20, 108, 64 |
shappy, 7/2-pyr | small heptagrammic pyramid | 0.650389 | 8, 14, 8 |
shexah | hyperbolic order 4 hexagonal-tiling honeycomb | 0.707107 i | |
shexatip | hyperbolic x x6o4o tesselation | 0.5 i | |
ship | bistrophic heptagrammic prism, heptagrammic prism of winding number 2, small heptagrammic prism, small stellated heptagonal prism | 0.811783 | 14, 21, 9 |
si | snub icosahedron, compound of 10 oct (but not gissi) | 0.707107 | |
sicdatrid | small complex (ditrigonary) rhombicosidodecahedron | 0.866025 | 60, 120, 62 |
siddid (old: siided) | snub dodecadodecahedron, chaugnar faugn | 60, 150, 84 | |
sidditdid | small ditrigonary dodekicosidodecahedron, small dodekified icosidodecahedron | 1.721489 | 60, 120, 44 |
siddo | snub disoctahedron, octahedral compound of 2 ike, vertex figure of sody | 0.951057 | |
siddy | small dodekicosahedron | 1.721489 | 60, 120, 32 |
... | siddy+12{10/4} (?) | 1.721489 | |
... | siddy+20{6/2} (?) | 1.721489 | |
siddykid | small didyakis dodecahedron | 26, 72, 48 | |
sided | snub icosidodecadodecahedron, dagon | 1.126898 | 60, 180, 104 |
sidhei | small dodecahemicosahedron, great dodecahemiicosahedron (but not gidhei) | 1 | 30, 60, 22 |
sidhid | small dodecahemidodecahedron | 1.618034 | 30, 60, 18 |
sidpicdoh | hyperbolic small disprismated cubical-dodecahedral honeycomb, hyperbolic prismated order 5 cubic honeycomb, hyperbolic runcinated order 5 cubic honeycomb, hyperbolic prismated order 4 dodecahedral honeycomb, hyperbolic runcinated order 4 dodecahedral honeycomb | 1.723155 i | |
sidpichexah | hyperbolic small disprismated cubic-hexagonal-tiling honeycomb, hyperbolic prismated order 6 cubical honeycomb, hyperbolic runcinated order 6 cubical honeycomb | 1.313295 i | |
sidtid | small ditrigonary icosidodecahedron, holosnub dodecahedron, vertex figure of sidtixhi | 0.866025 | 20, 60, 32 |
... | sidtid+ditdid (?) | 0.866025 | |
... | sidtid+ditdid+gidtid (?) | 0.866025 | |
... | sidtid+gidtid (?) | 0.866025 | |
sifodib | sidtid faceting sidtid-0-10-20-2 (i.e. with 10(=d) {3}, 20(=i) {4}, and 2(=b) {5}) | 0.866025 | 20, 60, 32 |
siid | small icosicosidodecahedron | 1.721489 | 60, 120, 52 |
..., s∞o2o3x6s | ... | ||
..., s∞o2s3s6s | full snub triangular prismatic honeycomb | ||
..., s∞o2s3s6x | edge-snub triangular prismatic honeycomb | ||
..., s∞o2s4s4s | full snub square prismatic honeycomb | ||
..., s∞o2s4x4s | edge-snub square prismatic honeycomb | ||
..., s∞o2s4x4x | alternating bistratic tosquat honeycomb | ||
..., s∞o2x3x6s | alternating bistratic hexat honeycomb | ||
..., s∞o2x4s4x | square-snub square prismatic honeycomb | ||
..., s∞x2o3x6s | ... | ||
..., s∞x2s3s6s | axial edge-snub triangular prismatic honeycomb | ||
sirco (alt.: esquobcu) | small rhombicuboctahedron, expanded octahedron, expanded cube, elongated square-orthobicupola | 1.398966 | 24, 48, 26 |
sird | small rhombidodecahedron | 2.232951 | 60, 120, 42 |
... | sird+12{10/2} (?) | 2.232951 | |
... | sird+20{6/2} (?) | 2.232951 | |
... | vertex figure of small retrofrustary trishecatonicosachoron | 0.816497 | 8, 12, 6 |
sirsei | small retrosnub icosiicosahedron, compound of 5 gike | 0.587785 | |
sirsid | small (inverted) retrosnub icosicosidodecahedron, retrosnub disicosidodecahedron, yog sothoth | 0.580695 | 60, 180, 112 |
sirsido | small retrosnub disoctahedron, compound of 2 gike | 0.587785 | |
sis | small snubihedron, compound of 6 tet (but not snu) | 0.612372 | |
sisquah | hyperbolic order 4 square-tiling honeycomb, hyperbolic honeycomb with seed point at vertex of right-angled octahedron domain | 0 i | |
sissid | small stellated dodecahedron, penta-stellahedron, vertex figure of gofix | 0.587785 | 12, 30, 12 |
... | sissid+3gike (?) | 0.587785 | |
skivcadach | small skewverted cubatiapeiroducubatic honeycomb | ||
skivpacoca | small skewverted prismatocubaticubatiapeiratic honeycomb | ||
sladid (old: sit) | small lanceal disdodecahedron, strombic icositetrahedron, deltoidal icositetrahedron, tetragonal icosikaitetrahedron | 26, 48, 24 | |
sladit | small lanceal ditriacontahedron, strombic hexecontahedron, deltoidal hexecontahedron, tetragonal hexecontahedron | 62, 120, 60 | |
snadow, J84 | snub disphenoid, snub digonal antiprism | 8, 18, 12 | |
snathaph | snub trigonal-hexagonal prismatic honeycomb | ||
sne | snub icosiicosahedron, compound of 5 ike | 0.951057 | |
snic | snub cube, snub cuboctahedron | 1.343713 | 24, 60, 38 |
snich, s4s3s4s | (full) snub cubical honeycomb, snub bicubic honeycomb | ||
snid | snub dodecahedron, snub icosidodecahedron | 2.155837 | 60, 150, 92 |
... | vertex figure of small spinofrustary trishecatonicosachoron | 0.816497 | 8, 14, 8 |
snisquap, J85 | snub square antiprism | 16, 40, 26 | |
snit | pyritohedron, pyritosnub tetrahedron, o2o2o symmetric ike variant, vertex figure of hyperbolic cube + n-prism honeycomb | sqrt[a2+c2] | 12, 30, 20 |
snit | pyritohedron, pyritosnub tetrahedron, vertex alternated toe | 1.581139 | 12, 30, 20 |
sno | snub octahedron, compound of 4 oct | 0.707107 | |
snu | snubihedron, compound of 6 tet (but not sis) | 0.612372 | |
... | complex polyhedron sp-4-o2-3-o2 , (γp 3)/p | sqrt(3/8) / sin(π/p) | p2, 3p2, p(p+3) |
so | stella octangula, star tetrahedron, compound of 2 tet | 0.612372 | |
sobath | small biambotetrahedral honeycomb | ||
socco | small cubicuboctahedron | 1.398966 | 24, 48, 20 |
spd{3,5,3} (old: spt{3,5,3}) | semi partial diminishing (old: truncation) of hyperbolic order 3 icosahedral tesselation | 0.509376 i | |
spidded | hyperbolic small prismated disdodecahedral honeycomb, hyperbolic prismated order 5 dodecahedral honeycomb, hyperbolic runcinated order 5 dodecahedral honeycomb | 1.272020 i | |
spiddih | hyperbolic (small) prismated order 3 icosahedral honeycomb, hyperbolic runcinated order 3 icosahedral honeycomb | 1.272020 i | |
spiddihexah | hyperbolic small prismatodishexagonal-tiling honeycomb, runcinated order 6 hexagonal-tiling honeycomb | 1 i | |
spiddish | hyperbolic small prismated dissquare-tiling honeycomb | 0.840896 i | |
spidditrah | hyperbolic small prismated distriangular-tiling honeycomb | 0.759836 i | |
squacu, J4 | square cupola | 1.398966 | 12, 20, 10 |
squah | hyperbolic order 3 square-tiling honeycomb, hyperbolic honeycomb with seed point in center of right-angled octahedron domain | 0.707107 i | |
squap | square antiprism | 0.822664 | 8, 16, 10 |
squatap | square tiling antiprism | ||
squattip | square tiling prism | ||
squigybcu, J29 | square gyrobicupola | 16, 32, 18 | |
squippy, 4pyr, J1 | tetragonal pyramid, half of oct | 0.707107 | 5, 8, 5 |
squit | (line) square tegum, Waterman polyhedron number 2 wrt. body-centered cubic lattice C3* centered at a hole | 6, 12, 8 | |
squobcu, J28 | square orthobicupola | 16, 32, 18 | |
sratoh (old: ratoh) | small rhombated tetrahedral-octahedral honeycomb, runcinated alternated cubic honeycomb, runcinated tetrahedral-octahedral honeycomb, runcic cubic honeycomb | ||
srich | small rhombated cubic honeycomb, cantellated cubic honeycomb | ||
srid | small rhombicosidodecahedron, expanded icosahedron, expanded dodecahedron | 2.232951 | 60, 120, 62 |
sriddoh | hyperbolic (small) rhombated (order 4) dodecahedral honeycomb, hyperbolic cantelated order 4 dodecahedral honeycomb | 2.131920 i | |
srih | hyperbolic (small) rhombated order 3 icosahedral honeycomb, hyperbolic cantelated order 3 icosahedral honeycomb | 2.120267 i | |
sripech | hyperbolic rhombated order 5 cubic tesselation, hyperbolic cantellated order 5 cubic tesselation | 2.053119 i | |
sripped | hyperbolic (small) rhombated order 5 dodecahedral honeycomb, hyperbolic cantelated order 5 dodecahedral honeycomb | 1.546658 i | |
sritrah | hyperbolic (small) rhombated triangular-tiling honeycomb | 1.467890 i | |
srocth | hyperbolic small rhombated order 4 octahedral honeycomb | 1.707107 i | |
sroh | small rhombihexahedron | 1.398966 | 24, 48, 18 |
... | sroh+8{6/2} (?) | 1.398966 | |
srothaph (old: rothaph) | (small) rhombitriangular-hexagonal prismatic honeycomb | ||
stacu | pentagrammic cupola, star cupola | 0.866025 | 15, 25, 12 |
stai | small triambic icosahedron, first stellation of the icosahedron | 32, 60, 20 | |
stap | bistrophic pentagrammic antiprism, stellar antiprism, 5/2-antiprism | 0.656431 | 10, 20, 12 |
stapper | star pentagonal retrohedron | 0.866025 | 12, 20, 10 |
stappy, 5/2-pyr | pentagrammic pyramid, stellated pentagonal pyramid | 0.587785 | 6, 10, 6 |
starp (old: restap) | tristrophic pentagrammic antiprism, stellar retroprism (retrograde stellar antiprism), 5/3-antiprism | 0.587785 | 10, 20, 12 |
starpglass | pentagrammic retroprismatic hourglass | 0.707107 | 10, 15, 7 |
stiddip | (tristrophic) decagrammic prism, stellated decagonal prism, 10/3-prism, 10-prism with winding number 3 | 0.794963 | 20, 30, 12 |
stip | stellated pentagonal prism, 5/2-prism, 5-prism with winding number 2, vertex figure of raggix | 0.725530 | 10, 15, 7 |
stiscu | pentagrammic cuploid, star semicupola | 0.866025 | 10, 20, 11 |
stop (old: sop) | (tristrophic) octagrammic prism, stellated octagonal prism, 8/3-prism, 8-prism with winding number 3 | 0.736813 | 16, 24, 10 |
stopper | star pentagonal rhombihedron | 0.866025 | 12, 24, 12 |
stut cadoca | small tritrigonary cubatidicubatiapeiratic honeycomb | ||
... | rhombical dodeca-augmented snub-dodecahedral variant, rhombi-propello-icosahedron | 72, 150, 80 | |
... | icosa-expanded rhombic enneacontahedron | 132, 240, 110 | |
... | rhombical octa-augmented truncated-octehedral variant | 32, 72, 42 | |
... | expanded octa-augmented truncated-octehedral variant | 48, 96, 50 | |
... | rhombical hexa-augmented snub-cubical variant, rhombi-propello-octahedron | 30, 60, 32 | |
tabatch | truncated bitruncated-cubic-honeycomb | ||
tacytatoh (old: tabtatoh) | truncated cyclotruncated tetrahedral-octahedral honeycomb (truncated bitruncated tetrahedral-octahedral honeycomb) | ||
tagyrid, J74 | trigyrated rhombicosidodecahedron | 2.232951 | 60, 120, 62 |
taki | truncated chiro-icosahedron, compound of 5 tut | 1.172604 | |
tapech | hyperbolic truncated alternated order-5 cubic honeycomb, hyperbolic cantic order-5 cubic honeycomb | 1.841352 i | |
tar (old: harie) | truncated rhombihedron, hyperhombicosicosahedron, compound of 5 tic | 1.778824 | |
targi | trireplenished great icosahedron | 0.587785 | 9, 15, 8 |
tassiph | truncated square prismatic honeycomb | ||
tatoh | truncated tetrahedral-octahedral honeycomb, truncated alternated cubic honeycomb, cantic cubic honeycomb | ||
taud, J61 | triaugmented dodecahedron | 23, 45, 24 | |
tauhip, J57 | triaugmented hexagonal prism | 15, 30, 17 | |
tautid, J71 | triaugmented truncated dodecahedron | 75, 135, 62 | |
tautip, J51 | triaugmented trigonal prism | 9, 21, 14 | |
te | truncated icosiicosahedron, compound of 10 tut | 1.172604 | |
teddi, J63 | tridiminished icosahedron, ursahedron, vertex figure of sadi | 0.951057 | 9, 15, 8 |
teddoe | tetrahedrally diminished dodecahedron, vertex figure of pd{3,5,3} | 1.401259 | 16, 30, 16 |
tedrid, J83 | tridiminished rhombicosidodecahedron, magnaursahedron | 2.232951 | 45, 75, 32 |
tehtrah (old: datha) | tetrahemitriangular honeycomb, ditetratihemiapeiratic honeycomb | ||
tekah | tetrakis hexahedron, apiculated cube | 14, 36, 24 | |
tepcus | tetrapod-cut-sirco | 1.398966 | 24, 40, 18 |
tepdid | tripentadiminished icosidodecahedron | 1.618034 | 15, 30, 17 |
tet | tetrahedron, 3D simplex (α3), pyrochor(id), regular trigonal pyramid, digonal antiprism, regular (di)sphenoid, hemicube, smaller Delone cell of face-centered cubic (fcc) lattice, regular line-scalene, regular (point-)tettene, vertex figure of pen, Gosset polytope 02, Waterman polyhedron number 1 wrt. face-centered cubic lattice A3 centered at a shallow hole | 0.612372 | 4, 6, 4 |
thah | tetrahemihexahedron, vertex figure of tho, triangular crossed cuploid | 0.707107 | 6, 12, 7 |
thaph | truncated-hexagonal prismatic honeycomb | ||
thattip | trihexagonal tiling prism | ||
thawro, J92 | triangular hebesphenorotunda | 18, 36, 20 | |
thiph | triangular-hexagonal prismatic honeycomb | ||
thon | hyperbolic order 6 tetrahedral honeycomb | 0 i | |
ti | truncated icosahedron, buckyball, Goldberg polyhedron GP(1,1) | 2.478019 | 60, 90, 32 |
tic | truncated cube, truncated hexahedron | 1.778824 | 24, 36, 14 |
tich | truncated cubic honeycomb | ||
tid | truncated dodecahedron | 2.969449 | 60, 90, 32 |
tiddoh | hyperbolic truncated (order 4) dodecahedral honeycomb | 2.246127 i | |
tiggy | truncated great icosahedron, great truncated icosahedron | 1.053292 | 60, 90, 32 |
tigid | truncated great dodecahedron | 1.876844 | 60, 90, 24 |
tih | hyperbolic truncated order 3 icosahedral honeycomb | 2.082108 i | |
tikit | triakis tetrahedron, apiculated tetrahedron | 8, 18, 12 | |
tikko | triakis octahedron, apiculated octahedron | 14, 36, 24 | |
tipech | hyperbolic truncated order 5 cubic tesselation | 1.734413 i | |
tiph | triangular prismatic honeycomb, Delone complex of unit-stacked hexagonal lattice | ||
tipped | hyperbolic truncated order 5 dodecahedral honeycomb | 1.383373 i | |
tisquah | hyperbolic trancated square-tiling honeycomb | 2.030104 i | |
tissish | hyperbolic truncated order 4 square-tiling honeycomb | 1.098684 i | |
tisso | truncated stella octangula, compound of 2 tut | 1.172604 | |
titch | hyperbolic x3x3o3x4*a tesselation, truncated tetrahedral-cubic honeycomb | 2.256021 i | |
titdi | tri-trigonally diminished icosahedron, (subsymmetrically) tristellated-dodecahedron, tri-kis-dodecahedron, dual of teddi, vertex figure of tridex | 8, 15, 9 | |
titdoh | hyperbolic x3x3x3o4*a tesselation, truncated tetrahedral-disoctahedral honeycomb | 2.085865 i | |
tithah | truncated tetrahemihexahedron | 1.581139 | 24, 36, 13 |
titrip | truncated triangular prism, expanded ambified trip | sqrt[(7y2+16y+16)/12] | 18, 27, 11 |
tobcu, J27 | triangular orthobicupola, vertex figure of gytoh | 1 | 12, 24, 14 |
tocth | hyperbolic truncated (order 4) octahedral honeycomb | 1.414214 i | |
toe (alt.: gratet) | truncated octahedron, omnitruncated tetrahedron, great rhombitetratetrahedron, Voronoi cell of body-centered cubic (bcc) lattice, Kelvin's tetrakaidecahedron, Waterman polyhedron number 10 wrt. face-centered cubic lattice A3 centered at a lattice point, permutohedron of 4 elements, equatorial cross-section of oct-first thex | 1.581139 | 24, 36, 14 |
toif | toroidal icosahedron faceting, edge faceting ike-6-6-a | 0.951057 | 12, 24, 12 |
topfu | two-op-fusion | 1.398966 | 24, 40, 16 |
... | toroidal pentagrammic bicuploid, star semicupolaic diabolo | 15, 35, 20 | |
... | toroidal tiler | 12, 24, 12 | |
totratip | hyperbolic truncated order 8 triangle tiling prism | 2.220806 i | |
trah | hyperbolic order 3 triangle-tiling honeycomb | 0 i | |
tratap | triangular tiling antiprism | ||
trattip | triangular tiling prism | ||
trazip | xx xw&#q, prism of (isosceles) trapezoid | 1.306704 | 8, 12, 6 |
tricu, J3 | triangular cupola, half of cuboctahedron | 1 | 9, 15, 8 |
tridpy (alt.: trit), J12 | trigonal dipyramid, (line-)triangle-tegum | 5, 9, 6 | |
trip, 3-p | triangular prism, digonal cupola, Delone cell of unit-stacked hexagonal lattice, vertex figure of rap | 0.763763 | 6, 9, 5 |
trippescu | tripod pentagonized semicupola, edge faceting sidtid-0-3-3-3 | 0.866025 | 10, 18, 9 |
trirp | (degenerate) trigonal retroprism, retrograde trigonal antiprism | ∞ i.e. flat in euclidean space | 6, 12, 8 |
trirp (variant) | vertex figure of faceted rectified pentachoron, taller trigonal retroprism (3/2 antiprism) variant | 0.763763 | 6, 12, 8 |
... | truncated Shephard's 3-generalised octahedron, complex polyhedron x2-3-x2-4-o3 | 54, 108, 36 | |
... | truncated Shephard's 4-generalised octahedron, complex polyhedron x2-3-x2-4-o4 | 96, 240, 76 | |
... | truncated Shephard's 5-generalised octahedron, complex polyhedron x2-3-x2-4-o5 | 150, 450, 140 | |
... | truncated Shephard's p-generalised octahedron, complex polyhedron x2-3-x2-4-op | 6p2, 3p2(p+1), (p2+3)p | |
... | complex polyhedron x2-4-x3-3-o3 | 432, 648, 126 | |
... | truncated Hessian polyhedron, complex polyhedron x3-3-x3-3-o3 | 216, 288, 54 | |
... | complex polyhedron x3-3-x3-4-o2 , complex polyhedron x3-3-x3-3-x3 | 648, 648, 126 | |
... | truncated 3-generalised Shephard cube, complex polyhedron x3-4-x2-3-o2 | 81, 108, 36 | |
... | truncated 4-generalised Shephard cube, complex polyhedron x4-4-x2-3-o2 | 192, 240, 76 | |
... | truncated 5-generalised Shephard cube, complex polyhedron x5-4-x2-3-o2 | 375, 450, 140 | |
... | truncated p-generalised Shephard cube, complex polyhedron xp-4-x2-3-o2 | 3p3, 3p2(p+1), (p2+3)p | |
... | truncated hyperbolic x4o3o4x4*b tesselation | ... | |
tucoh | hyperbolic x3x4x3o4*a tesselation, truncated cubic-octahedral honeycomb | 1.599084 i | |
tuhip | orthogonal blend of hexagonal prisms | 1.118034 | 16, 28, 12 |
tupip | orthogonal blend of pentagonal prisms, vertex figure of sadsadox | 0.986715 | 16, 26, 12 |
tuquith | blend of 2 quasitruncated cubes | 0.579471 | 32, 56, 24 |
tustip | orthogonal blend of pentagagramic prisms, vertex figure of gadsadox | 0.725530 | 16, 26, 12 |
tut | truncated tetrahedron, cantic cube, Waterman polyhedron number 2 wrt. face-centered cubic lattice A3 centered at a shallow hole | 1.172604 | 12, 18, 8 |
tutic | blend of 2 truncated cubes | 1.778824 | 32, 56, 24 |
tutrip | two trip cupolaic blend, gyrated blend of 2 digonal cupola, Phillips head | 0.763763 | 8, 14, 8 |
tutut | two tut cupolaic blend, gyrated blend of 2 truncated tetrahedra | 1.172604 | 18, 30, 14 |
twip | dodecagonal prism | 1.995508 | 24, 36, 14 |
... | u q3o, variation of triangular prism | 1.290994 | 6, 9, 5 |
... | u x3o, variation of triangular prism, vertex figure of rectified hecatonicosachoron | 1.154701 | 6, 9, 5 |
... | u x4o, variation of cube | 1.224745 | 8, 12, 6 |
... | u x5o, variation of pentagonal prism | 1.312862 | 10, 15, 7 |
... | u x6o, variation of hexagonal prism | 1.414214 | 12, 18, 8 |
... | u3o3x, variation of cuboctahedron, Waterman polyhedron number 3 wrt. face-centered cubic lattice A3 centered at a shallow hole | 1.541104 | 12, 24, 14 |
... | u3o4x, variation of small rhombicuboctahedron | 2.040640 | 24, 48, 26 |
... | u3x3o, variation of truncated tetrahedron | 1.732051 | 12, 18, 8 |
... | u3x4o, variation of truncated octahedron, Waterman polyhedron number 5 wrt. face-centered cubic lattice A3 centered at a lattice point | 2.236068 | 24, 36, 14 |
... | hexagonal dipyramid | 8, 18, 12 | |
... | uo ou&#h, shorter variant of digonal antiprism | 1.118034 | 4, 6, 4 |
... | Waterman polyhedron number 6 wrt. face-centered cubic lattice A3 centered at a lattice point | 32, 72, 42 | |
... | diagonal square wedge, line atop dual square | 1.069045 | 6, 11, 7 |
... | v f3o, variation of triangular prism, vertex figure of rasishi | 0.983956 | 6, 9, 5 |
... | v f5/2o, variation of 5/2-prism, vertex figure of ragashi | 0.905040 | 10, 15, 7 |
... | v x3o, variation of triangular prism, vertex figure of rectified great grand stellated hecatonicosachoron | 0.654847 | 6, 9, 5 |
... | v x5o, variation of pentagonal prism, vertex figure of ragishi | 0.905040 | 10, 15, 7 |
... | v3o3x, variation of cuboctahedron, vertex figure of gadtaxady | 0.820211 | 12, 24, 14 |
... | v3o5f, variation of srid, hull of tiggy | 2.757554 | 60, 120, 62 |
... | v3x3o, variation of truncated tetrahedron, vertex figure of sidtaxhi | 0.975835 | 12, 18, 8 |
... | v3x5f, variation of grid, hull of gaquatid | 4.323687 | 120, 180, 62 |
... | axially trigonal variant of pentagonal rotunda | ... | 12, 21, 11 |
... | w x4o, variation of cube | 1.398966 | 8, 12, 6 |
... | w x8o, variation of octagonal prism, hull of 8/3-prism | 1.778824 | 16, 24, 10 |
... | w3x3o, variation of truncated tetrahedron | 1.973010 | 12, 18, 8 |
... | w3x4x, variation of girco, hull of cotco | 3.193704 | 48, 72, 26 |
waco, J86 | sphenocorona | 10, 22, 14 | |
wamco, J88 | sphenomegacorona | 12, 28, 18 | |
wavicoca | sphenoverted cubaticubatiapeiratic honeycomb | ||
... | x f3o, variation of triangular prism | 1.059565 | 6, 9, 5 |
... | x f5/2o, variation of 5/2-prism, vertex figure of rofix | 0.986715 | 10, 15, 7 |
... | x h3o, variation of triangular prism | 1.118034 | 6, 9, 5 |
... | x q3o, variation of triangular prism, vertex figure of rectified icositetrachoron | 0.957427 | 6, 9, 5 |
... | x q4o, variation of cube | 1.118034 | 8, 12, 6 |
... | x u3o, variation of triangular prism | 1.258306 | 6, 9, 5 |
... | x v5o, variation of pentagonal prism, vertex figure of rigfix | 0.725530 | 10, 15, 7 |
... | hyperbolic xØo4x6o4o tesselation | 0.5 i | |
... | hyperbolic xØx3o5x *c4o tesselation | 0.747674 i | |
... | x3(-x)5f, variation of grid | 1.618034 | 120, 180, 62 |
... | x3/2β3x (?) | ... | |
... | x3f4o, variation of truncated octahedron, hull of siddo, hull of passipsido | 2.176251 | 24, 36, 14 |
... | x3f5o, variation of ti, hull of raded, hull of kri | 3.463334 | 60, 90, 32 |
... | hyperbolic x3o3o3x5*a tesselation | 1.272020 i | |
... | hyperbolic x3o3o5o3*a tesselation | 0.250437 i | |
... | hyperbolic x3o3x3o5*a tesselation | 1.118425 i | |
... | hyperbolic x3o4o3x5*a tesselation, cyclotruncated dodecahedral-octahedral honeycomb | ||
... | hyperbolic x3o4o4o4*a tesselation | 0 i | |
... | hyperbolic honeycomb x3o4x3o4x3o4*aØ*d *bØ*e *cØ*f | ... | |
... | hyperbolic x3o4x3o5*a tesselation | 0.919229 i | |
... | hyperbolic x3o5x3o5*a tesselation | ||
... | hyperbolic honeycomb x3o5x3o5x3o5*aØ*d *bØ*e *cØ*f | ... | |
... | hyperbolic x3o5x5o3*a tesselation | 0.747674 i | |
... | hyperbolic x3o5x *b4o tesselation | 0.747674 i | |
... | hyperbolic x3o6o3o6*a honeycomb, hyperbolic triangular-tiling - hexagonal-tiling honeycomb | 0 i | |
... | hyperbolic x3o:s3s4s honeycomb | ... i | |
... | hyperbolic x3o:s3s5s honeycomb | ... i | |
... | hyperbolic x3o:s3s6s honeycomb | ... i | |
... | hyperbolic x3o:s3sPs honeycomb | ... i | |
... | x3q3o, variation of truncated tetrahedron | 1.442951 | 12, 18, 8 |
... | x3β3o (?) | ... | 12, 30, 14 |
... | x3β4o (?) | 1.581139 | 24, 48, 20 |
... | x3β5o (?) | 2.478019 | 60, 150, 62 |
... | x3u3o, variation of truncated tetrahedron | 1.837117 | 12, 18, 8 |
... | x3u4o, variation of truncated octahedron | 2.549510 | 24, 36, 14 |
... | x3v3o, variation of truncated tetrahedron, vertex figure of dattady | 0.935414 | 12, 18, 8 |
... | x3w3o, variation of truncated tetrahedron | 2.120453 | 12, 18, 8 |
... | x3w4o, variation of truncated octahedron, hull of rah, hull of snu | 2.956796 | 24, 36, 14 |
... | hyperbolic x3x3o3o5*a tesselation | 1.072098 i | |
... | hyperbolic x3x3o3x5*a tesselation | 1.816256 i | |
... | x3x3u, variation of truncated octahedron, Waterman polyhedron number 5 wrt. face-centered cubic lattice A3 centered at a shallow hole | 2.091650 | 24, 36, 14 |
... | hyperbolic x3x3x3o5*a tesselation | 1.601395 i | |
... | hyperbolic x3x3x3x5*a tesselation | 2.339260 i | |
... | hyperbolic x3x4o3o5*a tesselation | 0.869999 i | |
... | hyperbolic x3x4o3x5*a tesselation | ||
... | hyperbolic x4x4o *b3x tesselation, hyperbolic runcicantic o3o4o4x tesselation | 2.090770 i | |
... | hyperbolic x3x4o6o tesselation | 0.447214 i | |
... | x3x4q, variation of great rhombicuboctahedron, Waterman polyhedron number 7 wrt. face-centered cubic lattice A3 centered at a lattice point | 2.645751 | 48, 72, 26 |
... | hyperbolic x3x4x3o5*a tesselation | ||
... | hyperbolic x3x4x3x5*a tesselation | ||
... | hyperbolic x3x5o3o5*a tesselation | 0.786151 i | |
... | hyperbolic x3x5x3x5*a tesselation, hyperbolic omnitruncated dodecahedral-icosahedral honeycomb | 1.798907 i | |
... | hyperbolic x3x:s3s4s honeycomb, hyperbolic truncated x3o:s3s4s honeycomb | ... i | |
... | hyperbolic x3x:s3s5s honeycomb, hyperbolic truncated x3o:s3s5s honeycomb | ... i | |
... | hyperbolic x3x:s3s6s honeycomb, hyperbolic truncated x3o:s3s6s honeycomb | ... i | |
... | hyperbolic x3x:s3sPs honeycomb, hyperbolic truncated x3o:s3sPs honeycomb | ... i | |
... | hyperbolic x4o3o4x4*b tesselation | 0.5 i | |
... | hyperbolic x4o3o5o3*a tesselation | 0.208191 i | |
... | hyperbolic x4o3x3x3*b tesselation | 1.553774 i | |
... | hyperbolic x4o4o *b3o tesselation, hyperbolic alternated o3o4o4x tesselation | 0.5 i | |
... | family of (generally hyperbolic) x4oPo4x honeycombs | ||
... | hyperbolic x4s4o *b3s tesselation | ... | |
... | hyperbolic x4x3o8o tesselation | 0.594604 i | |
... | hyperbolic x4x3x8o tesselation | 1.864101 i | |
... | hyperbolic x4x4o4o4*a tesselation | 0.594604 i | |
... | hyperbolic x4x4o5o tesselation | 0.720524 i | |
... | hyperbolic x5/2o5o4o honeycomb | 0.437016 | |
... | x5/2β5o (?) | 1.401259 | |
... | hyperbolic x5o3o3o3*a tesselation | 0.573060 i | |
... | hyperbolic x5o3o4o3*a tesselation | 0.336860 i | |
... | hyperbolic x5o3o5o3*a tesselation | ||
... | hyperbolic x5o5o *b5/2o honeycomb | 0.393076 i | |
... | hyperbolic x8o4o *b3o tesselation | 0.321797 i | |
... | xfo3foo5oxf&#zx | 140, 270, 132 | |
... | p60-r60, 41st stellation of ti | 152, 270, 120 | |
... | expansion of 41th stellation of truncated icosahedron | 260, 420, 162 | |
... | xfoE3fooo5xuFx&#zxt | 260, 420, 162 | |
... | hyperbolic honeycomb x∞x5o6o | 0.363271 i | |
... | xo oq&#q, tetrahedron with one shorter edge, vertex figure of tisdip | 0.836660 | 4, 6, 4 |
... | xo ox&#h, longer variant of digonal antiprism, vertex figure of deca | 0.935414 | 4, 6, 4 |
... | xo ox&#k, longer variant of digonal antiprism, vertex figure of cont | 0.989219 | 4, 6, 4 |
... | xo ox&#q, longer variant of digonal antiprism, vertex figure of triddip | 0.790569 | 4, 6, 4 |
... | xo3oo&#q, longer variant of trigonal pyramid, vertex figure of tepe | 0.774597 | 4, 6, 4 |
... | xo3ox&#h, longer variant of trigonal antiprism, cyclo-hexadiminished co, vertex figure of batatoh | 1 | 6, 12, 8 |
... | xo3ox&#q, longer variant of trigonal antiprism, vertex figure of spid | 0.866025 | 6, 12, 8 |
... | vertex figure of small prismated icositetrachoron | 0.541196 | 8, 16, 10 |
... | pentagonal rhombic barrel | 20, 40, 22 | |
... | Waterman polyhedron number 4 wrt. body-centered cubic lattice C3* centered at a hole | 16, 28, 14 | |
... | q-laced digonal cupola, vertex figure of srip | 0.906327 | 6, 9, 5 |
... | vertex figure of cope | 0.894427 | 5, 8, 5 |
Count of actually available polytopes: 1058
---- 4D ----
Acronym | Name | Circumradius | Face vector |
(2,2n)-pap | dyad - 2n-gon prismantiprismoid, s2s2s-2n-x, edge-alternated square - 4n-gon duoprism | ... | 8n, 20n, 18n+4, 6n+4 |
(n,2m)-pap | n-gon - 2m-gon prismantiprismoid, s-n-s-2-s-2m-x, edge-alternated 2n-gon - 4m-gon duoprism | ... | 4nm, 12nm, 10nm+2n+4m, 2nm+2n+4m |
... | mono-augmented trigonal mibdi-laced wedge | ... | 18, 62, 72, 28 |
10,n-dip | decagon - n-gon duoprism | sqrt[(3+sqrt(5))/2+1/(4 sin2(π/n))] | 10n, 20n, 11n+10, n+10 |
..., 10Y4-8T-0 | parallelly oct dissected octet | ||
..., 10Y4-8T-1-alt | alternating staggered 1×60°-gyrated 10Y4-8T-0 | ||
..., 10Y4-8T-1-hel | helical staggered 1×60°-gyrated 10Y4-8T-0 | ||
..., 10Y4-8T-2-alt | alternating staggered 2×60°-gyrated 10Y4-8T-0 | ||
..., 10Y4-8T-2-hel | helical staggered 2×60°-gyrated 10Y4-8T-0 | ||
..., 10Y4-8T-3 | 3×60°-gyrated 10Y4-8T-0, trat-mirrored 10Y4-8T-0 | ||
12,n-dip | dodecagon - n-gon duoprism | sqrt[2+sqrt(3)+1/(4 sin2(π/n))] | 12n, 24n, 13n+12, n+12 |
... | (1,4)-expanded bited | ... | 120, 420, 440, 140 |
... | 1/10-luna of hexacosachoron | 1.618034 | 31, 100, 113, 44 |
2,n-dap | digon - n-gon duoantiprism, hemiated square - 2n-gon duoprism | sqrt[A2/2+B2/(4 sin2(π/2n))] | 4n, 14n, 16n+4, 6n+4 |
... | Shephard's 3-generalised hexadecachoron, complex polychoron x2-3-o2-3-o2-4-o3 , β3 4 | 12, 54, 108, 81 | |
... | Shephard's 4-generalised hexadecachoron, complex polychoron x2-3-o2-3-o2-4-o4 , β4 4 | 16, 96, 256, 256 | |
... | Shephard's 5-generalised hexadecachoron, complex polychoron x2-3-o2-3-o2-4-o5 , β5 4 | 20, 150, 500, 625 | |
... | Shephard's p-generalised hexadecachoron, complex polychoron x2-3-o2-3-o2-4-op , βp 4 | 4p, 6p2, 4p3, p4 | |
... | 2affic (?) | 1.414214 | |
... | 2affidhi (?) | 2.236068 | |
... | 2cont (?) | 3.414214 | |
... | 2cuhsquah (?) | ||
... | 2deca (?) | 1.414214 | |
... | 2dittafady (?) | 1.414214 | |
... | 2ex (?) | 1.618034 | |
... | 2ex+fix (?) | 1.618034 | |
... | 2firgaghi (?) | 1.070466 | |
... | 2firgogishi (?) | 0.661585 | |
... | 2firp (?) | 0.774597 | |
... | 2firsashi (?) | 2.802517 | |
... | 2fix (?) | 1.618034 | |
... | 2frico (?) | 1.732051 | |
... | 2fry (?) | 4.534568 | |
... | 2gadtifady (?) | 0.874032 | |
... | 2gaghi (?) | 1 | |
... | 2gaghi+2paphacki (?) | 1 | |
... | 2gahi (?) | 1.618034 | |
... | 2garpop+20{6/2} | 1.183216 | |
... | 2gashi (?) | 0.618034 | |
... | 2gax (?) | 0.618034 | |
... | 2gidditdy (?) | 1.732051 | |
... | 2gidditpix+2dithix (?) | 1.732051 | |
... | 2gifdahihox (?) | 1 | |
... | 2gippapivady (?) | 0.726543 | |
... | 2giprapivady (?) | 1.902113 | |
... | 2gishi (?) | 0.618034 | |
... | 2gitphi (?) | 0.874032 | |
... | 2gofix (?) | 0.618034 | |
... | 2gogishi (?) | 0.540182 | |
... | 2gohi (?) | 1.618034 | |
... | 2grahi (?) | 11.252107 | |
... | 2grico (?) | 4.299451 | |
... | 2grip (?) | 1.843909 | |
... | 2grit (?) | 3.005916 | |
... | 2grix (?) | 9.124101 | |
... | 2hex+8oct (?) | 0.707107 | |
... | 2hi (?) | 3.702459 | |
... | 2huhoh+3tes+8co (?) | 1 | |
... | 2ico (?) | 1 | |
... | 2ico+2gico (?) | 1 | |
... | 2ico+48{4}+128{3} (?) | 1 | |
... | 2iddip (?) | 1.693527 | |
2n,2m-dip | 2n-gonal - 2m-gonal duoprism | sqrt[1/(4 sin2(π/2n))+1/(4 sin2(π/2m))] | 4nm, 8nm, 4nm+2n+2m, 2n+2m |
2n,m-dip | 2n-gonal - m-gonal duoprism | sqrt[1/(4 sin2(π/2n))+1/(4 sin2(π/m))] | 2nm, 4nm, 2nm+2n+m, 2n+m |
... | 2oh (?) | 1 | |
... | 2papvixhi (?) | 1.902113 | |
... | 2pen (?) | 0.632456 | |
... | 2prahi (?) | 8.278950 | |
... | 2prapvixhi (?) | 1.175571 | |
... | 2prico (?) | 3.498949 | |
... | 2prip (?) | 1.612452 | |
... | 2prit (?) | 2.370932 | |
... | 2prix (?) | 9.744610 | |
... | 2proh (?) | 2.613126 | |
... | 2quiphi (?) | 0.726543 | |
... | 2rahi (?) | 4.534568 | |
... | 2rahi+2400tet (?) | 4.534568 | |
... | 2rap (?) | 0.774597 | |
... | 2rap+20tet (?) | 0.774597 | |
... | 2ratho (?) | 1 | |
... | 2rico (?) | 1.732051 | |
... | 2rico+64{6}+128{3} (?) | 1.732051 | |
... | 2rico+64{6}+192{3} (?) | 1.732051 | |
... | 2ridditdy (?) | 1.732051 | |
... | 2rit+64tet (?) | 1.224745 | |
... | 2rox (?) | 3.077684 | |
... | 2rox+1440{5}+2400{3} (?) | 3.077684 | |
... | 2rox+sophi (?) | 3.077684 | |
... | 2sadtifady (?) | 2.288246 | |
... | 2sidditdy (?) | 1.732051 | |
... | 2sidditpix+2dithix (?) | 1.732051 | |
... | 2sifdahihox (?) | 1 | |
... | 2sishi (?) | 1 | |
... | 2sishi+2paphicki (?) | 1 | |
... | 2sitphi (?) | 2.288246 | |
... | 2sophi (?) | 3.077684 | |
... | 2spapivady (?) | 1.175571 | |
... | 2sprapivady (?) | 3.077684 | |
... | 2srahi (?) | 6.735034 | |
... | 2srahi+1440{10}+4800{3} (?) | 6.735034 | |
... | 2srahi+2400trip (?) | 6.735034 | |
... | 2srico (?) | 2.613126 | |
... | 2srico+144{8}+576{3} (?) | 2.613126 | |
... | 2srico+192trip (?) | 2.613126 | |
... | 2srip (?) | 1.183216 | |
... | 2srip+20{6}+40{3} (?) | 1.183216 | |
... | 2srip+20{6}+60{3} (?) | 1.183216 | |
... | 2srip+20trip (?) | 1.183216 | |
... | 2srit (?) | 1.847759 | |
... | 2srit+48{8}+128{3} (?) | 1.847759 | |
... | 2srit+64trip (?) | 1.847759 | |
... | 2srix (?) | 6.073594 | |
... | 2srix+2400{6}+4800{3} (?) | 6.073594 | |
... | 2srix+2400{6}+7200{3} (?) | 6.073594 | |
... | 2tah (?) | 2.121320 | |
... | 2tes (?) | 1 | |
... | 2thahp (?) | 0.866025 | |
... | 2thex (?) | 1.581139 | |
... | 2tho (?) | 0.707107 | |
... | 2tho+24{4} (?) | 0.707107 | |
... | 2titho (?) | 1.581139 | |
... | 2xhi (?) | 7.579634 | |
... | 2/10-luna of hexacosachoron | 1.618034 | 42, 171, 233, 104 |
3,n-dip, K-4.175 | triangle - n-gon duoprism, n-gon - n-prismatic wedge | sqrt[1/3+1/(4 sin2(π/n))] | 3n, 6n, 4n+3, n+3 |
... | Witting polychoron, complex polychoron x3-3-o3-3-o3-3-o3 | 1 | 240, 2160, 2160, 240 |
... | Shephard's 3-generalised tesseract, complex polychoron x3-4-o2-3-o2-3-o2 , γ3 4 | 81, 108, 54, 12 | |
... | general variant of triddap | sqrt[(a2+b2)/3] | 18, 72, 84, 30 |
..., {3} || gybef | {3} || gyrobifastegium | ... | 11, 31, 32, 12 |
... | 3doe-1pap-10mibdi-10teddi-diminished ex | 1.618034 | |
... | 3ex+2fix+gaghi (?) | 1.618034 | |
... | 3ex+fix (?) | 1.618034 | |
... | 3pen (?) | 0.632456 | |
..., 3Q4-T-2P8-P4 | parallelly sirco dissected ratoh | ||
... | 3rasishi (?) | 2.802517 | |
... | 3sishi (?) | 0.809017 | |
... | three squaf blend, "thah-squares star" atop cube | 0.879465 | |
... | three squippyp blend, "coord-axes edge star" atop cube | 0.866025 | |
... | three tisdip blend, "coord-planes squares star" atop cube | 0.912871 | |
... | 3/10-luna of hexacosachoron | 1.618034 | 53, 242, 353, 164 |
4,2n-dip | square - 2n-gon duoprism | sqrt[1/2+1/(4 sin2(π/2n))] | 8n, 16n, 10n+4, 2n+4 |
4,2n/d-dip | square - 2n/d-gram duoprism | sqrt[1/2+1/(4 sin2(πd/2n))] | 8n, 16n, 10n+4, 2n+4 |
4,n-dip, K-4.177 | square - n-gonal duoprism | sqrt[1/2+1/(4 sin2(π/n))] | 4n, 8n, 5n+4, n+4 |
4,n/d-dip | square - n/d-gramal duoprism | sqrt[1/2+1/(4 sin2(πd/n))] | 4n, 8n, 5n+4, n+4 |
... | Shephard's 4-generalised tesseract, complex polychoron x4-4-o2-3-o2-3-o2 , γ4 4 | 256, 256, 96, 16 | |
... | tetracontadisdiminished ex | 1.618034 | 78, 276, 300, 102 |
... | tetracontadisdiminished sidpixhi | 5.236068 | 1560, 3720, 2856, 696 |
... | 4D corner hypercubera | 1 | 12, 31, 31, 12 |
... | 4pen | 0.632456 | |
... | 4pen+160{3} (?) | 0.632456 | |
... | 4/10-luna of hexacosachoron | 1.618034 | 64, 313, 473, 224 |
5,n-dip | pentagon - n-gon duoprism | sqrt[(5+sqrt(5))/10+1/(4 sin2(π/n))] | 5n, 10n, 6n+5, n+5 |
... | Shephard's 5-generalised tesseract, complex polychoron x5-4-o2-3-o2-3-o2 , γ5 4 | 625, 500, 150, 20 | |
..., K-4.146 | pentagon - pentagonal-rotunda wedge, {5} || pero | 3.077684 | 25, 65, 58, 18 |
... | outer pentadiminished 2/10-luna of hexacosachoron | 1.618034 | 37, 116, 113, 34 |
..., 5Y4-4T-6P3-tri-0 | trat-elongated 10Y4-8T-0 | ||
..., 5Y4-4T-6P3-tri-1-alt | trat-elongated 10Y4-8T-1-alt | ||
..., 5Y4-4T-6P3-tri-1-hel | trat-elongated 10Y4-8T-1-hel | ||
..., 5Y4-4T-6P3-tri-2-alt | trat-elongated 10Y4-8T-2-alt | ||
..., 5Y4-4T-6P3-tri-2-hel | trat-elongated 10Y4-8T-2-hel | ||
..., 5Y4-4T-6P3-tri-3 | trat-elongated 10Y4-8T-3 | ||
6,n-dip | hexagon - n-gonal duoprism | sqrt[1+1/(4 sin2(π/n))] | 6n, 12n, 7n+6, n+6 |
... | 6pen | 0.632456 | |
..., 6Q4-2T | parallelly squobcu dissected pacratoh | ||
... | 6sishi (?) | 1 | |
... | 6tes (?) | 1 | |
... | general 7-2-stepprism | sqrt(A2+B2) | 7, 21, 28, 14 |
... | heptadiminished 2/10-luna of ex bidiminished inner pentadiminished 2/10-luna of ex | 35, 100, 89, 24 | |
8,n-dip | octagon - n-gonal duoprism | sqrt[(2+sqrt(2))/2+1/(4 sin2(π/n))] | 8n, 16n, 9n+8, n+8 |
... | triangular duoexpandoprism | sqrt[(a2+3b2)/3] | 36, 108, 120, 48 |
... | terminally edge-beveled hexadecachoron | 104, 256, 192, 40 | |
... | edge-beveled hexadecachoron | 168, 352, 224, 40 | |
... | tetracontoctachoron-derived Gévay polychoron | ... | 528, 2496, 2880, 912 |
afdec | antifrustic distetracontoctachoron | 1.414214 | 288, 1152, 816, 96 |
affic | antifrustary tetracontoctachoron | 1.414214 | |
affidhi | antifrustary dishecatonicosachoron | 2.236068 | |
affip | antifustric prismatochoron, compound of 16 hiddip | 1.414214 | |
affixthi | antifrustic hexacositrishecatonicosachoron | 2.236068 | 3600, 14400, 9120, 960 |
afpox (old: affopix) | antifustric prismatohexacosachoron, compound of 60 gippid | 2.236068 | |
... | aoc3ddd3cao *b3oca&#ze, general variant of prismatorhombisnub icositetrachoron | sqrt[(a2+ac+c2+2ad+2cd+2d2)/2] | 288, 1008, 960, 240 |
... | aoc3ooo3cao *b3oca&#zd | sqrt[(a2+ac+c2)/2] | 96, 432, 480, 144 |
apid (alt.: bamid) | antiprismatodecachoron, biambodecachoron, triangle based biambodecachoron | 0.774597 | 20, 90, 100, 30 |
arsdod depabdirox | around-symmetrical dodecadiminishing of deep parabidiminished rox | 3.077684 | 240, 780, 696, 156 |
arse aurap | around-symmetrically expanded augmented rectified pentachoron | 28, 84, 80, 24 | |
arse biscrahi | bistratic icosidodecahedron-first subsegment of small rhombihexacosachoron, around-symmetrically expanded biscrahi | 6.073594 | 240, 570, 414, 84 |
arspabd biscrox | around-symmetrically parabidiminished bistratic icosahedron-first cap of rectified hexacosachoron | 3.077684 | 80, 260, 234, 54 |
arsted biscrox | around-symmetrically tridiminished bistratic icosahedron-first cap of rectified hexacosachoron | 3.077684 | 69, 195, 165, 39 |
arsted diddidex | around-symmetrical tridiminishing of (axial) duo-disdodeca-icosa-diminished hexacosachoron | 1.618034 | 53, 129, 100, 24 |
aubautipip | augmented biaugmented-triangular-prism prism | 17, 50, 51, 18 | |
aurap | augmented rectified pentachoron | 11, 36, 42, 17 | |
auteddipe | augmented-tridiminished-icosahedron prism | ... | 20, 46, 38, 12 |
autepe | augmented tetrahedral prism | 9, 22, 23, 10 | |
autipip | augmented-triangular-prism prism | ... | 14, 33, 29, 10 |
autodip | augmented 3-8-duoprism | ... | 32, 76, 65, 21 |
autpen | augmented truncated pentachoron | ... | 26, 64, 56, 18 |
... | AxoFFxoox3oFFxofoxo xofofxFof3oxofxfoFf&#zx | 138, 549, 576, 165 | |
... | AxoFFxxo3oFFxofxx xofofxFo3oxofxfoF&#zx | 135, 531, 555, 159 | |
... | vertex figure of biprismatododecateron | 0.816497 | 9, 36, 42, 15 |
badhidy (old: buthi) | blendic dishecatonicosa-dishecatonicosachoron, compound of tigaghi and quit sishi | 2 | |
badohi | blendic dishecatonicosachoron | 2 | 2400, 8400, 6240, 240 |
bamic (old: apic) | biambotetracontoctachoron, antiprismatotetracontoctachoron, triangle based biambotetracontoctachoron | 1.732051 | 192, 864, 864, 192 |
baticot | bitruncated icositetrachoric tetracomb, small tetracontaoctachoric tetracomb | ||
batitit | bitruncated tesseractic tetracomb | ||
bauautipip | biaugmented augmented-triangular-prism prism | ... | 16, 49, 53, 20 |
baucubaike | bi-augmented cubaike | 22, 86, 116, 52 | |
baudeca | biaugmented decachoron | 38, 96, 84, 26 | |
bautipip | biaugmented-triangular-prism prism | 16, 42, 39, 13 | |
... | BAVFfxoo xFofxFVo3xxFxooxo5xooxFfoV&#zx | 980, 3120, 2780, 640 | |
... | vertex figure of biprismatointercepted dodecateron | 0.816497 | 9, 36, 45, 15 |
bhidtex | bi-hecatonicosidiminished truncated hexacosichoron | 4.643523 | 1200, 3600, 3240, 840 |
bichon (old: dubatch) | bicubical honeycomb, tetragonary disphenoidal honeycomb, bitruncated-cubical-honeycomb dual, Delone complex of body-centered cubic lattice A3* | ||
bicont (old: ducont) | bitetracontoctachoron, tetracontoctachoron dual, bi-apiculated icositetrachoron, tetradisphenoidal 288-cell | 1.306563 | 48, 336, 576, 288 |
bicypdex (alt.: bicypaugap) | bi-cyclopentadiminished hexacosachoron, bi-cyclopentaaugmented great antiprism | 1.618034 | 110, 600, 900, 410 |
bicypdrahi | (bistratic) bi-cyclopentadiminished rectified hecatonicosachoron | 4.534568 | 700, 1800, 1410, 310 |
bicypdrox | (bistratic) bi-cyclopentadiminished rectified hexacosachoron | 3.077684 | 300, 1000, 985, 285 |
bicyte ausodip | bicyclotetraugmented square-octagon duoprism | ... | 52, 176, 164, 40 |
bicyte gysrit | bicyclotetragyrated small rhombitesseract | 1.847759 | 96, 288, 264, 72 |
bideca (old: dudeca) | bidecachoron, decachoron dual, bi-apiculated pentachoron | 0.816497 | 10, 40, 60, 30 |
bidex | bi-icositetradiminished hexacosachoron | 1.618034 | 72, 216, 192, 48 |
bidoctaco, {4} || co, K-4.28 | square atop cuboctahedron, bidiminished octaco, square first rotunda of cytau tes | 1 | 16, 44, 43, 15 |
bidrap, K-4.8 | bidiminished rectified pentachoron, antiduowedge, square - tetrahedral wedge, digonal gyrobicupolaic ring, {4} || tet, line || ortho trip | 0.774597 | 8, 18, 17, 7 |
bidsid pixhi | bi-icositetra-diminished small disprismatohexacosihecatonicosachoron | 5.236068 | 1440, 3240, 2256, 456 |
bidsrip | bidiminished small rhombated pentachoron | 1.183216 | 24, 60, 51, 15 |
... | bilbiro wedge | ... | 16, 43, 42, 15 |
bimtec | bimesotruncatotetracontoctachoron | sqrt[3a2+4ab sqrt(2)+3b2] | 576, 1440, 1056, 192 |
bimted (old: bimtid) | bimesotruncatodecachoron | sqrt[(3a2+4ab+3b2)/5] | 60, 150, 120, 30 |
bipec | biprismatotetracontoctachoron | sqrt[a2+ab sqrt(2)+b2] | 288, 1296, 1536, 528 |
biped | biprismatodecachoron | sqrt[(2a2+ab+2b2)/5] | 40, 140, 160, 60 |
bipgy srit | bipara(bi)gyrated small rhombitesseract, pseudo cantellated tesseract | 1.847759 | 96, 288, 260, 68 |
birgax | bi-icositetra-replenished grand hexacosachoron | 0.618034 | 72, 216, 192, 48 |
biscex | bistratic vertex-first cap of hexacosachoron | 1.618034 | 33, 132, 182, 83 |
biscpoxic | bistratic vertex-first cap of poxic | 33, 92, 86, 27 | |
biscrahi | bistratic icosidodecahedron-first cap of rectified hecatonicosachoron | 4.534568 | 110, 270, 214, 54 |
biscrox | bistratic icosahedron-first cap of rectified hexacosachoron | 3.077684 | 102, 390, 372, 84 |
biscsrico | bistratic cuboctahedron-first cap of small rhombated icositetrachoron | 2.613126 | 84, 204, 156, 36 |
biscsrip | bistratic trip-cap of srip, {3}-diminished small rhombated pentachoron | 1.183216 | 27, 75, 66, 18 |
bitach | bitruncatocubic honeycomb, tegum sum of 2 inverted (x,y)-tichs | ||
bitapna | bitrigonal antiprismattic enenehexachoron, compound of 8 ico in rico army, compound of 2 kitapna | 1 | |
bitec (old: sidwapic) | bitruncatotetracontoctachoron, snub disphenic antiprismatotetracontoctachoron, general variant of hull of tastic, tegum sum of 2 inverted (x,y)-ticoes | sqrt(3y2+3y+1) | 384, 1920, 2592, 1056 |
bited (old: sidwapid) | bitruncatodecachoron, snub disphenic antiprismatodecachoron, general variant of hull of tisted, tegum sum of 2 inverted (x,y)-tips | sqrt[(3y2+3y+2)/5] | 40, 200, 280, 120 |
bitefa | bitegmic hecatontetracontatetrachoron, compound of 12 ico in spic army, compound of 2 kitefa | 1 | |
bithi | blendic trishecatonicosachoron | 2 | 2400, 8400, 5520, 360 |
bithit | bitruncated hexadecachoric tetracomb, bitruncated demitesseractic tetracomb, runcicantic tesseractic tetracomb | ||
... | bitruncated Witting polychoron, complex polychoron o3-3-x3-3-x3-3-o3 | 17280, 34560, 10800, 480 | |
... | bitruncated generalized Shephard tesseract, bitruncated generalized Shephard hexadecachoron, complex polychoron op-4-x2-3-x2-3-o2 | 12p3, 6p3(p+2), 2p2(2p2+2p+3), p(p3+4) | |
bricot | birectified icositetrachoric tetracomb, birectified demitesseractic tetracomb, runcic tesseractic tetracomb | ||
... | BxxFxfofx3oooxxxFFF3xBxfFxxof *b3xxBxfFfxo&#zx | 1152, 4176, 3984, 960 | |
... | vertex figure of cellibiprismatohexateron | 0.816497 | 9, 36, 48, 21 |
... | vertex figure of cellidishexateron | 0.816497 | 9, 36, 48, 15 |
cagoraht (old: gicaricot) | celligreatorhombated hexadecachoric tetracomb (great cellirhombated icositetrachoric tetracomb), stericantitruncated hexadecachoric tetracomb | ||
cagratit (old: gicartit) | celligreatorhombated tesseractic tetracomb (great cellirhombated tesseractic tetracomb), great rhombitesseractic-prismatotesseractic tetracomb, stericantitruncated tesseractic tetracomb | ||
cagricot (old: gicaroht) | celligreatorhombated icositetrachoric tetracomb (great cellirhombated hexadecachoric tetracomb), stericantitruncated icositetrachoric tetracomb | ||
capicot | celliprismated icositetrachoric tetracomb, great prismatotetracontaoctachoric tetracomb, steritruncated hexadecachoric tetracomb | ||
capirsit | celliprismatorhombisnub ico tetracomb | ||
capoht | celliprismated demitesseractic tetracomb, tomoicositetrachoric-diprismatotesseractic tetracomb, steritruncated icositetrachoric tetracomb | ||
capotat | celliprismated tesseractic tetracomb, tomotesseractic-diprismatotesseractic tetracomb, steritruncated tesseractic tetracomb | ||
capshot | celliprismatosnub hex tetracomb | ||
capsthat | celliprismatosnub truncated hex tetracomb | ||
captatit | celliprismatotruncated tesseractic tetracomb, great tomocubic-diprismatotesseractic tetracomb, steriruncitruncated tesseractic tetracomb | ||
capticot | celliprismatotruncated icositetrachoric tetracomb, celliprismatotruncated demitesseractic tetracomb, steriruncitruncated icositetrachoric tetracomb | ||
... | longer antiduowedge, vertex figure of cellirhombated dodecateron | 0.953463 | 8, 18, 17, 7 |
caricot (old: scaricot) | (small) cellirhombated icositetrachoric tetracomb, great disicositetrachoric tetracomb, stericantellated icositetrachoric tetracomb | ||
cartit (old: scartit) | (small) cellirhombated tesseractic tetracomb, small rhombitesseractic-prismatotesseractic tetracomb, stericantellated tesseractic tetracomb | ||
cesratit | octahedra-alternated faceting of scartit | ||
... | vertex figure of cellihemidodecateron | 0.866025 | 8, 24, 32, 12 |
chi | chirohecatonicosachoron, chiral compound of 5 ico | 1 | |
choatut | cubohemioctahedron atop truncated tetrahedron | 1.183216 | 24, 66, 54, 16 |
chont | hyperbolic (order 3) cubic-honeycomb tetracomb | 0.5 i | |
chope | cubohemioctahedron prism | 1.118034 | 24, 60, 44, 12 |
chopy, pt || cho | (degenerate) cubohemioctahedron pyramid | ∞ i.e. flat in euclidean space | 13, 36, 34, 11 |
... | augmented axially-octahedral ursachoron ofxo3xooo4oooo&#xt | ... | 25, 72, 70, 23 |
coaescu, co || escu, K-4.62 | cuboctahedron atop elongated square cupola | 1.447009 | 32, 100, 92, 24 |
coaop, co || op, K-4.63 | cuboctahedron atop octagonal-prism | 1.447009 | 28, 80, 72, 20 |
coasirco, co || sirco, K-4.61 | cuboctahedron atop small rhombicuboctahedron | 1.447009 | 36, 120, 112, 28 |
coatic, K-4.129 | cuboctahedron atop truncated cube, cuboctahedral cap of small rhombated icositetrachoron | 2.613126 | 36, 84, 64, 16 |
coaticbicu | coatic bicupola | 48, 132, 114, 30 | |
coatobcu | coatoe bicupola, equatorially contracted rectified icositetrachoron | 48, 132, 114, 30 | |
coatoe, co || toe, K-4.95 | cuboctahedron atop truncated octahedron, cuboctahedral cap of rectified icosatetrachoron | 1.732051 | 36, 84, 64, 16 |
coatotum | bistratic co-cap of prip, tut-diminished prip, Stott expansion of tip, (co,toe)-based tutsachoron, (co,toe)-based tutism | 1.612452 | 48, 108, 80, 20 |
coatut, co || tut, K-4.48 | cuboctahedron atop truncated tetrahedron, cuboctahedral cap of small rhombated pentachoron | 1.183216 | 24, 66, 58, 16 |
coatutu | expanded axially-tetrahedral ursachoron, (co,tut)-based ursulate | 1.328131 | 36, 90, 74, 20 |
cont | tetracontoctachoron, octagonny, bitruncated icositetrachoron | 3.414214 | 288, 576, 336, 48 |
contit | tetracontoctachoric tetracomb, lamina-truncate of hyperbolic o3x4x3o8o tesselation | 0.594604 i | |
cope, K-4.43 | cuboctahedron prism | 1.118034 | 24, 60, 52, 16 |
copy, pt || co | (degenerate) cuboctahedron pyramid | ∞ i.e. flat in euclidean space | 13, 36, 38, 15 |
coqroc | tetracontoctiquasirhombated tetracontoctachoron | 1.325654 | 1152, 2304, 1104, 96 |
cotcope | cuboctatruncated-cuboctahedron prism, cubitruncated-cuboctahedron prism | 1.414214 | 96, 192, 112, 22 |
croc | tetracontoctirhombated tetracontoctachoron | 3.200413 | 1152, 2304, 1104, 96 |
cubaco, cube || co, K-4.35 | cube atop cuboctahedron, cubical cupola | 1.031784 | 20, 60, 56, 16 |
cubaike, cube || ike, K-4.21 | cube atop icosahedron | 1 | 20, 66, 74, 28 |
cubasirco, cube || sirco, K-4.71 | cube atop small rhombicuboctahedron, cubical cap of small disprismatotesseractihexadecachoron | 1.485633 | 32, 84, 80, 28 |
cubatic, cube || tic | (degenerate) cube atop truncated cube | ∞ i.e. flat in euclidean space | 32, 72, 56, 16 |
... | pyrithohedral cube-doe-bilbiro honeycomb | ||
cubpy, K-4.26 | cubical pyramid, vertex-pyramid of ico | 1 | 9, 20, 18, 7 |
cuhsquah | cubihemisquare honeycomb, cell-alternated cubical honeycomb | ||
cute (old: cubdipy) | cubical (line-)tegum, cubical bipyramid | ... | 10, 28, 30, 12 |
cydadex | cyclical decadiminishing of ex | 1.618034 | 110, 610, 960, 460 |
cypit | cyclopentachoric tetracomb, pentachoric-dispentachoric tetracomb, Delone complex of lattice A4 | ||
cytau tes | cyclotetraaugmented tesseract, cyclotetradiminished icositetrachoron | 1 | 20, 64, 68, 24 |
cyte cubau sodip | cyclotetra cubaugmented sodip | ... | 36, 96, 84, 24 |
cyte gysrit | cyclotetragyrated small rhombitesseract | 1.847759 | 96, 288, 264, 72 |
cyte opau sodip | cyclotetra octagon-prism-augmented sodip | ... | 48, 144, 140, 44 |
cyted spic | cyclotetradiminished small prismatotetracontoctachoron | 1.847759 | 120, 432, 468, 156 |
cyted srit | cyclotetradiminished small rhombitesseract, cyclotetraugmented octagonal duoprism | 1.847759 | 80, 208, 172, 44 |
cythdex | cyclical triangularily-hexagonally diminished hexacosachoron | 1.618034 | 75, 306, 366, 135 |
cytid rico | cyclotridiminished rectified-icositetrachoron, metatridiminished rectified-icositetrachoron | 1.732051 | 60, 144, 111, 27 |
cytid srico | cyclotridiminished small rhombated icositetrachoron | 2.613126 | 180, 468, 369, 81 |
cytopit | cyclotruncated pentachoric tetracomb, small truncated-pentachoric tetracomb | ||
dahi | dishecatonicosachoron | 3 | 3600, 7200, 3840, 240 |
dahiquatady | dishecatonicosiquasitruncated dishecatonicosachoron | 4.134026 | 7200, 14400, 6000, 360 |
dahitady | dishecatonicositruncated dishecatonicosachoron | 2.431014 | 7200, 14400, 6000, 360 |
damibdrox | deep metabidiminished rectified hexacosachoron | 3.077684 | 312, 1270, 1245, 287 |
dapabdi poxic (alt.: hau sircope) | deep parabidiminished poxic, hexa-augmented sircope | 54, 168, 148, 34 | |
dapabdi spic | deep parabidiminished small prismatotetracontoctachoron, hexa-gyro-augmented truncated-cube prism | 1.847759 | 72, 216, 202, 58 |
dappip, K-4.96 | decagonal-antiprism prism | 1.747560 | 40, 100, 84, 24 |
dard tipady | diretroditetrahedronary prismatodishecatonicosachoron | 1.414214 | 600, 3600, 6480, 960 |
dastop | dodeca-star toroidi-prism | 0.707107 | 60, 240, 204, 36 |
... | dastop + 2 2did | 0.707107 | |
datap | ditetrahedronary prismatochoron, compound of 100 hiddip | 1.414214 | |
datcathi | ditetrahedronary coincidic trishecatonicosachoron | 1.414214 | 600, 7200, 5280, 360 |
dattady | ditetrahedronary dishecatonicosachoron | 1.414214 | 600, 3600, 2640, 240 |
dattathi | ditetrahedronary trishecatonicosachoron | 1.414214 | 600, 3600, 2880, 360 |
... | DCBAVFfxoo xxxFofxFVo3xoxxFxooxo5ofxooxFfoV&#zx | 1220, 3900, 3460, 780 | |
deca | decachoron, bitruncated pentachoron, equatorial cross-section of (vertex first) q-pent, equatorial cross-section of srip-first sibrid, equatorial cross-section of pen-first rin | 1.414214 | 30, 60, 40, 10 |
dedip (old: dadip) | decagon-decagon duoprism | 2.288246 | 100, 200, 120, 20 |
dexdap | dodecahedral extended double antiprism | 1.618034 | 100, 500, 720, 220 |
... | vertex figure of dodecabiprismatohemidodecateron | 0.866025 | 8, 24, 32, 12 |
... | did atop 3doe (?) | 1.414214 | |
dida raded, did || raded | dodecadodecahedron atop rhombidodecadodecahedron | 1.336349 | 90, 300, 258, 56 |
didadoe | did atop doe | 1.414214 | 50, 150, 126, 26 |
didamibdrox | diminished deep metabidiminished rectified hexacosachoron | 3.077684 | 270, 1020, 993, 243 |
diddatigid, did || tigid | dodecadodecahedron atop truncated great dodecahedron, did-first cap of sirfix | 4.352502 | 90, 210, 138, 26 |
diddip | dodecadodecahedron prism | 1.118034 | 60, 150, 108, 26 |
didhi | dodecahedronary dishecatonicosachoron | 1 | 120, 1200, 3120, 240 |
didpy, pt || did | (degenerate) did pyramid | ∞ i.e. flat in euclidean space | 31, 90, 84, 25 |
dihipap | dyad-hexagonal prismantiprismoid, s2s2s6x, edge-alternated sitwadip | ... | 24, 60, 58, 22 |
... | diminished 1/10-luna of hexacosachoron | 1.618034 | 30, 90, 93, 33 |
... | mono-diminished vertex-first rotunda of hexacosachoron | 1.618034 | 74, 372, 562, 264 |
... | diminished thawro-wedged 1/6-luna of hexacosachoron, {6},ike-wedge, ike,thawro,thawro-multiwedge | ... | 36, 138, 171, 69 |
dippit | disprismatotesseract | 1.485633 | 64, 192, 232, 64 |
diquitdi | disicositetraquasitruncated disicositetrachoron | 1.608038 | 576, 1440, 816, 96 |
dirico | diminished rectified icosatetrachoron | 1.732051 | 84, 240, 198, 42 |
disdi | disnub disicositetrachoron | 1 | 96, 816, 1248, 240 |
dispap | dyad-square prismantiprismoid, s2s2s4x, edge-alternated sodip | ... | 16, 40, 40, 16 |
distadedip | decagon-decagram duoprism | 1.732051 | 100, 200, 120, 20 |
disti | disnub tetrakisicositetrachoron | 1.618034 | |
ditdap | digon-triangle duoantiprism, hemiated shiddip | sqrt[A2/2+B2] | 12, 42, 52, 22 |
ditdi | disicositetratruncated disicositetrachoron | 2.326846 | 576, 1440, 816, 96 |
ditdidap | ditrigonary-dodecadodecahedron antiprism | 0.951057 | 40, 180, 168, 26 |
ditdiddip | ditrigonal-dodecadodecahedron prism | 1 | 40, 140, 108, 26 |
ditdidpy | ditdid pyramid, vertex pyramid of dittady | 1 | 21, 80, 84, 25 |
dithix | ditrigonary hecatonicosihexacosichoron | 1.732051 | 1200, 7200, 7440, 720 |
dittadphi | ditetrahedronary disprismatohecatonicosachoron | 1.414214 | 600, 3600, 6480, 1560 |
dittady | ditrigonary dishecatonicosachoron | 1 | 120, 1200, 2400, 240 |
... | dittady+dox (?) | 1 | |
dittafady | ditetrahedrofissary dishecatonicosachoron | 1.414214 | 600, 3600, 4080, 240 |
ditusna | disicosahedronary tetrasnubbachoron, compound of 20 ex in rahi army, compound of 2 kidisna | 1.618034 | |
... | Waterman polychoron number 5 wrt. alternated tessic lattice D4 centered at a hole | 2.121320 | 104, 384, 408, 128 |
doa pabidrid, doe || pabidrid, K-4.155 | dodecahedron atop parabidiminished rhombicosidodecahedron | 5.236068 | 70, 170, 144, 44 |
doaid, doe || id, K-4.77 | dodecahedron atop icosidodecahedron, dodecahedral cupola | 1.618034 | 50, 150, 134, 34 |
doasrid, doe || srid, K-4.152 | dodecahedron atop small rhombicosidodecahedron, dodecahedral cap of small disprismatohexacosihecatonicosachoron | 5.236068 | 80, 210, 194, 64 |
doasridaid | doe atop srid atop id | 110, 390, 406, 126 | |
doc | distetracontoctachoron | 2.449490 | 1152, 2304, 1248, 96 |
dod honho | disoctidishemioctintercepted hemioctachoron | 1 | 24, 96, 128, 28 |
... | rico-derived polychoron incorporating does | 2.802517 | 384, 1008, 768, 144 |
..., doe || 6-dim-id || f-ike || doe | axially-pyritohedral (2,24,12,6)-diminishing of ex | 1.618034 | 76, 300, 356, 132 |
doh honho | disoctihemihexadekintercepted hemioctachoron | 1 | 24, 96, 136, 28 |
dohitipady | dishecatonicositruncated prismatodishecatonicosachoron | 4.472136 | 14400, 28800, 14880, 1560 |
dope, K-4.74 | dodecahedron prism | 1.487792 | 40, 80, 54, 14 |
... | toroidally parabideepened dope, when drilled by two ikadoes | ... | 44, 222, 322, 144 |
dopix | dodecahedronary prismatohexacosachoron, compound of 60 spid | 1 | |
dox (old: gex) | dodecahedronary hexacosachoron (great hexacosachoron), compound of 25 ico | 1 | |
duhd | decahemidecachoron, copyropodichoron | 1 | 20, 60, 50, 15 |
dusidpith | small-prismated-tesseractihexadecachoron dual, triangular antitegmatic hexacontatetrachoron | 80, 208, 192, 64 | |
duspid | small-prismated-decachoron dual, triangular antitegmatic icosachoron, crystalic icosachoron | 30, 70, 60, 20 | |
dutip | truncated-pentachoron dual, apiculated pentachoron, tetrakis pentachoron | 10, 30, 40, 20 | |
dygytpuf, K-4.13 | dyadic gyrotegmipucofastegium, 3-prism atop reflected ortho 3-prism | 0.866025 | 12, 30, 30, 12 |
ebdah hithi | exoblendic dishemihecatonicostrishecatonicosachoron | 2 | |
ebuthi | exotic blendic tetrishecatonicosachoron | 2 | |
ecubedpy | elongated cubical bipyramid, hexadiminished icositetrachoron | 1 | 18, 48, 48, 18 |
ecubpy | elongated cubical pyramid, heptadiminished icositetrachoron | 1 | 17, 40, 36, 13 |
efdit xithi | exofissary ditrigonal hexacositrishecatonicosachoron | 1.732051 | |
eikedpy | elongated icosahedral bipyramid | 26, 96, 130, 60 | |
eikepy | elongated icosahedral pyramid | 25, 84, 100, 41 | |
eocta sirco | elongated octasirco | ... | 54, 156, 156, 54 |
eoctaco | elongated octaco | 30, 96, 90, 24 | |
eoctatut | elongated octatut | 30, 72, 60, 18 | |
eoctpy | elongated octahedral pyramid, diminished pex hex | 13, 36, 40, 17 | |
epipdapy | elongated pentagonal-prismatic bipyramid | ... | 22, 60, 59, 21 |
epippy | elongated pentagonal-prismatic pyramid | ... | 21, 50, 44, 15 |
escupe, K-4.68 | elongated-square-cupola prism | 1.485633 | 40, 92, 72, 20 |
esircoatic | elongated sircoatic, diminished srit | 72, 192, 156, 36 | |
esquidpyp | elongated square dipyramid prism, J15 prism | ... | 20, 50, 44, 14 |
esquippidpy | elongated square-pyramidal bipyramid, esquidpy-wedge, half of partially (mono-)expanded hex | 12, 31, 32, 13 | |
esquipuf | elongated square pucofastegium, square atop octagon-prism atop octagon-prism | 36, 84, 69, 21 | |
esquipyp | elongated square-pyramidal-prism, elongated-square-pyramid prism, external blend of square-pyramidal prism and tesseract | 18, 41, 34, 11 | |
etedpy | elongated tetrahedral bipyramid | 10, 24, 26, 12 | |
etepe | elongated tetrahedral-prism, elongated-triangular-pyramid prism, external blend of tetrahedral prism and (triangle,square)-duoprism | 14, 31, 26, 9 | |
etepy | elongated tetrahedral pyramid | 9, 20, 20, 9 | |
etetaco | elongated tetaco | ... | 28, 78, 80, 30 |
etripdapy | elongated trigonal-prismatic bipyramid | ... | 14, 36, 37, 15 |
etrippy | elongated trigonal-prismatic pyramid | ... | 13, 30, 28, 11 |
etripuf | elongated trigonal pucofastegium | ... | 27, 63, 53, 17 |
etutatoe | elongated tutatoe | ... | 60, 138, 108, 30 |
... | ex+fix (?) | 1.618034 | |
... | ex+gohi+120id (?) | 1.618034 | |
ex, pT | hexacosachoron, 600-cell, hydrochoron, tetraplex, polytetrahedron | 1.618034 | 120, 720, 1200, 600 |
... | f x3o3o, variation of tetrahedron prism, vertex figure of rectified hyperbolic hecatonicosachoric honeycomb | 1.014647 | 8, 16, 14, 6 |
... | FAxoAFxoxx3FxAAoxFxox oxofofxFof3ooxofxfoFf&#zx | 186, 612, 600, 174 | |
... | FAxoFFxoox3foFFxofoxo oxofofxFof3ooxofxfoFf&#zx | 144, 603, 648, 189 | |
... | FAxoFFxxo3foFFxofxx oxofofxFo3ooxofxfoF&#zx | 141, 585, 609, 183 | |
... | FAxoFFxxox3foFFxofxxo oxofofxFof3ooxofxfoFf&#zx | 159, 729, 849, 279 | |
... | FAxoFFxxox3foFFxofxxo xoxFxFoAxF3oxxofxFoFf&#zx | 198, 702, 705, 201 | |
... | vertex figure of facetospinopenteractidishexadecateron | 0.919866 | 10, 33, 34, 11 |
... | Ffxo oxFx3xfox5xoxx&#zx | 480, 1560, 1518, 438 | |
... | Ffxo xofo3ofox5xoxx&#zx | 360, 1470, 1608, 498 | |
... | vertex figure of facetoinverted decahexadecateron | 0.919866 | 10, 45, 45, 10 |
firgaghi | faceted rectified great grand hecatonicosachoron | 1.070466 | 1200, 3600, 2640, 240 |
firgogishi | facetorectified great grand stellated hecatonicosachoron | 0.661585 | 1200, 3600, 3120, 720 |
firp | faceted rectified pentachoron, retropyrohemiperichoron, vertex figure of dah, tetrahedral cuploid | 0.774597 | 10, 30, 35, 15 |
... | firp+rap+15{4} (?) | 0.774597 | |
firsashi | faceted rectified small stellated hecatonicosachoron | 2.802517 | 1200, 3600, 2640, 240 |
firt | facetorectified tesseract | 1.224745 | 32, 96, 96, 32 |
fitetaltet | faceted tet atop dual 3tet, vertex figure of phap | 0.707107 | 8, 24, 26, 10 |
fitetaoct | faceted 3tet atop oct | 0.774597 | 10, 30, 30, 10 |
... | fix+gahi+120id (?) | 1.618034 | |
fix, pI | icosahedral hecatonicosachoron, faceted hexacosichoron, polyicosahedron | 1.618034 | 120, 720, 1200, 120 |
... | fooo3xxoF3xfxo *b3oxFo&#zx | 248, 816, 784, 216 | |
... | triacontapenta-diminished hexacosachoron, fooo5ofxo xofx5oxox&#zx | 1.618034 | 85, 335, 360, 110 |
frico | facetorectified icositetrachoron | 1.732051 | 96, 288, 240, 48 |
frogfix | faceted rectified great faceted hexacosichoron | 0.726543 | 720, 3600, 4320, 720 |
froghi | facetorectified great hecatonicosachoron | 1.902113 | 720, 3600, 4320, 720 |
frogshi | facetorectified great stellated hecatonicosachoron | 1.175571 | 720, 3600, 2880, 240 |
frox | faceted rectified hexacosichoron | 3.077684 | 720, 3600, 4440, 840 |
... | frox+600 2thah (?) | 3.077684 | |
fry | facetorectified hecatonicosachoron | 4.534568 | 1200, 3600, 3120, 720 |
... | FxFox5xFoFx xofox5oxofx&#zx | 250, 750, 630, 130 | |
... | dodeca-diminished equatorial tetrastratic segment of rox | 3.077684 | 300, 1140, 1128, 288 |
... | Fxo oxf3xox5xfo&zxt | 300, 900, 776, 176 | |
... | equatorial tetrastratic segment of rectified hexacosachoron | 3.077684 | 312, 1260, 1248, 300 |
... | Fxox3xoxf3oFxx *b3oxfo&#zx | 336, 1200, 1176, 312 | |
... | Fxxox5ofxfo xofox5oxofx&#zx | 200, 850, 950, 300 | |
... | Fxxx3xxoF3xfxo *b3oxFo&#zx | 432, 1320, 1200, 312 | |
... | Fxxx5ofxo xofx5oxox&#zx | 175, 600, 625, 200 | |
gabbadipady | great blendic disprismatodishecatonicosachoron | 2 | 2400, 8400, 7200, 1680 |
gabbathi | great blendic trishecatonicosachoron | 2 | 2400, 8400, 4800, 360 |
... | vertex figure of great biprismatodiscellipenteract | 1.118034 | 8, 28, 38, 18 |
gabippady (old: gabbippady) | great blendic prismatodishecatonicosachoron | 2 | 2400, 8400, 7200, 960 |
gabred | great birhombatodecachoron | sqrt[(2a2+2ab+3b2)/5] | 60, 300, 360, 120 |
gabric | great birhombatotetracontoctachoron | sqrt[a2 + 2 sqrt(2) ab + 3b2] | 576, 2880, 3360, 1056 |
gacdupthix | small capped dipentary tetrishecatonicosahexacosichoron | 1.328131 | 1440, 7200, 9600, 1080 |
gacicot (old: otit) | great cellated icositetrachoric tetracomb, omnitruncated icositetrachoric tetracomb | ||
gacotat (old: otatit) | great cellated tesseractic tetracomb, omnitruncated tesseractic tetracomb | ||
gad phiddix | great dipentary hecatonicosadishexacosachoron | 1.328131 | 1440, 7200, 7200, 1320 |
gadadoe | great dodecahedron atop dodecahedron | 1.618034 | 32, 120, 142, 44 |
gadatady | grand ditetrahedral dishecatonicosachoron | 0.874032 | 600, 3600, 2160, 240 |
gadathiphi | grand ditetrahedronary hecatonicosaprismatohecatonicosachoron | 0.874032 | 600, 7200, 7440, 1440 |
... | gadathiphi+600 2tet (?) | 0.874032 | |
gaddadid, gad || did | great dodecahedron atop dodecadodecahedron, great-dodecahedral cupola | 1.064815 | |
gaddaraded, gad || raded | great dodecahedron atop rhombidodecadodecahedron, gad-first cap of quipdohi | 1.328131 | |
gaddatigid, gad || tigid | (degenerate) gad atop tigid | ∞ i.e. flat in euclidean space | |
gaddiddip | great-dodekicosidodecahedron prism | 0.874032 | 120, 300, 208, 46 |
gaddip | great-dodecahedron prism | 1.074481 | 24, 72, 54, 14 |
gaddit thix | grand ditrigonal trishecatonicosihexacosachoron | 1.732051 | 1200, 7200, 10440, 960 |
... | vertex figure of great dispinocellirhombated penteract | 0.907821 | 8, 22, 24, 10 |
gadixady | great dishexacosadishecatonicosachoron | 3.139124 | 2400, 7200, 6240, 1440 |
gadixhix (old: gixhix) | great dodecahedronary hexacosahemihexacosachoron, compound of 25 ihi (but not sadixhix) | 1 | |
gadpy | great-dodecahedral pyramid, vertex cap of fix | 1.618034 | 13, 42, 42, 13 |
gadsadox | great disnub dihexacosachoron | 0.726543 | 3600, 28800, 31200, 6000 |
gadtap | great ditetrahedronary prismatochoron, compound of 36 stadidip | 0.874032 | |
gadtaxady | grand ditetrahedronary hexacosadishecatonicosachoron | 0.874032 | 600, 3600, 3840, 840 |
gadtaxhi | great ditetrahedronary hexacosihecatonicosachoron | 0.874032 | 600, 3600, 3120, 720 |
gadtef pixady | great ditetrahedronary exofissary prismatohexacosadishecatonicosachoron | 0.874032 | 2400, 10800, 9840, 2040 |
gadtifady (old: gadtafady) | great ditetrahedronarofissary dishecatonicosachoron | 0.874032 | 600, 3600, 4560, 240 |
gaedit pathi | grand exoditetrahedronary prismatotriakishecatonicosachoron | 0.874032 | 2400, 10800, 8880, 1080 |
gafthi | great antifrustary trishecatonicosachoron | 2.236068 | 3600, 14400, 8880, 360 |
... | vertex figure of great facetosphenary penteract | 0.776106 | 8, 24, 32, 16 |
... | gaghi+didhi (?) | 1 | |
... | gaghi+idhi (?) | 1 | |
... | gaghi+paphacki+sridaphi (?) | 1 | |
... | gaghi+sridixhi (?) | 1 | |
gaghi, gapD | great grand hecatonicosachoron, greatened aggrandized polydodecahedron | 1 | 120, 1200, 720, 120 |
gahfipto | great hexadecafeceted prismatotesseractioctachoron | 0.890446 | 64, 192, 208, 48 |
... | gahi+gohi (?) | 1.618034 | |
gahi, apD | grand hecatonicosachoron, aggrandized polydodecahedron | 1.618034 | 120, 720, 720, 120 |
gaid tathi | grand inverted ditetrahedronary trishecatonicosachoron | 0.874032 | |
ganbathi | great spinoblendic trishecatonicosachoron | 2 | 2400, 8400, 6480, 960 |
ganbippady | great spinoblendic prismatodishecatonicosachoron | 2 | 2400, 8400, 6960, 960 |
... | vertex figure of great spinocelliprismated penteract | 0.920055 | 7, 18, 19, 8 |
gap | great antiprism, grand antiprism, pentagonal double antiprismoid (but not: great duoantiprism), bicyclical decadiminishing of ex | 1.618034 | 100, 500, 720, 320 |
... | pentagonal double antitegmoid, pentaantitegmatoswirlic hectochoron, dual of great antiprism | ... | 320, 720, 500, 100 |
gapript | great pseudorhombated prismatotesseract | 0.765367 | 96, 288, 256, 64 |
... | gapript+16 2thah (?) | 0.765367 | |
gapthi | grand prismatotriakishecatonicosachoron | 2.400819 | 7200, 18000, 10320, 1080 |
gaqri | great quasirhombated icositetrachoron | 1.230739 | 576, 1152, 720, 144 |
gaqrigafix | great quasirhombated great faceted hexacosachoron | 1.080363 | 7200, 14400, 7680, 960 |
gaqrigaghi | great quasirhombated great grand hecatonicosachoron | 1.679184 | 7200, 14400, 8160, 1440 |
gaqrigagishi | great quasirhombated great grand stellated hecatonicosachoron | 1.179024 | 7200, 14400, 9120, 1920 |
gaqrigashi | great quasirhombated great stellated hecatonicosachoron | 2.700333 | 7200, 14400, 8160, 960 |
gaqrigohi | great quasirhombated great hecatonicosachoron | 2 | |
gaqript | grand quasirhombated prismatotesseract | 0.765367 | 96, 288, 192, 32 |
gaqrisashi | great quasirhombated small stellated hecatonicosachoron | 5.018002 | 7200, 14400, 8160, 1440 |
gaqrit | great quasirhombated tesseract | 1.401594 | 192, 384, 248, 56 |
gaquapac | great quasiprismatotetracontoctachoron | 1.127864 | 1152, 2304, 1392, 240 |
gaquatiddip | great-quasitruncated-icosidodecahedron prism | 1.136572 | 240, 480, 304, 64 |
gaquidapixhi | great quasidisprismatohexacosihecatonicosachoron | 1.581630 | 14400, 28800, 17040, 2640 |
gaquidipdy | grand quasidisprismatodishecatonicosachoron | 1.695697 | 14400, 28800, 16080, 2160 |
gaquidphihi | great quasidisprismatohecatonicosihecatonicosachoron | 4.242641 | 14400, 28800, 16080, 1680 |
gaquidpoth | great quasidisprismatotesseractihexadecachoron | 1.938391 | 384, 768, 464, 80 |
gaquipadah | great quasiprismatodishexadecachoron | 0.890446 | 64, 192, 200, 72 |
garawv hixhi | great retrosphenoverted hecatonicosihexacosihecatonicosachoron | 1.054256 | 3600, 10800, 7440, 840 |
gard tadhix | grand retroditetrahedronary dishecatonicosihexacosachoron | 0.874032 | 600, 3600, 5280, 840 |
gardatady | grand retroditetrahedral dishecatonicosachoron | 0.874032 | 600, 3600, 3840, 240 |
... | gardatady+1440{5} | 0.874032 | |
gardatathi | grand retroditetrahedronary trishecatonicosachoron | 0.874032 | 600, 3600, 5280, 360 |
gardtapaxhi | grand retroditetrahedronary hexacosidishecatonicosachoron | 0.874032 | 600, 3600, 7440, 1440 |
gardtaxady | grand retroditetrahedronary hexacosidishecatonicosachoron | 0.874032 | 600, 3600, 3840, 840 |
garpit | grand rhombated dishexadecachoron | 1.847759 | 96, 288, 192, 32 |
garpop | grand rhombated prismatopentachoron | 1.183216 | 30, 90, 65, 15 |
gashi, aspD | grand stellated hecatonicosachoron, aggrandized stellated polydodecahedron | 0.618034 | 120, 720, 720, 120 |
... | vertex figure of great pteroprismated penteract | 0.837186 | 9, 24, 24, 9 |
... | gax+gashi+120gid (?) | 0.618034 | |
... | gax+gofix (?) | 0.618034 | |
gax, apT | grand hexacosachoron, aggrandized polytetrahedron | 0.618034 | 120, 720, 1200, 600 |
geedatepthi | great exoditetrahedrary prismatotrishecatonicosachoron | 1.414214 | 2400, 10800, 7920, 1080 |
gefdit dixdy | great exofissary ditrigonal dihexacosadihecatonicosachoron | 1.732051 | 3600, 14400, 11040, 1440 |
gefidtethi | great exofissary ditetrahedronary tetrakishecatonicosachoron | 0.874032 | 2400, 10800, 6720, 480 |
gefirdit xethi | great exofissary retroditetrahedronary hexacositrishecatonicosachoron | 1.414214 | 2400, 10800, 7680, 960 |
gefradit thix | great exofissary retroditetrahedronary triakishecatonicosihexacosachoron | 0.874032 | 2400, 10800, 6720, 960 |
gefridit xethi | great exofissary retroinverted ditetrahedronary hexacositrishecatonicosachoron | 1.414214 | 2400, 10800, 7680, 960 |
geihiddip | great-icosihemidodecahedron prism | 0.794963 | 60, 150, 112, 28 |
getatixady | great tritrigonary hexacosidishecatonicosachoron | 1.136572 | 2400, 10800, 9840, 840 |
getit dixady | great tritrigonal dihexacosidihecatonicosachoron | 1.136572 | 2400, 10800, 8640, 1440 |
getit phiddix | great tritrigonal prismatohecatonicosidishexacosachoron | 1.136572 | 2400, 10800, 9840, 2040 |
getit pixady | great tritrigonal prismatohexacosidihecatonicosachoron | 1.136572 | 2400, 10800, 8880, 1560 |
getit thix | great tritrigonal trishecatonicosihexacosachoron | 1.136572 | 2400, 10800, 7680, 960 |
getit xethi | great tritrigonal hexacositrishecatonicosachoron | 1.136572 | 2400, 10800, 7680, 960 |
getut | great tristetracosioctacontachoron | 1 | 120, 1200, 3840, 1440 |
ghahoh | great hexadecahemihexadecachoron | 1 | 24, 96, 112, 24 |
ghihi | great hecatonicosihecatonicosachoron | 0.854102 | 3600, 7200, 3360, 240 |
ghipady | great hecatonicosiprismatodishecatonicosachoron | 4.087567 | 7200, 18000, 11280, 1080 |
gibricot | great birhombated icositetrachoric tetracomb, great grand prismatodisicositetrachoric tetracomb | ||
gic | great tetracontoctachoron, octagrammy | 0.585786 | 288, 576, 336, 48 |
gichado | great cubihexadecadisoctachoron | 1.174172 | 192, 480, 320, 56 |
gico | great icositetrachoron, stella prismata, compound of 3 tes | 1 | |
... | gico+8co+16 2thah (?) | 1 | |
gid thipady | great ditrigonary hecatonicosiprismatodishecatonicosachoron | 4.087567 | 7200, 18000, 10320, 1080 |
gid tipathi | great ditrigonal prismatotriakishecatonicosachoron | 2.920251 | 7200, 18000, 11280, 1560 |
gidard tipady | great diretroditetrahedronary prismatodishecatonicosachoron | 1.414214 | 600, 3600, 6480, 960 |
giddatady | great ditetrahedronary dishecatonicosachoron | 1.414214 | 600, 3600, 2640, 240 |
giddic | great distetracontoctachoron | 0.765367 | 144, 576, 528, 96 |
giddip | great-icosidodecahedron prism | 0.794963 | 60, 150, 124, 34 |
giddit thix | great ditrigonal trishecatonicosihexacosachoron | 1.732051 | 1200, 7200, 9360, 960 |
gidditdid aidtid | great ditrigonary dodekicosidodecahedron atop icosidodecatruncated icosidodecahedron | 4.684471 | 180, 840, 268, 46 |
gidditdiddip | great-ditrigonary-dodekicosidodecahedron prism | 1.239546 | 120, 300, 208, 46 |
gidditdy | great ditrigonary dishecatonicosachoron | 1.732051 | 1200, 7200, 4560, 240 |
gidditpix | great ditrigonary prismatohexacosichoron | 1.732051 | 1200, 7200, 8520, 1320 |
gidhiddip | great-dodecahemidodecahedron prism | 0.794963 | 60, 150, 96, 20 |
gidhiquit paddy | great dishecatonicosaquasitruncated prismatodishecatonicosachoron | 2.140933 | 14400, 28800, 13920, 1080 |
gidipthi | great dipental trishecatonicosachoron | 1.328131 | 1440, 7200, 4560, 360 |
gidpith | great disprismatotesseractihexadecachoron, great prismated tesseract, omnitruncated tesseract | 3.498949 | 384, 768, 464, 80 |
gidpixathi | great dipentagonal hexacositrihecatonicosachoron | 1.328131 | 1440, 7200, 6240, 960 |
gidpixhi | great disprismatohexacosihecatonicosachoron, omnitruncated hecatonicosachoron, omnitruncated hexacosachoron | 12.786651 | 14400, 28800, 17040, 2640 |
gidriddip | great-dirhombicosidodecahedron prism, great-snub-disicosidisdodecahedron prism, prism of Miller's monster | 0.866025 | 120, 540, 488, 126 |
gidthidy hi | great ditrigonal hecatonicosadishecatonicosihecatonicosachoron | 1.732051 | 1200, 7200, 8400, 480 |
gidthixhi | great ditrigonary hecatonicosihexacosihecatonicosachoron | 3.139124 | 2400, 7200, 4560, 840 |
gidtidagiid | great ditrigonary icosidodecahedron atop great icosicosidodecahedron, gidtid cap of getit phiddix | 1.136572 | 80, 240, 204, 54 |
gidtidap | great-ditrigonary-icosidodecahedron antiprism | 0.951057 | 40, 180, 184, 54 |
gidtiddip | great-ditrigonary-icosidodecahedron prism | 1 | 40, 140, 124, 34 |
gidtidpy | gidtid pyramid, vertex pyramid of gidtixhi | 1 | 21, 80, 92, 33 |
gidtixhi | great ditrigonary hexacosihecatonicosachoron | 1 | 120, 1200, 2400, 720 |
... | gidtixhi+dox (?) | 1 | |
gifdahihox | great fissary dodecahedronary hecatonicosihemihexacosachoron | 1 | 120, 1200, 3000, 420 |
giidip | great-icosicosidodecahedron prism | 1.239546 | 120, 300, 224, 54 |
gik vadixady | great skewverted dishexacosidishecatonicosachoron | 2.013884 | 7200, 21600, 14640, 1440 |
gik vipathi | great skewverted prismatotriakishecatonicosachoron | 2.828427 | 7200, 21600, 13920, 1080 |
gik vixathi | great skewverted hexacositriakishecatonicosachoro | 2.013884 | 7200, 21600, 13680, 960 |
gikagid, gike || gid | great icosahedron atop great icosidodecahedron, great icosahedral cap of rectified grand hexacosachoron, great-icosahedral cupola | 0.726543 | |
gikaike | great icosahedron atop icosahedron | 1 | 24, 120, 160, 52 |
gikepy | great-icosahedral pyramid, vertex cap of gax | 0.618034 | 13, 42, 50, 21 |
gikkiv datapixady | great skewverted ditrigonary prismatohexacosadishecatonicosachoron | 2.013884 | 7200, 21600, 14880, 1560 |
giku | gike-based ursachoron | 0.965407 | 54, 162, 144, 34 |
gikviphado | great skewverted prismatohexadecadisoctachoron | 1.414214 | 192, 576, 416, 56 |
gipaht | great prismated demitesseractic tetracomb, runcicantitruncated hexadecachoric tetracomb | ||
... | vertex figure of great prismated biprismatopenteract | 0.837186 | 9, 36, 48, 21 |
gipdohiny | great pental dishecatonicosaintercepted hecatonicosachoron | 0.726543 | 720, 3600, 6360, 360 |
gipe | great-icosahedron prism | 0.771681 | 24, 72, 70, 22 |
giphado | great prismatohexadecadisoctachoron | 1.082392 | 192, 480, 336, 64 |
giphatit | great prismated demitesseractic tetracomb, great diprismatodemitesseractic tetracomb, steriruncicantic tesseractic tetracomb | ||
giphiddix | great prismatohecatonicosadishexacosachoron | 1.624598 | 7200, 18000, 12240, 2040 |
giphidy | great prismated hecatonicosadishecatonicosachoron | 1.348948 | 7200, 18000, 10320, 1080 |
giphihix | great prismatohecatonicosahecatonicosahexacosachoron | 1.893038 | 7200, 18000, 11280, 1560 |
giphixhi | great prismatohecatonicosihexacosihecatonicosachoron | 2.920251 | 7200, 18000, 12240, 2040 |
gippapivady | great pentagrammal antiprismatoverted dishecatonicosachoron | 0.726543 | 720, 3600, 3120, 240 |
gippic | great prismatotetracontoctachoron, omnitruncated icositetrachoron | 5.169905 | 1152, 2304, 1392, 240 |
gippict | great prismated icositetrachoric tetracomb, runcicantitruncated icositetrachoric tetracomb | ||
gippid | great prismatodecachoron, omnitruncated pentachoron, Voronoi cell of lattice A4*, permutochoron of 5 elements | 2.236068 | 120, 240, 150, 30 |
gippittit | great prismated tesseractic tetracomb, great diprismatotesseractic tetracomb, runcicantitruncated tesseractic tetracomb | ||
gippixady | great prismatohexacosadishecatonicosachoron | 1.207883 | 7200, 18000, 11280, 1560 |
gippixhihy | great prismatohexacosihecatonicosihecatonicosachoron | 1.021064 | 7200, 18000, 12240, 2040 |
giprapivady | great pentagonal retroprismatoverted dishecatonicosachoron | 1.902113 | 720, 3600, 2160, 240 |
gipriphi | great pseudorhombated prismatohecatonicosachoron | 0.799575 | 3600, 10800, 9240, 2040 |
... | gipriphi+600 2thah (?) | 0.799575 | |
gipthi | great prismatotriakishecatonicosachoron | 3.531591 | 7200, 18000, 10320, 1560 |
gipti | great prismatotriakisicositetrachoron | 1.938391 | 576, 1440, 960, 168 |
giqragashi | great quasirhombated grand stellated hecatonicosachoron | 2 | |
girc | great retrotetracontoctachoron | 0.765367 | 144, 576, 432, 48 |
gircope, K-4.125 | great-rhombicuboctahedron prism | 2.370932 | 96, 192, 124, 28 |
girdip | great-rhombidodecahedron prism | 0.874032 | 120, 300, 204, 44 |
girdo | great rhombic disoctachoron | 0.765367 | 96, 288, 208, 48 |
girfaddic | great retrofrustic distetracontoctachoron | 1.414214 | 288, 1152, 816, 96 |
girfix | great rhombated faceted hexacosachoron | 7.404918 | 7200, 14400, 7680, 960 |
girfixady | great retrofrustary hexacosidishecatonicosachoron | 2.236068 | 3600, 14400, 11040, 840 |
girfixthi | great retrofrustic hexacositrishecatonicosachoron | 2.236068 | 3600, 14400, 10080, 960 |
girfthi | great retrofrustary trishecatonicosachoron | 2.236068 | 3600, 14400, 7680, 360 |
girpdi | great rhombiprismic disicosatetrachoron | 1.938391 | 576, 1440, 912, 144 |
girpdo | great rhombiprismatodisoctachoron | 1.174172 | 192, 480, 304, 48 |
girpith | great rhombiprismated tesseractihexadecachoron | 1.082392 | 192, 480, 304, 48 |
girpixhi | great rhombiprismic hexacosahecatonicosachoron | 1.021064 | 7200, 18000, 11040, 1440 |
girsiddip | great-(inverted)-retrosnub-icosidodecahedron prism | 120, 360, 334, 94 | |
gisdiddip | great-snub-dodekicosidodecahedron prism | 120, 420, 388, 106 | |
gisdipthi | great stellated dipental trishecatonicosachoron | 1.328131 | 1440, 7200, 4560, 360 |
... | gishi+gashi (?) | 0.618034 | |
gishi, gspD | great stellated hecatonicosachoron, greatened stellated polydodecahedron | 0.618034 | 120, 720, 720, 120 |
gisiddip | great-inverted-snub-icosidodecahedron prism | 120, 360, 334, 94 | |
gisp | great swirlprism | 0.618034 | 120, 720, 720, 120 |
... | taller great stellated dodecahedron atop small stellated dodecahedron | 0.662791 | 32, 120, 142, 44 |
gissidagid, gissid || gid | great stellated dodecahedron atop great icosidodecahedron, great stellated dodecahedral cupola | 0.692924 | 50, 150, 134, 34 |
gissidagike | great stellated dodecahedron antiprism, great icosahedron antiprism, taller great stellated dodecahedron atop great icosahedron | 0.662791 | 32, 120, 152, 64 |
gissidasissid | shallower great stellated dodecahedron atop small stellated dodecahedron | 0.618034 | 32, 120, 142, 44 |
gissiddip | great-stellated-dodecahedron prism | 0.732444 | 40, 80, 54, 14 |
gissidpy | great-stellated-dodecahedral pyramid, vertex cap of gaghi | 0.591923 | 21, 50, 42, 13 |
gissidragike | great stellated dodecahedron retroprism, great icosahedron retroprism, narrower great stellated dodecahedron atop great icosahedron | 0.618034 | 32, 120, 152, 64 |
gistic | great stellated icositetrachoron, compound of 6 tes, compound of 2 gico | 1 | |
git thixady | great tritrigonal hecatonicosihexacosidishecatonicosachoron | 1.136572 | 2400, 10800, 7680, 960 |
gitphi | great tripesic hecatonicosachoron | 0.874032 | |
gitpodady | great (intersected) tripesic dodecahedronary dishecatonicosachoron | 1 | 120, 3600, 3120, 240 |
gittifcoth | great tesseractifaceted cubitesseractihexadecachoron | 0.890446 | 64, 192, 208, 48 |
gittith | great tesseractitesseractihexadecachoron | 0.890446 | 64, 192, 136, 32 |
gixathi | great hexacositriakishecatonicosachoron | 3.804226 | 7200, 18000, 11280, 960 |
gixhi | great hexacosihecatonicosachoron | 1.244649 | 3600, 7200, 4320, 720 |
gixhidy | great hexacosihecatonicosadishecatonicosachoron | 1.464888 | 2400, 7200, 5280, 960 |
gixhihy | great hexacosihecatonicosihecatonicosachoron | 0.763932 | 2400, 7200, 4560, 840 |
gixipady | great hexacosiprismatodishecatonicosachoron | 1.624598 | 7200, 18000, 11280, 1560 |
gnappoth | great spinoprismatotesseractihexadecachoron | 0.890446 | 64, 192, 184, 56 |
gocap | great cycloantiprism | 1 | 50, 200, 260, 110 |
goccoa cotco | great cubicuboctahedron atop cubotruncated cuboctahedron | 1.414214 | 72, 168, 112, 22 |
goccope | great-cubicuboctahedron prism | 0.890446 | 48, 120, 88, 22 |
gocyropit | great cyclorhombated pentachoric tetrachomb, great truncated-pentachoric tetracomb, cantitruncated pentachoric tetrachomb | ||
... | gofix+gishi+120gid (?) | 0.618034 | |
gofix, gpI | great icosahedral hecatonicosachoron, great faceted hexacosichoron, greatened polyicosahedron | 0.618034 | 120, 720, 1200, 120 |
gogishi, gaspD | great grand stellated hecatonicosachoron, greatened aggrandized stellated polydodecahedron | 0.540182 | 600, 1200, 720, 120 |
gohi, gpD | great hecatonicosachoron, greatened polydodecahedron | 1.618034 | 120, 720, 720, 120 |
gohihix | great hecatonicosihecatonicosihexacosachoron | 1.464888 | 2400, 7200, 5040, 540 |
gohiny | great hecatonicosintercepted hecatonicosachoron | 0.661585 | 1200, 3600, 3840, 240 |
gondip | great octagonal spinoduoprism | 0.890446 | 128, 512, 640, 256 |
goquidipdy | great quasidisprismatodishecatonicosachoron | 6.566933 | 14400, 28800, 16080, 2160 |
gosiddip | great-snub-icosidodecahedron prism | 120, 360, 334, 94 | |
gotdatixhi | great toroidoditrigonary hexacosihecatonicosachoron | 1.732051 | 1200, 7200, 5520, 720 |
gotditpix | great toroidoditrigonary prismatohexacosichoron | 1.732051 | 1200, 7200, 8520, 1320 |
gotto | great trisoctachoron, great triakisoctachoron | 1.224745 | 32, 96, 88, 24 |
grad tathi | great retroditetrahedronary trishecatonicosachoron | 1.414214 | 600, 3600, 5280, 360 |
graggix | great rhombated grand hexacosachoron | 1.658546 | 7200, 14400, 8640, 1440 |
graghi | great rhombated grand hecatonicosachoron | 4.550627 | 7200, 14400, 8160, 960 |
grahi | great rhombated hecatonicosachoron, cantitruncated hecatonicosachoron | 11.252107 | 7200, 14400, 9120, 1920 |
graphi | grand retropental hecatonicosachoron | 0.726543 | 720, 3600, 2520, 120 |
grawv ditathi | great retrosphenoverted ditrigonary triakishecatonicosachoron | 2.093315 | 3600, 10800, 6000, 360 |
grawv hidy | great retrosphenoverted hecatonicosadishecatonicosachoron | 1.589926 | 3600, 10800, 6000, 360 |
grawv hixhi | great retrosphenoverted hecatonicosihexacosihecatonicosachoron | 1.513868 | 3600, 10800, 6960, 840 |
grawvathi | great retrosphenoverted triakishecatonicosachoron | 2.572554 | 3600, 10800, 6960, 360 |
grawvixady | great retrosphenoverted hexacosadishecatonicosachoron | 2.036148 | 3600, 10800, 7440, 840 |
grico | great rhombated icositetrachoron, cantitruncated icositetrachoron | 4.299451 | 576, 1152, 720, 144 |
gricot | great rhombated icositetrachoric tetracomb, great prismatodisicositetrachoric tetracomb | ||
..., xFoFx3xxxxx5xofox&#xt (F=ff=x+f) | bilunabirotundic great rhombicosidodecahedron prism | 420, 1080, 828, 168 | |
gridaphi | great retroinverted dodecahedronary prismatohecatonicosachoron | 1 | 120, 1200, 4200, 1320 |
griddip, K-4.150 | great-rhombicosidodecahedron prism | 3.835128 | 240, 480, 304, 64 |
gridixhi | great retroinverted dodecahedronary hexacosahecatonicosachoron | 1 | 120, 1200, 3120, 720 |
gridtathi | great retroinverted ditetrahedronary trishecatonicosachoron | 1.414214 | 600, 3600, 5280, 360 |
grip | great rhombated pentachoron, cantitruncated pentachoron | 1.843909 | 60, 120, 80, 20 |
gripady | great rhombiprismic dishecatonicosachoron | 1.207883 | 7200, 18000, 11040, 1440 |
griphi | great retropental hecatonicosachoron | 1.175571 | 720, 3600, 1920, 120 |
grit | great rhombated tesseract, cantitruncated tesseract | 3.005916 | 192, 384, 248, 56 |
grittit | great prismatotesseractic tetracomb, cantitruncated tesseractic tetracomb | ||
grix | great rhombated hexacosachoron, cantitruncated hexacosachoron | 9.124101 | 7200, 14400, 8640, 1440 |
grohp | great-rhombihexahedron prism | 0.890446 | 48, 120, 84, 20 |
gudap (old: gedap) | great duoantiprism, (old: great double antiprism – but not: great antiprism) | 1 | 50, 200, 220, 70 |
guti | great tetrakisicositetrachoron | 2.326846 | 576, 1440, 960, 96 |
gwav ditathi | great sphenoverted ditrigonary triakishecatonicosachoron | 2.036148 | 3600, 10800, 6480, 360 |
gwavathi | great sphenoverted triakishecatonicosachoron | 1.027486 | 3600, 10800, 5520, 360 |
gwavixady | great sphenoverted hexacosadishecatonicosachoron | 0.799575 | 3600, 10800, 6960, 840 |
gyautisdip | gyro-augmented 3-4-duoprism | ... | 14, 33, 31, 12 |
gybeffip | gybef prism | 16, 36, 30, 10 | |
gyepipa pero, K-4.140 | gyroelongated pentagonal pyramid atop pentagonal rotunda | 3.077684 | 31, 100, 93, 24 |
gyepippip | gyroelongated-pentagonal-pyramid prism | 1.074481 | 22, 61, 57, 18 |
gypasp | great pyramidic swirlprism | 0.618034 | 120, 600, 720, 240 |
gyprip | gyrated prip | 1.612452 | 60, 150, 124, 34 |
gyspid (alt: tetacobcu) | gyrated small prismatodecachoron, orthobicupola of runcinated pentachoron, tetaco orthobicupola | 1 | 20, 60, 70, 30 |
haddet | demidistesseract, hexadecadistesseract, compound of 2 hex | 0.707107 | |
hadedip | hexagon - decagon duoprism | 1.902113 | 60, 120, 76, 16 |
haf, K-4.46 | hexagonal antifastegium, hexagon - hap wedge, {6} || gyro hip | 1.130454 | 18, 48, 45, 15 |
hagy gircope | hexa-gyro-augmented gircope | 120, 312, 250, 58 | |
happip, K-4.53 | hexagonal-antiprism prism | 1.197085 | 24, 60, 52, 16 |
hatho | hemitesseractihemioctachoron | 0.707107 | 8, 20, 20, 8 |
hau gircope | hexa-augmented gircope | 120, 312, 274, 82 | |
hau ticcup | hexa-(ortho-)augmented ticcup | 72, 216, 214, 70 | |
haucope | hexa-augmented cope | 30, 108, 124, 46 | |
hautope | hexa-augmented tope | 54, 144, 136, 46 | |
... | external blend of the hebesphenomegacorona-prism and a cube-pyramid, cubic-pyramid-augmented hebesphenomegacorona-prism | 29, 88, 87, 28 | |
hedip | heptagonal-heptagonal duoprism | 1.629715 | 49, 96, 63, 14 |
... | hex+8oct (?) | 0.707107 | |
hex, K-4.2 (alt: octit, trapt) | hexadecachoron, tetracross (β4), orthoplex, hemitesseract, hemioctachoron, 16-cell, aeroter(id), tetrahedral antiprism, vertex figure of tac, (line-)octahedral tegum, (line-)trigonal-antirprismatic tegum, Gosset polytope 11,1, 8-3-stepprism, lattice C4 contact polytope (span of its small roots), equatorial cross-section of vertex-first tac | 0.707107 | 8, 24, 32, 16 |
hexdex | hexadecadiminished hexacosachoron | 1.618034 | 104, 528, 716, 296 |
hext | hexadecachoric tetracomb, demitesseractic tetracomb, Delone complex of body-centered tesseractic lattice, Gosset polytope 11,1,1 | ||
hi, pD | hecatonicosachoron, 120-cell, dodecacontachoron, twelftychoron, cosmochoron, dodecaplex, polydodecahedron, hyperdodecahedron | 3.702459 | 600, 1200, 720, 120 |
... | hi dimpled in by 120 ikadoes | ... | 1320, 8400, 13200, 6120 |
hibbit | hexagonal biprismated tetracomb, hexagonal duoprismatic tetracomb, hexagonal tiling duocomb, Voronoi complex of bihexagonal lattice A2×A2 | ||
hiddip | hexagonal-hexagonal duoprism, Voronoi cell of lattice A2×A2 | 1.414214 | 36, 72, 48, 12 |
hidhi | hecatonicosa-diminished hecatonicosachoron | 3.702459 | 480, 1440, 1200, 240 |
hidicau pretasto | hexadeca-diminished icositetra-augmented pentagonorhombic-trisnub-trisoctachoron | 208, 872, 1000, 336 | |
hihiquatady | hecatonicosihecatonicosiquasitruncated dishecatonicosachoron | 3.605551 | 7200, 14400, 6480, 360 |
hinhi | hecatonicosintercepted hecatonicosachoron | 2.802517 | 1200, 3600, 3360, 240 |
hinnit | hexadekintercepted tesseract | 1.224745 | 32, 96, 120, 24 |
hippyp | hexagon-pyramidal prism, line || hip | ∞ i.e. flat in euclidean space | 14, 31, 26, 9 |
histodip | hexagon - octagram duoprism | 1.137055 | 48, 96, 62, 14 |
... | vertex figure of hexadecateron | 0.774597 | 10, 45, 45, 10 |
hitte | hyperbolic (order 3) hecatonicosachoric tetracomb | 2.301105 i | |
hitwadip | hexagon - dodecagon duoprism | 2.175328 | 72, 144, 90, 18 |
hixady | hecatonicosihexacosidishecatonicosachoron | 3 | 7200, 18000, 11280, 960 |
hixquathix | hecatonicosihexacosaquasitruncated hecatonicosihexacosachoron | 2.174739 | 7200, 14400, 6960, 840 |
hixquitixhi | hecatonicosihexacosiquasitruncated hexacosihecatonicosachoron | 2.351141 | 7200, 18000, 9120, 960 |
hixquitphix | hecatonicosihexacosiquasitruncated prismatohecatonicosihexacosachoron | 2.483382 | 14400, 28800, 14880, 1560 |
hixtaphix | hecatonicosihexacositruncated prismatohecatonicosihexacosachoron | 7.735167 | 14400, 28800, 14880, 1560 |
hixthix | hecatonicosihexacositruncated hecatonicosihexacosachoron | 6.186316 | 7200, 14400, 6960, 840 |
hixtixhi | hecatonicosihexacositruncated hexacosihecatonicosachoron | 3.804226 | 7200, 18000, 9120, 960 |
hocoaso | hollow cuboctahedron atop stella octangula, tetrahedral cupolaic blend | 1 | 20, 60, 64, 23 |
hoctaoho | hollow 2oct atop oho | 1 | 18, 60, 52, 13 |
hocubasiddo | hollow cube atop snub disoctahedron, icosahedral cupolaic blend | 1 | |
hocucup | hollow cuboid cupoliprism, six tepe blend, "coord-planes squares star" atop "coord-planes squares star" | 0.790569 | 24, 72, 72, 18 |
hoddated ex | (shallow-)hexa-octa-diminished deep-tetra-diminished hexacosachoron | 1.618034 | 54, 138, 112, 28 |
hodho | hexadecoctidishemioctachoron | 1 | 24, 96, 136, 32 |
hodip | hexagon - octagon duoprism | 1.645329 | 48, 96, 62, 14 |
hog dhidicup | hollow gidhid cupoliprism | 0.732444 | 60, 240, 216, 36 |
hoh honho | hexadecoctihemihexadekintercepted hemioctachoron | 1 | 24, 96, 152, 36 |
hohoh | hexadecoctihemihexadecachoron | 1 | 24, 96, 128, 32 |
hossdap | hollow small stellated dodecahedral antiprism, pseudo sissid atop pseudo sissid | 0.707107 | 24, 120, 144, 36 |
... | hossdap + 2 2sissid | 0.707107 | |
hot thibbit | hexagonal-omnitruncated-trihexagonal duoprismatic tetracomb | ||
hotet aoho | hollow 2tet atop oho | 1 | 16, 42, 40, 13 |
hotetahoct | hollow tet atop hollow oct | 0.774597 | 10, 30, 32, 12 |
hothahacho | hollow tetrahemihexahedron atop cubohemioctahedron | 1 | 18, 60, 53, 15 |
... | vertex figure of hexadecasphenohexadecateron | 0.957427 | 10, 21, 18, 7 |
huhoh | hexadecahemihexadecachoron | 1 | 24, 96, 96, 24 |
icau pretasto | icositetra-augmented pentagonorhombic-trisnub-trisoctachoron | 224, 1032, 1168, 360 | |
icau prissi | icositetra-augmented prismatorhombisnub icositetrachoron | 312, 1296, 1680, 696 | |
ico (alt.: jot) | icositetrachoron, 24-cell, xylochoron, octaplex, rectified hexadecachoron, birectified tesseract, hyperdiamond, joined tesseract, trisoctachoron, vertex figure of hext, Voronoi cell of lattice F4, Voronoi cell of lattice D4*, surtegmated tesseract, Gosset polytope 01,1,1, lattice B4 contact polytope (span of its small roots), lattice D4 contact polytope (span of its roots), lattice F4 contact polytope (span of its small roots), equatorial cross-section of hex-first rat | 1 | 24, 96, 96, 24 |
... | ico+gico+72{4} (?) | 1 | |
... | ico+gico+24co (?) | 1 | |
icot | icositetrachoric tetracomb, Voronoi complex of body-centered tesseractic (bct) lattice, Gosset polytope 01,1,1,1 | ||
... | (0,0,20,0,0)-diminished vertex-first-rotunda of ex, icosi-diminished vertex-first-rotunda of ex, mono-augmented axially-icosahedral ursachoron ofxo3xooo5oooo&#xt | 1.618034 | 55, 174, 172, 53 |
... | id - srid - F-ike - ti tower, thawro'd rox | ... | 162, 630, 714, 246 |
idasrid, id || srid, K-4.131 | icosidodecahedron atop small rhombicosidodecahedron, icosidodecahedron cupola, ike-first supra-cap of rox | 3.077684 | 90, 300, 274, 64 |
idasridati | id atop srid atop ti | 150, 510, 486, 126 | |
idati, id || ti, K-4.158 | icosidodecahedron atop truncated icosahedron, icosidodecahedral cap of small rhombated hexacosachoron | 6.073594 | 90, 210, 154, 34 |
iddip, K-4.90 | icosidodecahedron prism | 1.693527 | 60, 150, 124, 34 |
idhi | invertidodecahedronary hecatonicosachoron | 1 | 120, 1200, 1440, 120 |
ididdip | icosidodecadodecahedron prism | 1.414214 | 120, 300, 208, 46 |
idim sidpixhi | icosa-diminished small disprismatohexacosihecatonicosachoron | 5.236068 | 2000, 5400, 4800, 1400 |
idimex | spid-diminished ex, icosidiminished ex | 1.618034 | 100, 480, 600, 220 |
idimsrahi | icosa-diminished small rhombated hecatonicosachoron | 6.735034 | 2400, 6000, 4520, 920 |
idimsrix | icosa-diminished small rhombated hexacosachoron | 6.073594 | 3000, 8400, 6600, 1200 |
idprahi | icositetra-diminished prismatorhombated hecatonicosachoron | 8.278950 | 4320, 9360, 6192, 1152 |
idprix | icositetra-diminished prismatorhombated hexacosachoron | 9.744610 | 5760, 12960, 8832, 1632 |
idsid pixhi | icositetra-diminished small disprismatohexacosihecatonicosachoron | 5.236068 | 1920, 5040, 4272, 1152 |
idsrahi | icositetra-diminished small rhombated hecatonicosachoron | 6.735034 | 2160, 5040, 3600, 720 |
idsrix | icositetra-diminished small rhombated hexacosachoron | 6.073594 | 2880, 7920, 6192, 1152 |
idtiddip | icosidodecatruncated-icosidodecahedron prism, icositruncated-dodecadodecahedron prism | 2.061553 | 240, 480, 268, 46 |
ihi | icositetrahemiicositetrachoron | 1 | 24, 96, 168, 36 |
ikadoaid | (1,0,0,12,0)-diminished vertex-first-rotunda of ex, trideca-diminished vertex-first rotunda of hexacosachoron, ike atop (pseudo) doe atop id | 1.618034 | 62, 240, 262, 84 |
ikadobcu | ikadoe bicupola | ... | 44, 210, 292, 126 |
... | toroidal (ikadobcu, ipe)-blend | ... | 44, 222, 322, 144 |
ikadoe (alt.: ikap), ike || doe, K-4.78 | icosahedron atop dodecahedron, icosahedral antiprism, dodecahedral antiprism, segment of vertex-first hexacosachoron | 1.618034 | 32, 120, 152, 64 |
ikaid, ike || id, K-4.137 | icosahedron atop icosidodecahedron, icosahedral cap of rectified hexacosachoron, icosahedral cupola | 3.077684 | 42, 150, 142, 34 |
... | (1,0,8,12,0)-diminished vertex-first-rotunda of ex, (subsymmetrical) icosiena -diminished vertex-first rotunda of hexacosachoron | 1.618034 | 54, 168, 166, 52 |
... | (1,0,4,12,0)-diminished vertex-first-rotunda of ex, heptadeca-diminished vertex-first rotunda of hexacosachoron | 1.618034 | 58, 204, 214, 68 |
ikepy, K-4.84 | icosahedral pyramid, vertex cap of hexacosachoron | 1.618034 | 13, 42, 50, 21 |
iktum | bistratic icosahedron-first cap of truncated hexacosachoron, ike-based tutsatope, ike-based tutism | 4.643523 | 84, 192, 142, 34 |
iku | (1,0,20,0,0)-diminished vertex-first-rotunda of ex, (full-symmetrical) icosiena -diminished vertex-first-rotunda of ex, axially-icosahedral ursachoron ofx3xoo5ooo&#xt, ike-based ursulate | 1.618034 | 54, 162, 142, 34 |
ini | icositetrintercepted icositetrachoron | 1.732051 | 96, 288, 336, 48 |
... | inner pentadiminished 2/10-luna of ex 1/5-luna of xfooo5xofxo oxofx5ooxox&#zx | 37, 121, 133, 49 | |
inpac | icositetraintercepted prismatotetracontaoctachoron | 1.847759 | 144, 576, 744, 168 |
... | inpac+72{4} (?) | 1.847759 | |
ipe, K-4.36 | icosahedron prism, vertex figure of rectified hyperbolic pentachoric honeycomb | 1.074481 | 24, 72, 70, 22 |
ipixady | invertopental hexacosadishecatonicosachoron | 3.077684 | 720, 3600, 5760, 840 |
iquatoc | icositetraquasitruncated tetracontoctachoron | 2 | 576, 1152, 576, 72 |
iquatpic | icositetraquasitruncated prismatotetracontoctachoron | 2.828427 | 1152, 2304, 1248, 168 |
iquipadah | inverted quasiprismatodishexadecachoron | 1.485633 | 64, 192, 200, 72 |
... | vertex figure of invertiretrolepidoteron | 0.912871 | 12, 42, 42, 14 |
... | vertex figure of invertiretrohexadecalepidohemipenteract | 0.912871 | 12, 54, 58, 18 |
isdiddip | inverted-snub-dodecadodecahedron prism | 120, 360, 318, 86 | |
ite (old: it, older: ikedpy) | (line-)ikosahedron-tegum, icosahedral bipyramid | 14, 54, 80, 40 | |
... | vertex figure of spikifacetospinodishexadecateron | 0.951190 | 9, 24, 24, 9 |
kavahto | skewverted hexadecatrisoctachoron | 1.414214 | 192, 576, 336, 40 |
kavipathi | skewverted prismatotrishecatonicosachoron | 2.828427 | 7200, 21600, 14880, 1560 |
kaviphdit | skewverted prismatohexadecadistesseract | 1.414214 | 192, 576, 432, 64 |
kepisna | chiropental snubbachoron, chiral compound of 6 ex in rox army | 1.618034 | |
kidisna | chiro-icosahedronary disnubbachoron, chiral compound of 10 ex in rahi army | 1.618034 | |
kitapna | chirotrigonal antiprismattic enenahexachoron, chiral compound of 4 ico in rico army | 1 | |
kitefa | chirotegmic hecatontetracontatetrachoron, chiral compound of 6 ico in spic army | 1 | |
koho | skew octahemioctachoron | 0.707107 | 8, 24, 28, 12 |
... | vertex figure of lepidosphenary hexateron | 0.921954 | 8, 18, 17, 7 |
lifpipixhi | polar facetopental prismatohexacosahecatonicosachoron | 3.077684 | 720, 3600, 7560, 1440 |
... | lamina-truncate of hyperbolic x3x4x338o tesselation | 1.864101 i | |
... | great-rhombated-pentachoron dual | 20, 80, 120, 60 | |
... | small-rhombated-pentachoron dual | 20, 80, 90, 30 | |
mabred | medial birhombatodecachoron | sqrt[(2a2+2ab+3b2)/5] | 60, 300, 380, 140 |
mabric | medial birhombatotetracontoctachoron | sqrt[a2 + 2 sqrt(2) ab + 3b2] | 576, 2880, 3552, 1248 |
mardatathi | medial retroditetrahedral triakishecatonicosachoron | 1.414214 | 600, 3600, 4080, 360 |
... | maximally expanded Witting polychoron, complex polychoron x3-3-o3-3-o3-3-x3 | 6480, 34560, 30240, 4800 | |
... | maximally expanded generalized Shephard tesseract, complex polychoron xp-4-o2-3-o2-3-x2 | 4p4, 6p3(p+2), 4p2(p2+3p+3), p(p3+4p2+6p+4) | |
mesdi | medial snub disicositetrachoron | 1 | 96, 720, 864, 144 |
mibdiadoe, mibdi || doe, K-4.82 | metabidiminished icosahedron atop dodecahedron, metabidiminished segment of vertex-first hexacosachoron | 1.618034 | 30, 100, 114, 44 |
mibdip | metabidiminished-icosahedron prism | 1.074481 | 20, 50, 44, 14 |
mibdipy, K-4.87 | metabidiminished-icosahedral pyramid | 1.618034 | 11, 30, 32, 13 |
mibdirit | metabidiminished rectified tesseract, wedge-diminished rectified tesseract, bistratic cuboctahedron based wedge | 1.224745 | 24, 60, 51, 15 |
middit thix | medial ditrigonal trishecatonicosihexacosachoron | 1.732051 | 1200, 7200, 10440, 960 |
mif pixady | circumfacetopental hexacosadishecatonicosachoron | 0.726543 | 720, 3600, 6840, 840 |
mipthi | medial prismatotriakishecatonicosachoron | 3.199386 | 7200, 18000, 10320, 1080 |
mix | medial hexacosachoron, mete-star, compound of 120 pen | 0.632456 | |
mohiny | medial hecatonicosintercepted hecatonicosachoron | 1.070466 | 1200, 3600, 3360, 240 |
mrawv hixhi | medial retrosphenoverted hecatonicosihexacosihecatonicosachoron | 3.963358 | 3600, 10800, 6960, 840 |
mriphi | medial retropental hecatonicosachoron | 1.902113 | 720, 3600, 1920, 120 |
n,m-dap | n-gon - m-gon duoantiprism, hemiated 2n-gon - 2m-gon duoprism | sqrt[A2/(4 sin2(π/2n))+B2/(4 sin2(π/2m))] | 2nm, 8nm, 8nm+2n+2m, 2nm+2n+2m |
n,m-dip | n-gon - m-gon duoprism | sqrt[1/(4 sin2(π/n))+1/(4 sin2(π/m))] | nm, 2nm, nm+n+m, n+m |
n,n-dip | n-gon - n-gon duoprism | 1/(sqrt(2) sin(π/n)) | n2, 2n2, n2+2n, 2n |
n-af, K-4.174 | n-gonal antifastegium, n-gonal - n-antiprismatic wedge, {n} || gyro n-prism | sqrt[(1+2 cos(π/n)-2 cos2(π/n))/(2+4 cos(π/n)-6 cos2(π/n))] | 3n, 8n, 7n+3, 2n+3 |
n-appip, K-4.176 | n-antiprism prism | sqrt[(5-4 cos(π/n))/(8-8 cos(π/n))] | 4n, 10n, 8n+4, 2n+4 |
n-appy | n-antiprismatical pyramid | sqrt[(2-2 cos(π/n))/(5-6 cos(π/n))] | 2n+1, 6n, 6n+2, 2n+3 |
n-apt | (line-)n-antiprismatic tegum, n-antiprismatic bipyramid, n-pyramidal antiprism | 2n+2, 8n, 10n+2, 4n+4 | |
n-aw, {2n} || n-ap | anti-n-wedge, n-gonal anti-wedge, 2n-gon - n-antiprismatic wedge, n-gonal gyrobicupolaic ring, {2n} || n-antiprism, {n} || gyrated n-cupola | sqrt[(3-2 cos(π/n))/(5-6 cos(π/n))] | 4n, 10n, 8n+3, 2n+3 |
... | n-fold dissected cubic polytwister, n-fold dissected cubiter, cubiswirlic 6n-choron | ... | 8n, 32n, 30n, 6n |
n-cuf | n-gonal cupofastegium, 2n-gon - n-prismatic wedge, n-gonal orthobicupolaic ring, {2n} || n-prism, {n} || n-cupola | sqrt[(5+2 cos(π/n)-4cos2(π/n))/(8-12 cos2(π/n))] | 4n, 9n, 7n+3, 2n+3 |
n-cufbil | n-gonal cupofastegia biluna | 5n, 13n, 12n+4, 4n+4 | |
n-dep | n-gonal duoexpandoprism, expanded n-n-duoprism, tegum sum of 2 alternated n-2n-duoprisms | sqrt[1/(4 sin2(π/2n))+1/(4 sin2(π/n))] | 4n2, 12n2, 12n2+4n, 4n2+4n |
... | n-fold dissected dodecahedron polytwister, n-fold dissected doter, dodecaswirlic 12n-choron | ... | 20n, 80n, 72n, 12n |
... | n-fold dissected great-dodecahedral polytwister, n-fold dissected gaditer, great-dodecaswirlic 12n-choron | ... | 12n, 72n, 72n, 12n |
n-gytpuf | n-gonal gyrotegmicupolafastegium, n-cupola atop inverted gyrated n-cupola, 2n-prismatic gyrated bi-wedge | 6n, 16n, 14n+4, 4n+4 | |
... | n-fold dissected icosahedral polytwister, n-fold dissected ikter, icosaswirlic 20n-choron | ... | 12n, 72n, 80n, 20n |
... | (n,m)-double antiprismatoid | ... | 4nm, 20nm, 28nm+2n+2m, 12nm+2n+2m |
n-m-det | (n,m)-ditetragoltriate | ... | 2nm, 5nm, 4nm+n+m, nm+n+m |
... | n-fold dissected octahedral polytwister, n-fold dissected octer, octaswirlic 8n-choron | ... | 6n, 30n, 32n, 8n |
n-pidpy | n-prismatic bipyramid | 2n+2, 7n, 7n+2, 2n+4 | |
n-pipy | n-prism pyramid, general vertex pyramid of o-3-x-3-o-n-o | 1/sqrt[3 - 1/sin2(π/n)] | 2n+1, 5n, 4n+2, n+3 |
n-puf | n-gonal pucofastegium, n-gon - 2n-prismatic wedge, n-gonal magnabicupolaic ring, {n} || 2n-prism, {2n} || n-cupola | sqrt[(2 cos2(π/n)-2 cos(π/n)-3)/(6 cos2(π/n)-2)] | 5n, 11n, 8n+3, 2n+3 |
n-sc, n-pyr-pyr | {n}-scalene, {n}-pyramidal pyramid, n tet rosette, line atop fully orthogonal {n} | sqrt[(4 sin2(π/n)-1)/(3 sin2(π/n)-1)]/2 | n+2, 3n+1, 3n+1, n+2 |
n-tepuf | n-gonal tegmipucofastegium, n-cupola atop inverted ortho n-cupola, 2n-prismatic ortho bi-wedge | 6n, 16n, 14n+4, 4n+4 | |
... | n-fold dissected tetrahedral polytwister, n-fold dissected tetter, tetraswirlic 4n-choron | ... | 4n, 16n, 16n, 4n |
n/d,2n/d-dip | n/d-gram - 2n/d-gram duoprism | sqrt[1/(4 sin2(π d/n))+1/(4 sin2(π d/2n))] | 2n2, 4n2, 2n2+3n, 3n |
n/d,m/b-dip | n/d-gram - m/b-gram duoprism | sqrt[1/(4 sin2(π d/n))+1/(4 sin2(π b/m))] | nm, 2nm, nm+n+m, n+m |
n/d-af | n/d-grammal antifastegium, n/d-grammal - n/d-antiprismatic wedge, {n/d} || gyro n/d-prism | sqrt[(1+2 cos(π d/n)-2 cos2(π d/n))/(2+4 cos(π d/n)-6 cos2(π d/n))] | 3n, 8n, 7n+3, 2n+3 |
n/d-appip | n/d-antiprism prism | sqrt[(5-4 cos(π d/n))/(8-8 cos(π d/n))] | 4n, 10n, 8n+4, 2n+4 |
n/d-cuf | n/d-grammal cupofastegium, 2n-gon - n/d-prismatic wedge, n/d-grammal orthobicupolaic ring, {2n/d} || n/d-prism, {n/d} || n/d-cupola | sqrt[(5+2 cos(π d/n)-4cos2(π d/n))/(8-12 cos2(π d/n))] | 4n, 9n, 7n+3, 2n+3 |
n/d-cupe | n/d-cupola prism, n/d-prism atop 2n/d-prism | sqrt[(5+2 cos(π d/n)-4 cos2(π d/n))/(6-8 cos2(π d/n))] | 6n, 13n, 9n+4, 2n+4 |
n/d-pyp | n/d-pyramidal prism, line || n/d-prism | sqrt[1/4+1/(4-1/sin2[π d/n])] | 2n+2, 5n+1, 4n+2, n+3 |
... | vertex figure of spinotriacontaditeron | 0.912871 | 12, 36, 36, 12 |
... | n/d-grammic retroantiprismatic hemiantiprism | 0.707107 | 4n, 12n, 10n+4, 2n+4 |
nipdip | spinoprismatodispentachoron | 1 | 20, 60, 60, 20 |
nipixady | intercepted invertopental hexacosadishecatonicosachoron | 3.077684 | 720, 3600, 6840, 840 |
... | omni-pecu-augmented (10,10)-duoprism | 150, 450, 420, 120 | |
... | omni-pecu-augmented (10,20)-duoprism | 250, 650, 520, 120 | |
... | omni-pippy-augmented (5,10)-duoprism | 60, 200, 205, 65 | |
... | omni-pippy-augmented (5,20)-duoprism | 110, 300, 255, 65 | |
... | omni-pecu-gyroaugmented (10,10)-duoprism | 150, 450, 420, 120 | |
... | omni-pecu-gyroaugmented (10,20)-duoprism | 250, 650, 520, 120 | |
... | hyperbolic o3o3o3o *b3x3*c tesselation | 0.5 i | |
... | hyperbolic order 3 small-stellated-hecatonicosachoral tetracomb | 0.242934 i | |
... | o3o3q4x, variation of tat | 2.645751 | 64, 128, 88, 24 |
... | o3o3β4o (?) | ... | 32, 240, 224, 56 |
... | o3o3β4x (?) | ... | 64, 320, 272, 56 |
... | o3o3β5o (?) | ... | 1200, 10800, 9120, 1920 |
... | o3o3β5x (?) | ... | 2400, 12000, 9120, 1920 |
... | hyperbolic (order 3) cubic-honeycomb-tetracomb snub | ... | |
... | hyperbolic great-hecatonicosachoral tetracomb | 0.393076 i | |
... | o3q3o4x, variation of srit | 2.236068 | 96, 288, 248, 56 |
... | o3β3o4β (?) | ... | 96, 624, 608, 152 |
... | o3β3o5β (?) | ... | 3600, 25200, 23520, 5520 |
... | o3β3β3o (?) | ... | 30, 180, 180, 40 |
... | o3β3β4o (?) | ... | 96, 528, 544, 128 |
... | o3β3β4β (?) | ... | 192, 960, 1008, 256 |
... | o3β3β5o (?) | ... | 3600, 21600, 21120, 4320 |
... | o3β3β5β (?) | ... | 7200, 36000, 36240, 9240 |
... | o3β3x3o (?) | ... | 30, 120, 90, 20 |
... | o3β3x4o (?) | ... | 96, 384, 264, 48 |
... | o3β3x4β (?) | ... | 192, 768, 656, 152 |
... | o3β3x4x (?) | ... | 192, 576, 392, 80 |
... | o3β3x5o (?) | ... | 3600, 14400, 9360, 1440 |
... | o3β3x5β (?) | ... | 7200, 28800, 23520, 5520 |
... | o3β3x5x (?) | ... | 7200, 21600, 14160, 2640 |
... | o3β4o3o (?) | ... | 96, 576, 576, 168 |
... | o3β4β3o (?) | ... | 288, 1728, 1632, 336 |
... | o3β4x3o (?) | ... | 288, 1152, 960, 168 |
... | hyperbolic o3x3o3o *b3o3*c tesselation | 0.632456 i | |
... | o3x3β4o (?) | ... | 96, 336, 256, 56 |
... | o3x3β5o (?) | ... | 3600, 14400, 10320, 1920 |
... | hyperbolic o3x4x3o8o tesselation | 0.594604 i | |
... | hyperbolic o4s4o3*a4s4o3*a tetracomb | 0.25 i | |
... | hyperbolic o4x4o3*a4x4o3*a tetracomb | 0.353553 i | |
... | hyperbolic birectified order 5 hecatonicosachoric tetracomb | 0.747674 i | |
... | icositetrachoron-derived Gévay polychoron, rectified o3m4o3o | ... | 240, 864, 768, 144 |
... | tesseract-derived Gévay polychoron, rectified o4m3o3o | ... | 88, 288, 256, 56 |
... | hecatonicosachoron-derived Gévay polychoron, rectified o5m3o3o | ... | 3120, 10800, 9600, 1920 |
oaf, K-4.58 | octagonal antifastegium, octagon - oap wedge, {8} || gyro op | 1.409438 | 24, 64, 59, 19 |
oappip, K-4.65 | octagonal-antiprism prism | 1.463603 | 32, 80, 68, 20 |
... | augmented axially-tetrahedral ursachoron ofxo3xooo3oooo&#xt | ... | 15, 38, 36, 13 |
... | oxFxofx3xooxFxo3ofxfooo&#xt (F=ff=x+f) | 76, 258, 250, 68 | |
... | oxFxoo3xooxFx3ofxfox&#xt (F=ff=x+f) | 72, 222, 202, 52 | |
... | oxFxofx3xfoxFxo3ooxfooo&#xt (F=ff=x+f) | 76, 264, 258, 70 | |
... | oxFxoo3xfoxFx3ooxfox&#xt (F=ff=x+f) | 72, 228, 210, 54 | |
octacho | octahedron atop cubohemioctahedron | 1 | 18, 60, 54, 16 |
octaco, K-4.29 | octahedron atop cuboctahedron, half of icositetrachoron (its oct-first rotunda), rectified octahedron-pyramid | 1 | 18, 60, 58, 16 |
octacube (alt.: octap), oct || cube, K-4.15 | octahedron atop cube, octahedral antiprism, cubical antiprism, vertex figure of icoap | 0.879465 | 14, 48, 62, 28 |
octasirco, oct || sirco, K-4.107 | octahedron atop small rhombicuboctahedron, octahedral cap of small prismatotetracontoctachoron | 1.847759 | 30, 84, 82, 28 |
octasircoacube | oct atop sirco atop cube | 38, 120, 136, 54 | |
octatoe, oct || toe | (degenerate) octahedron atop truncated octahedron | ∞ i.e. flat in euclidean space | 30, 72, 58, 16 |
octatricu, oct || tricu, K-4.30 | octahedron atop trigonal cupola, 2/6-luna of icositetrachoron | 1 | 15, 45, 43, 13 |
octatut, oct || tut, K-4.52 | octahedron atop truncated tetrahedron, octahedral cap of small rhombated pentachoron | 1.183216 | 18, 42, 34, 10 |
... | octatut,tricuf-blend | 21, 54, 47, 14 | |
octatutbicu | octatut bicupola | ... | 24, 66, 60, 18 |
octpy, K-4.3 | octahedral pyramid, half of hex (its vertex-first rotunda) | 0.707107 | 7, 18, 20, 9 |
octsnich | hyperbolic octahedral - snub-cubic honeycomb | 0.380999 i | |
octu | axially-octahedral ursachoron ofx3xoo4ooo&#xt, oct-based ursulate, vertex figure of s3s4o3o4o | 1.144123 | 24, 66, 58, 16 |
octum | octahedron-first rotunda of truncated hexadecachoron, oct-based tutsatope, oct-based tutism | 1.581139 | 36, 78, 58, 16 |
odedip | octagon-decagon duoprism | 2.079697 | 80, 160, 98, 18 |
odho | octidishemioctachoron | 1 | 24, 96, 72, 16 |
... | octa-diminished thawro-wedged 2/6-luna of hexacosachoron | ... | 14, 177, 193, 64 |
odip | octagon-octagon duoprism | 1.847759 | 64, 128, 80, 16 |
odipt | octagonal-duoprismatic tetracomb | 0.321797 i | |
oditico | octadiminished truncated icositetrachoron, Waterman polychoron number 4 wrt. alternated tessic lattice D4 centered at a hole | 2.645751 | 128, 320, 240, 48 |
... | oFfoo3ooxxF3Fxoxo3ooffx&#zx | 190, 660, 650, 180 | |
... | oFFxx3xxoof3fooxo3ooffx&#zx | 190, 870, 990, 310 | |
... | oFFxx3xxoof3fooxx3xxFFo&#zx | 260, 900, 840, 200 | |
... | oFFxx3xxoxf3Fxxox3oofFx&#zx | 330, 1170, 1150, 310 | |
ofiddady | omnifacetododecahedronary dishecatonicosachoron | 1 | 120, 1200, 3120, 240 |
... | ofoxFxo3xxFxoox3xoofxfo&#xt (F=ff=x+f) | 84, 318, 362, 128 | |
ofpipixhi | omnifacetopental prismatohexacosahecatonicosachoron | 0.726543 | 720, 3600, 7560, 1440 |
... | oFxFox5AxFoFx2oxofox5ooxofx&#zx | 255, 800, 695, 150 | |
... | oFxx3xxof3foxo3oofx&#zx | 170, 690, 750, 230 | |
... | axially pyritohedral octa-diminishing of telex, hexa-diminishing of oofoo3oxoxo5xooox&#xt | 100, 348, 340, 92 | |
... | oFxxox5Fofxfo oxofox5ooxofx&#zx | 205, 900, 1015, 320 | |
... | oFxxx5Fofxo oxofx5ooxox&#zx | 180, 650, 690, 220 | |
ogasc | octagram-scalene, octagram-pyramidal pyramid, line atop fully orthogonal octagram | 0.621876 | 10, 25, 25, 10 |
oh | octahemihexadecachoron | 1 | 24, 96, 80, 16 |
ohoa hotut | oho atop hollow 2tut | 1.183216 | 24, 66, 52, 13 |
ohope | octahemioctahedron prism | 1.118034 | 24, 60, 48, 14 |
ohopy, pt || oho | (degenerate) octahemioctahedron pyramid | ∞ i.e. flat in euclidean space | 13, 36, 36, 13 |
ohuhoh | octihexadecahemihexadecachoron | 1 | 24, 96, 144, 32 |
omfapaxady | omnicircumfacetopental hexacosadishecatonicosachoron | 0.726543 | 720, 3600, 5760, 840 |
ondip | octagonal spinoduoprism | 1.485633 | 128, 512, 640, 256 |
... | medial tetrastratic segment of telex | 112, 450, 484, 146 | |
... | ooofxfooo3xoxxoxxox5ofxofoxfo&#xt | 400, 1500, 1468, 368 | |
... | ooofxxFfooFoofo3oxFxoFxxxFooFxx3xfoxFoofFxxFoox&#xt | 176, 696, 724, 204 | |
... | ooofxxFfooFxofx3oxFxoFxxxFoxFxo3xfoxFoofFxxfooo&#xt | 188, 804, 880, 264 | |
... | oooxfxooo3xoxoxoxox5ofxfofxfo&#xt | 400, 1260, 1140, 280 | |
... | ooxf3xfox3oxFx&#xt | 54, 150, 128, 32 | |
opatic, op || tic, K-4.106 | octagonal prism atop truncated cube | 1.847759 | 40, 92, 72, 20 |
ope, K-4.11 (alt: dytpuf) | octahedron prism, vertex figure of rat, dyadic tegmipucofastegium, equatorial cross-section of tet-first dot | 0.866025 | 12, 30, 28, 10 |
... | pentachoron-derived Gévay polychoron, rectified o3m3o3o | 1.095445 | 30, 90, 80, 20 |
... | hexacosachoron-derived Gévay polychoron, rectified o3m3o5o | 6.412847 | 3600, 10800, 8640, 1440 |
... | Waterman polychoron number 5 wrt. primitive tesseractic lattice C4 centered at a hole | 3 | 208, 672, 592, 128 |
... | Waterman polychoron number 5 wrt. primitive tesseractic lattice C4 centered at a lattice point | 64, 312, 352, 104 | |
ostodip | octagon-octagram duoprism | 1.414214 | 64, 128, 80, 16 |
otathisbit | omnitruncated-trihexagonal-square duoprismatic tetracomb | ||
otbaquitit | octagonnally tetrablended quasitruncated tesseract | 0.615370 | 128, 384, 320, 80 |
otbott | octagonnally tetrablended truncated tesseract | 2.149726 | 128, 384, 320, 80 |
otcypit | omnitruncated cyclopentachoric tetracomb, great-prismatodecachoric tetracomb, Voronoi complex of lattice A4* | ||
otwadip | octagon - dodecagon duoprism | 2.332200 | 96, 192, 116, 20 |
owau prit (alt.: pox spic, alt.: phic prico) | octa-augmented prismatorhombated tesseract, partially octa-expanded small prismated (dis)icositetrachoron, partially hexadeca-contracted prismatorhombated icositetrachoron | 240, 768, 768, 240 | |
owaudope | omni-augmented dodecahedral-prism | 52, 200, 234, 86 | |
... | ox3/2ox3xo&#x | 0.707107 | 16, 48, 48, 16 |
... | oxFxofo3xfoxFxx3ooxfoox&#xt (F=ff=x+f) | 84, 324, 370, 130 | |
... | oxofofoxo3oofoxofoo5xxoxxxoxx&#xt | 400, 1650, 1872, 622 | |
... | oxofxfooo3xxxxoxxox5ooxofoxfo&#xt | 440, 1710, 1800, 530 | |
... | oxofxfoxo3xxFxoxFxx5xxoxFxoxx&#xt | 720, 2160, 1912, 472 | |
... | oxofxfoxo3xxxxoxxxx5ooxofoxoo&#xt | 480, 1920, 2132, 692 | |
... | oxoofooxo3oofxoxfoo5xxoxxxoxx&#xt | 400, 1320, 1310, 390 | |
... | oxoxfxooo3xxxoxoxox5ooxfofxfo&#xt | 440, 1410, 1280, 310 | |
... | oxoxfxoxo3xxxoxoxxx5ooxfofxoo&#xt | 480, 1560, 1420, 340 | |
... | oxqw wxwx3ooxx4qwox&#zx | 216, 600, 488, 104 | |
... | oxqwQ wxwxx3ooxxx4qwoxo&#zx | 264, 768, 648, 144 | |
... | proh-cap augmented bistratic prit-cap | ... | 120, 300, 240, 60 |
... | oxwQ wxoo3xxxx4oxxo&#zx | ... | 192, 576, 498, 114 |
... | point atop tet atop co | 17, 46, 48, 19 | |
... | oct atop tut atop toe | 42, 102, 84, 24 | |
... | oxxFxoAFxxFoxFx3xofxxFoooFxxfox3xFxoFxxFAoxFxxo&#xt | 228, 792, 780, 216 | |
... | Shephard's p-generalised tesseract, complex polychoron xp-4-o2-3-o2-3-o2 , γp 4 | p4, 4p3, 6p2, 4p | |
pabdi skiviphado | parabidiminished small skewverted prismatohexadecadisoctachoron | 1.414214 | 192, 576, 416, 56 |
pabdico | parabidiminished icositetrachoron, hexa-augmented tesseract | 1 | 22, 80, 84, 26 |
pabdiproh | parabidiminished prismatorhombated hexadecachoron, tristratic tic-first central segment of proh | 2.613126 | 144, 312, 212, 44 |
pabdirico | parabidiminished rectified icosatetrachoron, bistratic co-first central segment of rico, axis-orthogonal partial Stott expanded rit | 1.732051 | 72, 192, 156, 36 |
pabex thex | partially biexpanded truncated hexadecachoron, partially bicontracted prismatorhombated tesseract | ... | 104, 260, 200, 44 |
pabexrico | partially bi-expanded rico, partially bi-contracted proh | 144, 384, 304, 64 | |
pabexrit | partially bi-expanded rit, partially bi-contracted tat | 48, 112, 88, 24 | |
pabextah | partially bi-expanded tesseractihexadecachoron, partially bi-contracted great rhombated tesseract | 144, 288, 184, 40 | |
pabextico | partially bi-expanded tico, partially bi-contracted gidpith | 288, 576, 352, 64 | |
pac gidpith | partially (mono-)contracted gidpith | 336, 672, 408, 72 | |
pac grit | partially (mono-)contracted great rhombated tesseract | 168, 336, 216, 48 | |
pacprit | partially (mono-)contracted prit | ... | 144, 360, 276, 60 |
pacproh | partially (mono-)contracted proh | 168, 432, 336, 72 | |
pacsid pith (alt: cuba sircobcu) | partially (mono-) contracted sidpith, partially expanded quawros, cubasirco bicupola | 40, 120, 134, 54 | |
pacsrit | partially (mono-)contracted small rhombated tesseract | ... | 72, 228, 204, 48 |
pactat | partially (mono-)contracted tat | 56, 120, 88, 24 | |
padedip | pentagon - decagon duoprism | 1.828016 | 50, 100, 65, 15 |
padiap | prismatic double inverted antiprism, pentagrammic double antiprismoid | 0.618034 | 100, 500, 720, 320 |
padohi | prismatodishecatonicosachoron | 2.497212 | 1440, 7200, 7440, 2160 |
paf, K-4.22 | pentagonal antifastegium, pentagon - pap wedge, {5} || gyro pip | 1 | 15, 40, 38, 13 |
pafirp | partially faceted rap, reduced 3tet atop 2thah self-blend, tet atop "squares of thah" | 0.774597 | 10, 30, 31, 11 |
pahtex prit | partially demitesseractic-expanded prit, partially demitesseractic-contracted gidpith | 288, 624, 416, 80 | |
pahtex sidpith | partially demitesseractic-expanded sidpith, partially demitesseractic-contracted proh | 128, 336, 288, 80 | |
pahtex srit | partially demitesseractic-expanded srit, partially demitesseractic-contracted grit | 144, 336, 248, 56 | |
pahtex tes | partially demitesseractic-expanded tesseract, partially demitesseractic-contracted truncated tesseract, hexadecachorally truncated tesseract | 40, 80, 56, 16 | |
paltite | prismatoaltitruncated ico tetracomb | ||
... | dodecaswirlic triacosihexacontachoron, thirtyfold dissected dodecahedral polytwister, thirtyfold dissected doter | ... | 600, 2400, 2160, 360 |
papadoe, pap || doe, K-4.81 | pentagonal-antiprism atop dodecahedron, parabidiminished segment of vertex-first hexacosachoron, pentagonal-antiprism-first cap of grand antiprism | 1.618034 | 30, 100, 114, 44 |
papaid, pap || id, K-4.142 | pentagonal-antiprism atop icosidodecahedron | 3.077684 | 40, 130, 124, 34 |
paphacki | pentagon-prismatic heptacosicosachoron, great prismasaurus (also: great prismosaurus) | 1 | 120, 1200, 2520, 720 |
paphicki | pentagram-prismatic heptacosicosachoron, small prismasaurus (also: small prismosaurus) | 1 | 120, 1200, 2520, 720 |
pappip, K-4.39 | pentagonal-antiprism prism | 1.074481 | 20, 50, 44, 14 |
pappy | pentagon-antiprismatical pyramid | 1.618034 | 11, 30, 32, 13 |
papvixhi | pentagonal prismatoverted hexacosahecatonicosachoron | 1.902113 | 720, 3600, 3600, 720 |
paqri | prismatoquasirhombated icositetrachoron | 1.938391 | 576, 1440, 1104, 240 |
paqrigafix (old: paquerfix) | prismatoquasirhombated great facetted hexacosachoron | 1.878261 | 7200, 18000, 12480, 2160 |
paqrigagishi (old: paqrahi) | prismatoquasirhombated great grand stellated hecatonicosachoron | 1.207883 | 7200, 18000, 13440, 2640 |
paqrigshi (old: paqraghi) | prismatoquasirhombated great stellated hecatonicosachoron (prismatoquasirhombated grand hecatonicosachoron) | 3.199386 | 7200, 18000, 12480, 1680 |
paqrit | prismatoquasirhombated tesseract | 1.174172 | 192, 480, 368, 80 |
pataht | prismatotruncated demitesseractic tetracomb, prismatodiprismatodisicositetrachoric tetracomb, runcitruncated hexadecachoric tetracomb | ||
paticot | prismatotruncated icositetrachoric tetracomb, small diprismatodisicositetrachoric tetracomb, runcitruncated icositetrachoric tetracomb | ||
pautpen | penta-augmentated truncated pentachoron | ... | 50, 160, 160, 50 |
paw, K-4.133, {10} || pap | antipentawedge, decagon - pentagonn-antiprismatic wedge, pentagonal gyrobicupolaic ring, {10} || pap, {5} || gyrated pecu | 3.077684 | 20, 50, 43, 13 |
pecuf, K-4.154 | pentagonal cupofastegium, decagon - pentagon-prismatic wedge, pentagonal orthobicupolaic ring, {10} || pip, {5} || pecu, 2/5-luna of stawros | 5.236068 | 20, 45, 38, 13 |
pecupe | pentagonal-cupola prism, pentagonal-prism atop decagonal-prism | 2.288246 | 30, 65, 49, 14 |
pedap | pentagonal duoantiprism | ... | 50, 200, 220, 70 |
pedip | pentagon-pentagon duoprism | 1.203002 | 25, 50, 35, 10 |
pedisna | pental disnubbachoron, compound of 12 ex in rox army, compound of 2 kepisna | 1.618034 | |
pedpedip | pentadiminished pentagonal duoprism | 1.203002 | 20, 60, 55, 15 |
pen, K-4.1 | pentachoron, 4D simplex (α4), 5-cell, pyroter(id), tetrahedral pyramid, triangle-pyramidal pyramid, regular triangle-scalene, regular line-tettene, regular (point-)pennene, 3 tet rosette, vertex figure of hix, Gosset polytope 03, 5-2-stepprism | 0.632456 | 5, 10, 10, 5 |
pente (old: pennit) | hyperbolic order 5 pentachoric tetracomb | 0.393076 i | |
peppia pero, K-4.139 | pentagonal-pyramid atop pentagonal-rotunda | 3.077684 | 26, 75, 68, 19 |
peppyp, K-4.38 | pentagon-pyramidal prism, J2 prism, line || pip | 1.074481 | 12, 26, 22, 8 |
pepuf, K-4.165 | pentagonal pucofastegium, pentagon - decagon-prismatic wedge, pentagonal magnabicupolaic ring, {5} || dip, {10} || pecu, {5}-first cap of srahi | 6.735034 | 25, 55, 43, 13 |
perope, K-4.92 | pentagonal-rotunda prism | 1.693527 | 40, 90, 69, 19 |
pesc (old: peppypy), K-4.86 | pentagon scalene, pentagon-pyramidal pyramid, line atop fully orthogonal pentagon, 5 tet rosette | 1.618034 | 7, 16, 16, 7 |
pex hex | partially (mono-)expanded hex, partially contracted quawros | 14, 42, 52, 24 | |
pex thex | partially (mono-)expanded thex | ... | 72, 180, 140, 32 |
pexic | partially (mono-)expanded icositetrachoron | ... | 36, 132, 128, 32 |
pexrico | partially (mono-)expanded rico | 120, 336, 272, 56 | |
pexrit | partially (mono-)expanded rit | 40, 104, 88, 24 | |
pextah | partially (mono-)expanded tesseractihexadecachoron | 120, 240, 152, 32 | |
pextico | partially (mono-)expanded tico | 240, 480, 296, 56 | |
phiddip | pentagon hexagon duoprism | 1.312862 | 30, 60, 41, 11 |
phitte | hyperbolic order 5 hecatonicosachoric tetracomb | 0.206652 i | |
phud | prismatohemidecachoron | 1 | 20, 60, 60, 25 |
pibhaki | pentagonal-bipyramidal heptacosiicosachoron, rectified-hexacosachoron dual, surtegmated hecatonicosachoron | 720, 3600, 3600, 720 | |
pibox srico | partially bi-octa-expanded small rhombitetracontoctachoron | 480, 1056, 720, 144 | |
pibox tico | partially bi-octa-expanded truncated icositetrachoron | 448, 896, 560, 112 | |
picnut | prismatocubiintercepted tesseract | 0.890446 | 64, 192, 232, 64 |
pikap (alt.: snittap) | pyritohedral icosahedral antiprism, snub-tetrahedral antiprism, non-uniform alternation of tope | ... | 24, 96, 112, 40 |
pinnip | prismatointercepted pentachoron, retropyroinvertirectichoron, vertex figure of han | 0.774597 | 10, 30, 45, 15 |
... | pinnip+5 2thah (?) | 0.774597 | |
pinnipdip | pentaintercepted prismatodispentachoron, prismatopentaintercepted dispentachoron | 1.183216 | 30, 90, 115, 30 |
... | pinnipdip+15{4} (?) | 1.183216 | |
pinpith | prismatointercepted prismatotesseractihexadecachoron | 1.847759 | 96, 288, 344, 80 |
... | pinpith+48{4} | 1.847759 | |
pinpixhi | prismatointercepted prismatohexacontahecatonicosachoron | 6.735034 | 3600, 10800, 12360, 2640 |
... | pinpixhi+1800{4} (?) | 6.735034 | |
piphid | prismatopentahemidecachoron, copyrofacetoretropodichoron | 1 | 20, 60, 70, 20 |
... | piphid+10tet (?) | 1 | |
pippindip | prismatopentintercepted dispentachoron | 1.183216 | 30, 90, 115, 25 |
pippy, K-4.141 | pentagonal-prismatic pyramid, vertex pyramid of the rectified hexacosachoron | 3.077684 | 11, 25, 22, 8 |
pirgady | pseudorhombated great dishecatonicosachoron | 1.054256 | 3600, 10800, 8160, 960 |
pirgaghi | prismatorhombated great grand hecatonicosachoron | 1.893038 | 7200, 18000, 12480, 2160 |
pirghi | prismatorhombated great hecatonicosachoron | 4.917351 | 7200, 18000, 11520, 1680 |
pirhatit | prismatorhombated demitesseractic tetracomb, great prismatodemitesseractic tetracomb, steriruncic tesseractic tetracomb | ||
pirpop | pseudorhombated prismatopentachoron | 1.183216 | 30, 90, 85, 25 |
... | pirpop+5 2thah (?) | 1.183216 | |
pirsady | pseudorhombated small dishecatonicosachoron | 6.073594 | 3600, 10800, 8160, 960 |
pirshi | prismatorhombated (small) stellated hecatonicosachoron | 5.515107 | 7200, 18000, 12480, 2160 |
pistadedip | pentagon - decagram duoprism | 1.051462 | 50, 100, 65, 15 |
pistodip | pentagon - octagram duoprism | 1.008216 | 40, 80, 53, 13 |
pitest | hyperbolic order 5 tesseractic tetracomb | 0.242934 i | |
pithatit | prismatotruncated demitesseractic tetracomb, small prismatodemitesseractic tetracomb, stericantic tesseractic tetracomb | ||
pittip | prismatotriakispentachoron | 1.612452 | 60, 150, 110, 25 |
poc gippic | partially octa-contracted great prismatotetracontoctachoron | 960, 2016, 1296, 240 | |
poc prico (alt.: phex spic) | partially octa-contracted prismatorhombated icositetrachoron, partially hexadeca-expanded small prismated (dis)icositetrachoron | ... | 384, 1056, 912, 240 |
poccont | partially octa-contracted tetracontoctachoron | 224, 480, 304, 48 | |
pocsric (alt.: phixic) | partially octa-contracted small rhombated icositetrachoron, partially hexadeca-expanded icositetrachoron, octa-augmented truncated tesseract | ... | 160, 512, 464, 112 |
... | pocuro wedge | ... | 30, 85, 83, 28 |
podip | pentagon - octagon duoprism | 1.559075 | 40, 80, 53, 13 |
potatit | prismatotruncated tesseractic tetracomb, small tomocubic-diprismatotesseractic tetracomb, runcitruncated tesseractic tetracomb | ||
pox prico | partially octa-expanded prismatorhombated icositetrachoron | 768, 1728, 1200, 240 | |
pox rico | partially octa-expanded rectified icositetrachoron | 160, 384, 272, 48 | |
pox srico | partially octa-expanded small rhombated icositetrachoron | 384, 960, 720, 144 | |
pox tico | partially octa-expanded truncated icositetrachoron | 320, 640, 400, 80 | |
poxic (alt.: phic srico, alt.: owau sidpith) | partially octa-expanded icositetrachoron, partially hexadeca-contracted small rhombated icositetrachoron, octa-augmented small diprismated tesseractithexadecachoron | ... | 72, 256, 256, 72 |
prahi | prismatorhombated hecatonicosachoron, runcitruncated hexacosachoron | 8.278950 | 7200, 18000, 13440, 2640 |
praht | prismatorhombated demitesseractic tetracomb, great tetracontaoctachoric tetracomb, runcicantellated hexadecachoric tetracomb | ||
prap vixhi | pentagonal retroprismatoverted hexacosahecatonicosachoron | 1.175571 | 720, 3600, 3600, 720 |
prarsi | prismatorhombiretrosnub icositetrachoron | 1.328131 | 288, 1008, 960, 240 |
pretasto | pentagonorhombic trisnub trisoctachoron | 176, 624, 592, 144 | |
prico | prismatorhombated icositetrachoron, runcitruncated icositetrachoron | 3.498949 | 576, 1440, 1104, 240 |
pricot | prismatorhombated icositetrachoric tetracomb, great diprismatodisicositetrachoric tetracomb, runcicantellated icositetrachoric tetracomb | ||
prip | prismatorhombated pentachoron, runcitruncated pentachoron | 1.612452 | 60, 150, 120, 30 |
prishi | prismatorhombisnub hecatonicosachoron | 3.625437 | 3600, 21600, 20640, 3960 |
prisquah | hyperbolic prismatorhombated square-tiling honeycomb, hyperbolic prismatotruncated order 4 octahedral honeycomb, hyperbolic runcitruncated order 4 octahedral honeycomb | 2.345208 i | |
prissi | prismatorhombisnub icositetrachoron, prismato-semistruncated icositetrachoron, runcic snub icositetrachoron | 2.497212 | 288, 1008, 960, 240 |
prissibich, 5Y4-3T-3Q3-T3 | prismatorhombisnub bicubic honeycomb | ||
pristrah | hyperbolic prismatorhombisnub triangular-tiling honeycomb, hyperbolic runcisnub triangular tiling honeycomb, edge-alternated hyperbolic prismatorhombated triangular-tiling honeycomb | ... | |
prit | prismatorhombated tesseract, prismatotruncated hexadecachoron, runcitruncated hexadecachoron | 2.370932 | 192, 480, 368, 80 |
prittit | prismatorhombated tesseractic tetracomb, rhombitesseractic-diprismatotesseractic tetracomb, runcicantellated tesseractic tetracomb | ||
prix | prismatorhombated hexacosichoron, runcitruncated hecatonicosachoron | 9.744610 | 7200, 18000, 13440, 2640 |
proh | prismatorhombated hexadecachoron, prismatotruncated tesseract, runcitruncated tesseract | 2.613126 | 192, 480, 368, 80 |
... | (0,0,0,12,0)-diminished vertex-first-rotunda of ex, dodeca-diminished vertex-first rotunda of hexacosachoron | 1.618034 | 63, 252, 292, 103 |
pta cubaike | cube-augmented cubaike | 1 | 21, 74, 86, 33 |
ptaika cube | ike-augmented cubaike | 21, 78, 104, 47 | |
pybiscrox | pyritohedral bistratic icosahedron-first cap of rectified hexacosachoron | 3.077684 | 96, 330, 318, 84 |
pysna | s2s3s4x, pyritosnub alterprism, edge-alternated great-rhombicuboctahedronal prism, edge-snub octahedral hosochoron | ... | 48, 144, 136, 40 |
pysnet | s3s3s4x, pyritosnub tesseract, edge-alternated great diprismated tesseractihexadecachoron, edge-snub hexadecachoron | ... | 192, 672, 656, 176 |
... | q x3o3o, variation of tetrahedron prism, vertex figure of rectified penteract | 0.935414 | 8, 16, 14, 6 |
... | q3o3o4x, variation of sidpith | 1.732051 | 64, 192, 208, 80 |
... | q3o4o3x, variant of spic | 2.236068 | 144, 576, 672, 240 |
... | qo3oo3oo&#x, shallower variant of tetrahedral pyramid, vertex pyramid of tes | 1 | 5, 10, 10, 5 |
... | Waterman polychoron number 4 wrt. primitive tesseractic lattice C4 centered at a hole | 2.645751 | 128, 416, 400, 112 |
... | qo3oq3oo&#x, shallower variant of rap, segment of tes | 1 | 10, 30, 30, 10 |
... | Q3o3o4x, variation of sidpith | 2.645751 | 64, 192, 208, 80 |
qragishi (old: qraghi) | quasirhombated grand stellated hecatonicosachoron | 1.662508 | 3600, 10800, 8160, 960 |
qrico | quasirhombated icositetrachoron | 1.082392 | 288, 864, 720, 144 |
qridaquit gissidu | expanded axially-great-icosahedral ursachoron, (qrid,quit gissid)-based ursulate | 1.020794 | 180, 450, 346, 76 |
qriddip | quasi-rhombicosidodecahedron prism | 0.874032 | 120, 300, 244, 64 |
qrigfix (old: querfix) | quasirhombated great faceted hexacosachoron | 1.027486 | 3600, 10800, 7680, 960 |
qrigogishi (old: qrahi) | quasirhombated great grand stellated hecatonicosachoron | 0.799575 | 3600, 10800, 9120, 1920 |
qrit | quasirhombated tesseract | 0.765367 | 96, 288, 248, 56 |
... | vertex figure of quasicellated penteractitriacontiditeron | 1.118034 | 8, 24, 32, 16 |
quad pagaxhi | quasidisprismatogrand hexacosihecatonicosachoron | 0.874032 | 2400, 7200, 7440, 2640 |
quadippady | quasidisprismatodishecatonicosachoron, Unholey Terror | 1.414214 | 2400, 7200, 6480, 1680 |
quawros | quadratic ({8} || cube-)wedge rosette, bridge cyclotetraaugmented tesseract, ring-augmented tesseract, cube || {8} || cube, {4} || squobcu || {4} | 24, 72, 84, 36 | |
quercoa quithu | (querco,quith)-based ursachoron | 0.986869 | 72, 180, 142, 34 |
quercope | quasirhombicuboctahedron prism | 0.890446 | 48, 120, 100, 28 |
quidex | quatro-icositetradiminished hexacosachoron, tristellatododecahedral enneacontahexachoron, dual of sadi | 144, 480, 432, 96 | |
quidpith (old: qippith) | quasi(dis)prismatotesseractihexadecachoron | 0.890446 | 64, 192, 208, 80 |
quidpixhi | quasidisprismatohexacosihecatonicosachoron | 0.763932 | 2400, 7200, 7440, 2640 |
quipdohi | quasiprismatodishecatonicosachoron | 1.328131 | 1440, 7200, 7440, 2160 |
quiphi | quasiprismatohecatonicosachoron | 0.726543 | 720, 3600, 3240, 840 |
quippic | quasiprismatotetracontoctachoron | 0.765367 | 144, 576, 672, 240 |
quippirfix | quasiprismatorhombated faceted hexacosachoron | 3.531591 | 7200, 18000, 12480, 2160 |
quippirgashi | quasiprismatorhombated grand stellated hecatonicosachoron | 1.348948 | 7200, 18000, 11520, 1680 |
quippirgax | quasiprismatorhombated grand hexacosachoron | 1.021064 | 7200, 18000, 13440, 2640 |
quippirghi | quasiprismatorhombated grand hecatonicosachoron | 2.400819 | 7200, 18000, 12480, 1680 |
quiproh | quasiprismatorhombated hexadecachoron | 1.082392 | 192, 480, 368, 80 |
quit gashi | quasitruncated grand stellated hecatonicosachoron | 0.953850 | 1440, 4320, 2160, 240 |
quit gishi | quasitruncated great stellated hecatonicosachoron | 0.953850 | 1440, 4320, 3120, 240 |
quit gissiddip | quasitruncated-great-stellated-dodecahedron prism | 0.826058 | 120, 240, 144, 34 |
quit gogishi | quasitruncated great grand stellated hecatonicosachoron | 0.677481 | 2400, 4800, 3120, 720 |
quit sishi | quasitruncated small stellated hecatonicosachoron | 2 | 2400, 4800, 2160, 240 |
quit sissidagird | quit sissid atop gird | 0.874032 | 120, 330, 246, 56 |
quit sissiddip | quasitruncated-small-stellated-dodecahedron prism, small-stellated-truncated-dodecahedron prism | 0.988665 | 120, 240, 138, 26 |
quitcope | quasitruncated-cuboctahedron prism | 1.174172 | 96, 192, 124, 28 |
quitdiddip | quasitruncated-dodecadodecahedron prism | 1.732051 | 240, 480, 288, 56 |
quithaquitco | quasitruncated hexahedron atop quasitruncated cuboctahedron | 1.082392 | 72, 156, 112, 28 |
quithip | quasitruncated-hexahedron prism | 0.765367 | 48, 96, 64, 16 |
quithpy | quasitruncated-hexahedral pyramid | 0.613502 | 25, 60, 50, 15 |
quitit | quasitruncated tesseract | 0.615370 | 64, 128, 88, 24 |
... | vertex figure of retrocellitriacontadiahexadecateron | 0.912871 | 12, 48, 64, 22 |
... | vertex figure of retrodishexadecateron | 0.774597 | 10, 45, 50, 15 |
radatathi | retroditetrahedronary dishecatonicosachoron | 1.414214 | 600, 3600, 2880, 360 |
raded adoe | raded atop 3doe | 1.432173 | 120, 330, 258, 56 |
raded adoe | rhombidodecadodecahedron atop dodecahedron | 1.432173 | 80, 240, 126, 56 |
radeda tigid, raded || tigid | rhombidodecadodecahedron atop truncated great dodecahedron | 2.363565 | 120, 330, 258, 56 |
radiddip (old: radedip) | rhombidodecadodecahedron prism | 1.414214 | 120, 300, 228, 56 |
rafficdi | retrofrustic tetracontoctadisicositetrachoron | 1.414214 | 288, 1152, 960, 96 |
raffixthi | retrofrustic hexacositrishecatonicosachoron | 2.236068 | 3600, 14400, 9120, 960 |
ragaghi | rectified great grand hecatonicosachoron | 1.070466 | 1200, 3600, 2160, 240 |
ragashi | rectified grand stellated hecatonicosachoron | 1.175571 | 720, 3600, 2160, 240 |
raggix | rectified grand hexacosachoron | 0.726543 | 720, 3600, 3600, 720 |
raghi | rectified grand hecatonicosachoron | 1.902113 | 720, 3600, 3120, 240 |
ragishi | rectified great stellated hecatonicosachoron | 1.175571 | 720, 3600, 3120, 240 |
rahi | rectified hecatonicosachoron | 4.534568 | 1200, 3600, 3120, 720 |
rahitte | rectified hyperbolic hecatoniicosachoric tetracomb | 2.910693 i | |
rap (old: rip, alt.: tetaoct), tet || oct, K-4.5 | rectified pentachoron, pyrorectichoron, tetrahedral cupola, vertex figure of hin, tetrahedron atop octahedron, Gosset polytope 02,1 | 0.774597 | 10, 30, 30, 10 |
rapente | rectified hyperbolic order 5 pentachoric tetracomb | 1.272020 i | |
raphitte | rectified hyperbolic order 5 hecatonicosachoric tetracomb | 0.668740 i | |
rappisdi | retroantiprismatosnub disicositetrachoron | 1 | 96, 720, 864, 144 |
... | rappisdi+mesdi+288{4} (?) | 1 | |
rapsady | retroantiprismatosnub dishecatonicosachoron | 1.618034 | 2400, 21600, 22080, 1680 |
rasdi | retrosnub icositetrachoron, retrosnub disicositetrachoron | 0.618034 | 96, 432, 480, 144 |
rasishi | rectified small stellated hecatonicosachoron | 2.802517 | 1200, 3600, 2160, 240 |
... | vertex figure of retrotriacontidicellihemitriacontaditeron | 0.866025 | 12, 54, 82, 28 |
ratho | rectified tesseractihemioctachoron | 1 | 24, 96, 88, 20 |
rathotathibit | rhombitrihexagonal-omnitruncated-trihexagonal duoprismatic tetracomb | ||
... | vertex figure of retrosphenary cellihexateron | 0.921954 | 8, 28, 38, 18 |
rawvathi | retrosphenoverted triakishecatonicosachoron | 2.689994 | 3600, 10800, 6000, 360 |
rawvatoth | retrosphenoverted tesseractitesseractihexadacachoron | 1.847759 | 96, 288, 200, 32 |
rawvaty | retrosphenoverted triakisicositetrachoron | 2.613126 | 288, 864, 576, 72 |
rawvhiddix | retrosphenoverted hecatonicosadishexacosachoron | 1.258409 | 3600, 10800, 7920, 1320 |
rawvhitto | retrosphenoverted hexadecatesseractioctachoron | 1.732051 | 96, 288, 208, 32 |
rawvid tixady | retrosphenoverted ditrigonary hexacosadishecatonicosachoron | 5.330704 | 3600, 10800, 6960, 840 |
rawvtip | retrosphenoverted triakispentachoron | 1.183216 | 30, 90, 70, 15 |
recont | rectified tetracontoctachoron | 6.754807 | 576, 1728, 1488, 336 |
... | rectified Shephard's hexadecachoron, complex polychoron op-4-o2-3-x2-3-o2 | 6p2, 12p3, 4p3(p+1), p(p3+4) | |
... | rectified Witting polychoron, complex polychoron o3-3-x3-3-o3-3-o3 | 2160, 17280, 8640, 480 | |
... | rectified hyperbolic o4x4o3*a4x4o3*a tetracomb | ... | |
... | rectified Shephard's tesseract, complex polychoron op-4-x2-3-o2-3-o2 | 4p3, 6p4, 2p2(2p2+3), p(p3+4) | |
redeca | rectified decachoron | 2.828427 | 60, 180, 160, 40 |
... | reduced( ofx3/2oxx3ooo&xt by 2tet ) | 0.874032 | 17, 42, 38, 13 |
... | reduced( ofx3/2oxx3xxx&xt by 4x {6/2} ) | 1.136572 | 40, 102, 78, 20 |
... | reduced( ofx3/2oxx4ooo&xt by oct+6{4} ) | 0.899454 | 31, 84, 69, 20 |
... | cuboctahedral retro-cuploid | 1 | 18, 60, 53, 15 |
regikaike | rectified gikaike | 1.732051 | 120, 480, 424, 76 |
rerahi | o3x3o5f, rectified rectified-hecatonicosachoron, variation of srahi | 9.013835 | 3600, 10800, 9120, 1920 |
rerico | x3o4q3o, rectified rectified-icositetrachoron, variation of small rhombated icositetrachoron | 3.316625 | 288, 864, 720, 144 |
rerit | o3x3o4q, rectified rectified-tesseract, variation of srit | 2.236068 | 96, 288, 248, 56 |
residpith (alt.: amsidpith) | rectified/ambified small-disprismated-tesseractihexadecachoron | 2.797933 | 192, 768, 720, 144 |
residpixhi (alt.: amsidpixhi) | rectified/ambified small-disprismated-hexacosihecatonicosachoron | 10.424281 | 7200, 28800, 26640, 5040 |
respic | rectified small prismated tetracontoctachoron | 3.557647 | 576, 2304, 2112, 384 |
respid | rectified small prismated decachoron | 1.732051 | 60, 240, 230, 50 |
resrip (alt.: amsrip) | rectified/ambified srip | 2.144761 | 90, 270, 230, 50 |
retah (alt.: amtah) | rectified/ambified tesseractihexadecachoron | 4.123106 | 192, 576, 504, 120 |
retdip (old: retriddip) | rectified triddip | 1.290994 | 18, 54, 51, 15 |
retepe (alt.: amtepe) | rectified/ambified tepe | 1.224745 | 16, 48, 46, 14 |
retisdip (alt.: amtisdip) | rectified/ambified tisdip | 1.527525 | 24, 72, 67, 19 |
rexhi (alt.: amxhi) | rectified/ambified hexacosihecatonicosachoron | 15.126249 | 7200, 21600, 18720, 4320 |
... | (small) rhombated generalized Shephard hexadecachoron, complex polychoron x2-3-o2-3-x2-4-op | 12p3, 12p3(p+1), 2p2(5p2+2p+6), p(p3+6p+4) | |
... | (small) rhombated Witting polychoron, complex polychoron x3-3-o3-3-x3-3-o3 | 17280, 69120, 32400, 2640 | |
... | (small) rhombated generalized Shephard tesseract, complex polychoron xp-4-o2-3-x2-3-o2 | 6p4, 12p3(p+1), 2p2(4p2+6p+3), p(p3+4p2+4) | |
rico | rectified icosatetrachoron, cantellated hexadecachoron, hexadecachoron-derived Gévay polychoron, equatorial cross-section of ico-first sart | 1.732051 | 96, 288, 240, 48 |
... | rico-cap augmented thex-rotunda | ... | 48, 126, 108, 30 |
ricot | rectified icositetrachoric tetracomb | ||
ridatathi | retroinverted ditetrahedral triakishecatonicosachoron | 1.414214 | 600, 3600, 4080, 360 |
ridditdy | retroditrigonary dishecatonicosachoron | 1.732051 | 1200, 7200, 4680, 240 |
ridhi | retroinverted dishecatonicosachoron | 1.902113 | 720, 3600, 2880, 240 |
ridimex (alt.: idimrox) | rectified icosidiminished hexacosachoron, icosidiminished rectified hexacosachoron | 3.077684 | 480, 1800, 1640, 320 |
ridtidohi | rectified ditrigonary dishecatonicosachoron | 1.732051 | 1200, 7200, 5280, 360 |
rigfix | rectified great faceted hexacosichoron | 0.726543 | 720, 3600, 2640, 240 |
riggidtixhi | rectified great ditrigonary hexacosihecatonicosachoron | 1.732051 | 1200, 7200, 6420, 840 |
righi | rectified great hecatonicosachoron | 1.902113 | 720, 3600, 2160, 240 |
rigogishi | rectified great grand stellated hecatonicosachoron | 0.661585 | 1200, 3600, 3120, 720 |
rihix | retroinverted hecatonicosihexacosachoron | 1.175571 | 720, 3600, 4320, 720 |
... | vertex figure of retropenteractihexadecateron | 0.774597 | 10, 45, 60, 15 |
ripahi | retroinverted prismatohecatonicosachoron | 4.534568 | 720, 3600, 4440, 840 |
... | ripahi+600 2thah (?) | 4.534568 | |
ripdip | rhombiprismato dispentachoron | 1.612452 | 60, 150, 100, 20 |
risadi (alt.: idrox) | rectified snub icositetrachoron, icositetradiminished rectified hexacosachoron | 3.077684 | 432, 1440, 1248, 240 |
risadit | rectified/ambified snub icositetrachoric tetracomb | ||
rissidtixhi | rectified small ditrigonary hexacosihecatonicosachoron | 1.732051 | 1200, 7200, 6240, 840 |
rit | rectified tesseract, rectified octachoron, birectified hexadecachoron, runcic tesseract, equatorial cross-section of ico-first nit | 1.224745 | 32, 96, 88, 24 |
rite (alt.: ikaidbicu) | rectified ite, ikaid bicupola | ... | 54, 240, 252, 66 |
rithsithbit | rhombitrihexagonal-simotrihexagonal duoprismatic tetracomb | ||
rittit | rectified tesseractic tetracomb, quartertesseractic tetracomb | ||
rixhi | retroinverted hexacosahecatonicosachoron | 3.077684 | 720, 3600, 4320, 720 |
rofix | rectified faceted hexacosichoron | 3.077684 | 720, 3600, 2640, 240 |
... | vertex-first rotunda of hexacosachoron | 1.618034 | 75, 384, 592, 283 |
rox | rectified hexacosachoron | 3.077684 | 720, 3600, 3600, 720 |
... | rox+720pip (?) | 3.077684 | |
... | s-2N-x-2-x-M-o, M-prism-alternated 4N-gon - M-gon duoprism | ... | 2nm, 4nm, 2nm+2n+m, 2n+m |
... | s2x2s4x, square-alternated sodip | ... | 16, 32, 24, 8 |
... | β3o3o4β (?) | ... | 64, 480, 576, 176 |
... | β3o3o5β (?) | ... | 2400, 21600, 23040, 5040 |
... | β3o3β3o (?) | ... | 30, 210, 200, 50 |
... | β3o3β4β (?) | ... | 192, 1152, 1184, 296 |
... | β3o3β4x (?) | ... | 192, 864, 800, 200 |
... | β3o3β5o (?) | ... | 3600, 25200, 23040, 5040 |
... | β3o3β5β (?) | ... | 7200, 43200, 43680, 10560 |
... | β3o3β5x (?) | ... | 7200, 32400, 27840, 6420 |
... | β3o4o3β (?) | ... | 144, 1728, 1824, 384 |
... | β3o4β3o (?) | ... | 288, 1728, 1728, 432 |
... | β3β3o3β (?) | ... | 60, 360, 380, 100 |
... | β3β3o4β (?) | ... | 192, 1056, 1152, 328 |
... | β3β3o5β (?) | ... | 7200, 43200, 44640, 11040 |
... | β3β3β3o (?) | ... | 60, 300, 320, 85 |
... | β3β3β3x (?) | ... | 120, 420, 400, 105 |
... | β3β3β5o (?) | ... | 7200, 36000, 37440, 9240 |
... | β3β3β5x (?) | ... | 14400, 50400, 47040, 11640 |
... | β3β3x3β (?) | ... | 120, 420, 380, 100 |
... | β3β3x4β (?) | ... | 384, 1344, 1248, 328 |
... | β3β3x5β (?) | ... | 14400, 50400, 44640, 11040 |
... | β3β3x *b3o (?) | ... | 96, 432, 368, 72 |
... | s3s4o3o, mere hemiation of truncated icositetrachoron, snub rhombatohexadecachoron | 2.645751 | 96, 432, 480, 144 |
... | alternated truncated hyperbolic order 4 icositetrachoral tetracomb | ||
... | β3β4o3β (?) | ... | 576, 3168, 3456, 936 |
... | β3β4β3o (?) | ... | 576, 2880, 2976, 744 |
... | β3β4β3x (?) | ... | 1152, 4032, 3744, 936 |
... | β3β4x3β (?) | ... | 1152, 4032, 3744, 936 |
... | shi+120x 2sissid(?) | ... | 1440, 14400, 12480, 1680 |
... | prishi+120x 2did (?) | ... | 7200, 28800, 23520, 4080 |
... | β3x3o4β (?) | ... | 192, 672, 640, 176 |
... | β3x3o5β (?) | ... | 7200, 28800, 25440, 5040 |
... | β3x3β3o (?) | ... | 60, 240, 200, 50 |
... | β3x3β3x (?) | ... | 120, 360, 270, 50 |
... | β3x3β4β (?) | ... | 384, 1344, 1184, 296 |
... | β3x3β4x (?) | ... | 384, 1152, 896, 200 |
... | β3x3β5o (?) | ... | 7200, 28800, 23040, 5040 |
... | β3x3β5β (?) | ... | 14400, 50400, 43680, 10560 |
... | β3x3β5x (?) | ... | 14400, 43200, 31440, 6240 |
... | β3x3x3β (?) | ... | 120, 300, 220, 50 |
... | β3x3x4β (?) | ... | 384, 960, 736, 176 |
... | β3x3x5β (?) | ... | 14400, 36000, 25440, 5040 |
... | β3x4β3o (?) | ... | 576, 2304, 2016, 432 |
... | β3x4β3x (?) | ... | 1152, 3456, 2688, 528 |
... | β3x4x3β (?) | ... | 1152, 2880, 1968, 384 |
... | hyperbolic s4o3o4s4*b tesselation | 0.353553 i | |
... | s4x2s4x (?) | ... | 32, 80, 72, 24 |
... | s4x2x3o, trip-alternated todip | ... | 12, 24, 19, 7 |
sabbadipady | small blendic disprismatodishecatonicosachoron | 2 | 2400, 8400, 7200, 1680 |
sabbathi | small blendic trishecatonicosachoron | 2 | 2400, 8400, 4800, 360 |
sabippady (old: sabbippady) | small blendic prismatodishecatonicosachoron | 2 | 2400, 8400, 7200, 960 |
sabred | small birhombatodecachoron | sqrt[(2a2+2ab+3b2)/5] | 60, 300, 340, 100 |
sabric | small birhombatotetracontoctachoron | sqrt[a2 + 2 sqrt(2) ab + 3b2] | 576, 2880, 3168, 864 |
sad phiddix | small dipentary hecatonicosadishexacosachoron | 2.497212 | 1440, 7200, 7200, 1320 |
saddiddip | small-dodekicosidodecahedron prism | 2.288246 | 120, 300, 208, 46 |
sadi (alt.: idex) | snub icositetrachoron, snub disicositetrachoron, semistruncated icositetrachoron, icositetradiminished hexacosachoron, snub rhombatohexadecachoron | 1.618034 | 96, 432, 480, 144 |
sadit | snub icositetrachoric tetracomb, Gosset's non-Wythoffian tetracomb | ||
sadixady | small dishexacosadishecatonicosachoron | 1.773668 | 2400, 7200, 6240, 1440 |
sadixhix (old: sixhix) | small dodecahedronary hexacosahemihexacosachoron, compound of 25 ihi (but not gadixhix) | 1 | |
sadsadox | small disnub dihexacosachoron | 3.077684 | 3600, 28800, 31200, 6000 |
sadtap | small ditetrahedronary prismatochoron, compound of 36 dedip | 2.288246 | |
sadtef pixady | small ditetrahedronary exofissary prismatohexacosadishecatonicosachoron | 2.288246 | 2400, 10800, 9840, 2040 |
sadtifady | small ditetrahedronarofissary dishecatonicosachoron | 2.288246 | 600, 3600, 4560, 240 |
safthi | great retrofrustary trishecatonicosachoron | 2.236068 | 3600, 14400, 7680, 360 |
sanbathi | small spinoblendic trishecatonicosachoron | 2 | 2400, 8400, 6480, 960 |
sanbippady | small spinoblendic prismatodishecatonicosachoron | 2 | 2400, 8400, 6960, 960 |
sand tathi | small intercepted ditetrahedronary trishecatonicosachoron | 2.288246 | 600, 3600, 5280, 360 |
saquid paxhi | small quasidisprismatohexacosihecatonicosachoron, Holey Terror | 2.288246 | |
sazdideta | square antitrapezary disicositetratidistesseratiapeiratic tetracomb | ||
scadupthix | small capped dipentary tetrishecatonicosahexacosichoron | 2.497212 | 1440, 7200, 9600, 1080 |
scicot | small cellated icositetrachoric tetracomb, small cellated demitesseractic tetracomb, stericated icositetrachoric tetracomb | ||
scyropot | small cyclorhombated pentachoric tetrachomb, small prismatodispentachoric tetracomb, cantellated pentachoric tetrachomb | ||
sedit pathi | small exoditetrahedronary prismatotriakishecatonicosachoron | 2.288246 | 2400, 10800, 8880, 1080 |
... | hyperbolic honeycomb with seed point at edge of right-angled octahedron domain | ||
seedatepthi | small exoditetrahedrary prismatotrishecatonicosachoron | 1.414214 | 2400, 10800, 7920, 1080 |
sefdit dixdy | small exofissary ditrigonal dihexacosadihecatonicosachoron | 1.732051 | 3600, 14400, 11040, 1440 |
sefidtethi | small exofissary ditetrahedronary tetrakishecatonicosachoron | 2.288246 | 2400, 10800, 6720, 480 |
sefradit thix | small exofissary retroditetrahedronary triakishecatonicosihexacosachoron | 2.288246 | 2400, 10800, 6720, 960 |
sesidip | small-snub-icosicosidodecahedron prism | 1.541531 | 120, 420, 404, 114 |
setut | small tristetracosioctacontachoron | 1 | 120, 1200, 3840, 1440 |
sgysrahi | swirl-gyrated small rhombated hecatonicosachoron, swirl-gyrated cantellated hecatonicosachoron | 6.735034 | 3600, 10800, 9720, 2520 |
shafipto | small hexadecafaceted prismatotesseractioctachoron | 1.485633 | 64, 192, 208, 48 |
... | shafipto+32tet (?) | 1.485633 | |
shahoh | small hexadecahemihexadecachoron | 1 | 24, 96, 112, 24 |
shasc | small heptagrammic scalene, small-heptagrammic-pyramidal pyramid, line atop fully orthogonal small heptagramm | 0.658240 | 9, 22, 22, 9 |
shi | snub hecatonicosachoron (but not snahi) | 2.739576 | 1440, 10800, 11040, 1560 |
shiddip, K-4.54 | square - hexagon duoprism | 1.224745 | 24, 48, 34, 10 |
shihi | small hecatonicosihecatonicosachoron | 5.854102 | 3600, 7200, 3360, 240 |
shihix | small hecatonicosihecatonicosihexacosachoron | 2.975584 | 2400, 7200, 5040, 840 |
shinhi | small hecatonicosintercepted hecatonicosachoron | 4.534568 | 1200, 3600, 3840, 240 |
shipady | small hecatonicosiprismatodishecatonicosachoron | 1.814331 | 7200, 18000, 11280, 1080 |
shitte | hyperbolic order 4 hecatonicosachoric tetracomb | 0.899454 i | |
sibricot | small birhombated icositetrachoric tetracomb, grand prismatodisicositetrachoric tetracomb | ||
sichado | small cubihexadecadisoctachoron | 2.370932 | 192, 480, 320, 56 |
sid pippady | small dipentary prismatodishecatonicosachoron | 2.497212 | 1440, 7200, 6480, 960 |
sid thipady | small ditrigonary hecatonicosiprismatodishecatonicosachoron | 1.814331 | 7200, 18000, 10320, 1080 |
sid tipathi | small ditrigonary prismatotriakishecatonicosachoron | 4.179968 | 7200, 18000, 11280, 1560 |
siddapady | small disprismatodishecatonicosachoron | 2 | 2400, 7200, 6480, 1680 |
siddatady | small ditetrahedral dishecatonicosachoron | 2.288246 | 600, 3600, 2160, 240 |
siddic | small distetracontoctachoron | 1.847759 | 144, 576, 528, 96 |
siddiddip | snub-dodecadodecahedron prism | 120, 360, 318, 86 | |
siddit paxhi | small ditetrahedronary hexacosidishecatonicosachoron | 2.288246 | 600, 3600, 7440, 1440 |
siddit thix | small ditrigonal trishecatonicosihexacosachoron | 1.732051 | 1200, 7200, 9360, 960 |
sidditdiddip | small-ditrigonary-dodekicosidodecahedron prism | 1.792631 | 120, 300, 208, 46 |
sidditdy | small ditrigonary dishecatonicosachoron | 1.732051 | 1200, 7200, 4560, 240 |
sidditpix | small ditrigonary prismatohexacosichoron | 1.732051 | 1200, 7200, 8520, 1320 |
sidhiquit paddy | small dishecatonicosaquasitruncated prismatodishecatonicosachoron | 5.605034 | 14400, 28800, 13920, 1080 |
sididdip | snub-icosidodecadodecahedron prism | 120, 420, 388, 106 | |
sidipthi | small dipental trishecatonicosachoron | 2.497212 | 1440, 7200, 4560, 360 |
... | sidpippady+120 2sissid (?) | 2.497212 | |
sidpith | small disprismatotesseractihexadecachoron, runcinated tesseract, small prismated tesseract | 1.485633 | 64, 192, 208, 80 |
sidpixathi | small dipentagonal hexacositrihecatonicosachoron | 2.497212 | 1440, 7200, 6240, 960 |
sidpixhi | small disprismatohexacosihecatonicosachoron, runcinated hecatonicosachoron, runcinated hexacosachoron | 5.236068 | 2400, 7200, 7440, 2640 |
sidrebcu | stellidodecahedral rectibicupola, orbiform bistratc stack of small stellated dodecahedron atop pseudo dodecadodecahedron atop great dodecahedron | 1.064815 | 54, 240, 228, 50 |
sidsrahi | swirl-diminished small rhombated hecatonicosachoron, swirl-diminished cantellated hecatonicosachoron | 6.735034 | 3000, 7800, 6240, 1440 |
sidtaxady | small ditetrahedronary hexacosidishecatonicosachoron | 2.288246 | 600, 3600, 3840, 840 |
sidtaxhi | small ditetrahedronary hexacosihecatonicosachoron | 2.288246 | 600, 3600, 3120, 720 |
sidthidy hi | small ditrigonal hecatonicosadishecatonicosihecatonicosachoron | 1.732051 | 1200, 7200, 8400, 480 |
sidthixhi | small ditrigonary hecatonicosihexacosihecatonicosachoron | 1.773668 | 2400, 7200, 4560, 840 |
sidtidap | small-ditrigonary-icosidodecahedron antiprism | 0.951057 | 40, 180, 184, 54 |
sidtidasiid | small ditrigonary icosidodecahedron atop small icosicosidodecahedron, sidtid cap of stut phiddix | 3.835128 | 80, 240, 204, 54 |
sidtiddip | small-ditrigonary-icosidodecahedron prism | 1 | 40, 140, 124, 34 |
sidtidpy | sidtid pyramid, vertex pyramid of sidtixhi | 1 | 21, 80, 92, 33 |
sidtixhi | small ditrigonary hexacosihecatonicosachoron | 1 | 120, 1200, 2400, 720 |
... | sidtixhi+dox (?) | 1 | |
sifdahihox | small fissary dodecahedronary hecatonicosihemihexacosachoron | 1 | 120, 1200, 3000, 420 |
siida (alt.: siidcup) | small icosicosidodecahedral alterprism, small icosicosidodecahedral cupoliprism, closer siid atop siid | 1.765796 | 120, 360, 284, 54 |
siidip | small-icosicosidodecahedron prism | 1.792631 | 120, 300, 224, 54 |
sik vadixady | small skewverted dishexacosidishecatonicosachoron | 4.684471 | 7200, 21600, 14640, 1440 |
sik vipathi | small skewverted prismatotriakishecatonicosachoron | 2.828427 | 7200, 21600, 13920, 1080 |
sik vixathi | small skewverted hexacositriakishecatonicosachoro | 4.684471 | 7200, 21600, 13680, 960 |
siphado | small prismatohexadecadisoctachoron | 2.613126 | 192, 480, 336, 64 |
siphatit | small diprismatodemitesseractic tetracomb, steric tesseractic tetracomb | ||
siphidy | small prismated hecatonicosadishecatonicosachoron | 4.917351 | 7200, 18000, 10320, 1080 |
sipthi | small prismatotriakishecatonicosachoron | 1.878261 | 7200, 18000, 10320, 1560 |
sipti | small prismatotriakisicositetrachoron | 3.498949 | 576, 1440, 960, 168 |
sirc | small retrotetracontoctachoron | 1.847759 | 144, 576, 432, 48 |
sirco aticu | expanded axially-octahedral ursachoron, (sirco,tic)-based ursulate | 1.806144 | 72, 180, 142, 34 |
sircoa gircotum | bistratic cap of prismatorhombated tesseract, rhombicuboctahedral rotunda, (sirco,girco)-based tutschoron, (sirco,girco)-based tutism | 2.370932 | 96, 216, 154, 34 |
sircoagirco, sirco || girco | (degenerate) small rhombicuboctahedron atop great rhombicuboctahedron | ∞ i.e. flat in euclidean space | 72, 168, 124, 28 |
sircoatic, sirco || tic, K-4.100 | small rhombicuboctahedron atop truncated cube, small-rhombicuboctahedral cap of small rhombated tesseract | 1.847759 | 48, 132, 112, 28 |
sircoatoe, sirco || toe, K-4.75 | small rhombicuboctahedron atop truncated octahedron | 1.582890 | 48, 132, 112, 28 |
sircope, K-4.66 | small-rhombicuboctahedron prism, medial (cube-first) subsegment of sidpith | 1.485633 | 48, 120, 100, 28 |
sirdatady | small retroditetrahedral dishecatonicosachoron | 2.288246 | 600, 3600, 3840, 240 |
... | sirdatady+1440{5/2} | 2.288246 | |
sirdo | small rhombic disoctachoron | 1.847759 | 96, 288, 208, 48 |
sirdop | small rhombidispentachoron | 1.183216 | 30, 90, 70, 20 |
... | sirdop+10{6/2} (?) | 1.183216 | |
sirdtapady | small retroditetrahedronary prismatodishecatonicosachoron | 2.288246 | 600, 7200, 7440, 1440 |
... | sirdtapady+600 2tet (?) | 2.288246 | |
sirdtaxady | small retroditetrahedronary hexacosidishecatonicosachoron | 2.288246 | 600, 3600, 3840, 840 |
sirfix | small rhombated faceted hexacosachoron | 4.352502 | 3600, 10800, 7680, 960 |
sirfixady | small retrofrustary hexacosidishecatonicosachoron | 2.236068 | 3600, 14400, 11040, 840 |
sirfixthi | small retrofrustic hexacositrishecatonicosachoron | 2.236068 | 3600, 14400, 11280, 960 |
sirfthi | small retrofrustary trishecatonicosachoron | 2.236068 | 3600, 14400, 8880, 360 |
sirgaghi | small rhombated great grand hecatonicosachoron | 1.513868 | 3600, 10800, 8160, 1440 |
sirgashi | small rhombated grand stellated hecatonicosachoron | 1.589926 | 3600, 10800, 7200, 960 |
sirgax | small rhombated grand hexacosachoron | 1.054256 | 3600, 10800, 8640, 1440 |
sirghi | small rhombated great hecatonicosachoron | 3.387054 | 3600, 10800, 7200, 960 |
sirpaxhi | small rhombiprismic hexacosahecatonicosachoron | 9.744610 | 7200, 18000, 11040, 1440 |
sirpdi | small rhombiprismic disicosatetrachoron | 3.498949 | 576, 1440, 912, 144 |
sirpdo | small rhombiprismatodisoctachoron | 2.370932 | 192, 480, 304, 48 |
sirphinady | small inverted retropental hecatonicosaintercepted dishecatonicosachoron | 3.077684 | 720, 3600, 6360, 360 |
sirpith | small rhombiprismated tesseractihexadecachoron | 2.613126 | 192, 480, 304, 48 |
sirsashi | small rhombated small stellated hecatonicosachoron | 3.963358 | 3600, 10800, 8160, 1440 |
sirsiddip | small-(inverted)-retrosnub-icosicosidodecahedron prism | 0.766294 | 120, 420, 404, 114 |
sisdipthi | small stellated dipental trishecatonicosachoron | 2.497212 | 1440, 7200, 4560, 360 |
... | sishi+gaghi+120did (?) | 1 | |
... | sishi+gaghi+idhi (?) | 1 | |
... | sishi+gridixhi (?) | 1 | |
... | sishi+idhi (?) | 1 | |
... | sishi+ofiddady (?) | 1 | |
... | sishi+paphicki+gridaphi (?) | 1 | |
sishi, spD | small stellated hecatonicosachoron, stellated polydodecahedron | 1 | 120, 1200, 720, 120 |
sisp | small swirlprism | 1.618034 | 120, 720, 720, 120 |
sissid || 3doe | (degenerate) sissid atop 3doe | ∞ i.e. flat in euclidean space | 72, 180, 126, 26 |
sissidadid, sissid || did | small stellated dodecahedron atop dodecadodecahedron, small-stellated-dodecahedral cupola | 1.064815 | 42, 150, 126, 26 |
sissidadoe | (degenerate) sissid atop doe | ∞ i.e. flat in euclidean space | 32, 120, 114, 26 |
sissidagad, sissid || gad | small stellated decahedron atop great dodecahedron, sissid antiprism, gad antiprism | 1 | 24, 120, 144, 56 |
sissidaraded, sissid || raded | small stellated dodecahedron atop rhombidodecadodecahedron, sissid-first cap of padohi | 2.497212 | 72, 210, 186, 56 |
sissiddip | small-stellated-dodecahedron prism | 0.771681 | 24, 72, 54, 14 |
sissidpy | small-stellated-dodecahedral pyramid, vertex cap of unit gofix, vertex cap of v-scaled gohi | 0.618034 | 13, 42, 42, 13 |
sistadip | square-pentagram duoprism | 0.881132 | 20, 40, 29, 9 |
sistic | small stellated icositetrachoron, compound of 6 hex, compound of 2 stico | 0.707107 | |
sistodip | square - octagram duoprism | 0.890446 | 32, 64, 44, 12 |
sistople (old: stodop) | square-octagram plus-prism, octagram diorthoprism, compound of 2 sistodip | 1.485633 | |
sit thixady | small tritrigonal hecatonicosihexacosidishecatonicosachoron | 3.835128 | 2400, 10800, 7680, 960 |
sitphi | small tripesic hecatonicosachoron | 2.288246 | |
sitpodady | small (intersected) tripesic dodecahedronary dishecatonicosachoron | 1 | 120, 3600, 3120, 240 |
sitwadip | square - dodecagon duoprism | 2.057195 | 48, 96, 64, 16 |
six fipady | small hexacosafaceted prismatodishecatonicosachoron | 5.236068 | 2400, 7200, 7440, 1440 |
sixathi | small hexacositriakishecatonicosachoron | 2.351141 | 7200, 18000, 11280, 960 |
... | six fipady+1200tet (?) | 5.236068 | |
sixhidy | small hexacosihecatonicosadishecatonicosachoron | 2.975584 | 2400, 7200, 5280, 960 |
sixhihy | small hexacosihecatonicosihecatonicosachoron | 5.236068 | 2400, 7200, 4560, 840 |
sixipady | small hexacosiprismatodishecatonicosachoron | 6.881910 | 7200, 18000, 11280, 1560 |
skiv datapixady | small skewverted ditrigonary prismatohexacosadishecatonicosachoron | 4.684471 | 7200, 21600, 14880, 1560 |
skiviphado | small skewverted prismatohexadecadisoctachoron | 1.414214 | 192, 576, 416, 56 |
snappoth | small spinoprismatotesseractihexadecachoron | 1.485633 | 64, 192, 184, 56 |
snet | s3s3s4s, snub tesseract, non-uniform alternation of gidpith | ... | 192, 864, 944, 272 |
sni (old: snico) / snoc | s3s4s3s, (fully) snubbed icositetrachoron (but not sadi) / snubbed tetracontoctachoron, non-uniform alternation of gippic | ... | 576, 2592, 2832, 816 |
sniccap | s2s3s4s, snub-cubic antiprism, non-uniform alternation of gircope | ... | 48, 192, 220, 76 |
sniccup, K-4.60 | snub-cube prism, snub-cuboctahedron prism | 1.433724 | 48, 144, 136, 40 |
sniddap | s2s3s5s, snub-dodecahedral antiprism, non-uniform alternation of griddip | ... | 120, 480, 544, 184 |
sniddip, K-4.110 | snub-dodecahedron prism, snub-icosidodecahedron prism | 2.213060 | 120, 360, 334, 94 |
snifthi | small spinofrustary trishecatonicosachoron | 2.236068 | 3600, 14400, 7680, 360 |
snip / snad | s3s3s3s, snub pentachoron / snub decachoron, non-uniform alternation of gippid | ... | 60, 270, 300, 90 |
snixhi (old: snahi) | s3s3s5s, snub hexacosihecatonicosachoron, (snub hecatonicosachoron (but not shi)), non-uniform alternation of gidpixhi | ... | 7200, 32400, 35040, 9840 |
... | complex polychoron sp-4-o2-3-o2-3-o2 , (γp 4)/p | p3, 6p3, 2p2(2p+3), p(p2+4) | |
sobcated | small bicuntitruncated decachoron, general variant of expanded decachoron, general variant of expanded bideca | sqrt[(2a2+3ab+3b2+2ac+4bc+3c2)/5] | 120, 360, 380, 140 |
sobcotic | small bicuntitruncated tetracontoctachoron, general variant of expanded tetracontoctachoron, general variant of expanded bicont | sqrt[a2+3ab+3b2+2ac sqrt(2)+4bc sqrt(2)+3c2] | 1152, 3456, 3552, 1248 |
soccope | small-cubicuboctahedron prism | 1.485633 | 48, 120, 88, 22 |
socdip | stellated-octagonal duoprism, compound of 4 tes in odip army | 1 | |
sodip, K-4.70 | square - octagon duoprism | 1.485633 | 32, 64, 44, 12 |
sody | small deckishecatonicosachoron, snub decahecatonicosachoron, compound of 10 ex in hi army, compound of 2 spohi | 1.618034 | |
sophi | small prismatohecatonicosachoron | 3.077684 | 720, 3600, 3240, 840 |
sople (old: odop) | square-octagon plus-prism, octagonal diorthoprism, compound of 2 sodip | 1.485633 | |
spaht | small prismated hexadecachoric tetracomb, small disicositetrachoric tetracomb, runcinated demitesseractic tetracomb | ||
spapivady | small pentagrammal antiprismatoverted dishecatonicosachoron | 1.175571 | 720, 3600, 2160, 240 |
... | hexaconta-sphenated id-first deep parabidiminished rahi | ... | 860, 2520, 2180, 520 |
sphiddix | small prismatohecatonicosadishexacosachoron | 6.881910 | 7200, 18000, 12240, 2040 |
sphihix | small prismatohecatonicosahecatonicosahexacosachoron | 5.515107 | 7200, 18000, 11280, 1560 |
sphixhi | small prismatohecatonicosihexacosihecatonicosachoron | 4.179968 | 7200, 18000, 12240, 2040 |
spic | small prismatotetracontoctachoron, runcinated icositetrachoron, expanded icositetrachoron | 1.847759 | 144, 576, 672, 240 |
spict | small prismated icositetrachoric tetracomb, small prismatotetracontaoctachoric tetracomb, runcinated icositetrachoric tetracomb | ||
spid | small prismatodecachoron, runcinated pentachoron, expanded pentachoron, pyroperichoron, tetaco gyrobicupola, vertex figure of cypit, lattice A4 contact polytope (span of its roots), equatorial cross-section of pen-first scad, equatorial cross-section of rap-first rat | 1 | 20, 60, 70, 30 |
spidrico | swirlprismatodiminished rectified icositetrachoron, 24-diminished rectified icositetrachoron | 1.732051 | 72, 288, 288, 72 |
spidrox (alt.: hidrox) | swirlprismatodiminished rectified hexacosachoron, 120-diminished rectified hexacosachoron | 3.077684 | 600, 2400, 2640, 840 |
spidy | swirlprismattic dishecatonicosachoron, compound of 24 starpedip | 1 | |
spittit (old: sidpitit) | small prismatotesseractic tetracomb, small diprismatotesseractic tetracomb, runcinated tesseractic tetracomb | ||
... | q-laced {3} || gyro trip, vertex figure of srix | 0.907485 | 9, 24, 24, 9 |
spixady | small prismatohexacosadishecatonicosachoron | 8.278950 | 7200, 18000, 11280, 1560 |
spixhihy | small prismatohexacosihecatonicosihecatonicosachoron | 9.744610 | 7200, 18000, 12240, 2040 |
spohi | small pentishecatonicosachoron, snub pentahecatonicosachoron, chiral compound of 5 ex in hi army | 1.618034 | |
sporraggix | swirlprismatoreplenished rectified grand hexacosachoron | 0.726543 | 600, 2400, 2640, 840 |
sprapivady | small pentagonal retroprismatoverted dishecatonicosachoron | 3.077684 | 720, 3600, 3120, 240 |
spriphi | small pseudorhombated prismatohecatonicosachoron | 6.735034 | 3600, 10800, 9240, 2040 |
... | spriphi+600 2thah (?) | 6.735034 | |
spript | small pseudorhombated prismatotesseract | 1.847759 | 96, 288, 256, 64 |
... | spript+16 2thah (?) | 1.847759 | |
spysp | small pyramidic swirlprism | 1.618034 | 120, 600, 720, 240 |
squacufbil | square-cupofastegia biluna, rotunda of quawros, square atop squobcu | 20, 52, 51, 19 | |
squacupe, K-4.69 | square-cupola prism, cube atop octagonal prism | 1.485633 | 24, 52, 40, 12 |
squadedip, K-4.97 | square - decagon duoprism | 1.765796 | 40, 80, 54, 14 |
squaf, K-4.14 | square antifastegium, square - squap wedge, {4} || gyro cube, bidiminished octahedral antiprism | 0.879465 | 12, 32, 31, 11 |
... | cubiswirlic heptacontidichoron, twelvefold dissected cubic polytwister, twelvefold dissected cubiter | 1.538189 | 96, 384, 360, 72 |
... | external blend of the square-antiprism prism and 2 cube-pyramids, cubic-pyramid-biaugmented square-antiprism prism | 18, 56, 60, 22 | |
... | external blend of the square-antiprism prism and 2 squap-pyramids, squap-pyramid-biaugmented square-antiprism prism | 18, 56, 68, 30 | |
squappip, K-4.19 | square-antiprism prism | 0.962692 | 16, 40, 36, 12 |
squappy | square-antiprismatical pyramid | 0.879465 | 9, 24, 26, 11 |
squapt | (line-)square-antiprismatic tegum, square-antiprismatic bipyramid, square-pyramidal antiprism | 10, 32, 42, 20 | |
squasc (old: squippypy, alt: edihex), 4pyr-pyr, K-4.4 | square-scalene, square-pyramidal pyramid, line atop fully orthogonal square, 1/4-luna of hex, 4 tet rosette, edge-diminished hex | 0.707107 | 6, 13, 13, 6 |
... | squashed hexaconta-sphenated id-first deep parabidiminished rahi | ... | 600, 1740, 1488, 348 |
squaw, K-4.64, {8} || squap | antitetrawedge, octagon - square-antiprismatic wedge, square gyrobicupolaic ring, {8} || squap, {4} || gyrated squacu | 1.447009 | 16, 30, 35, 11 |
squicuf, K-4.73 | square cupofastegium, octagon - cube wedge of sidpith, square orthobicupolaic ring, {8} || cube, {4} || squacu, 1/4-luna of quawros | 1.485634 | 16, 36, 31, 11 |
squipdip, K-4.42 | square-pentagon duoprism | 1.106168 | 20, 40, 29, 9 |
squippia squacu, K-4.109 | square pyramid atop square cupola | 1.847759 | 17, 40, 35, 12 |
squippiaco, K-4.31 | square-pyramid atop cuboctahedron | 1 | 17, 52, 51, 16 |
squippiatricu, K-4.32 | square-pyramid atop triangular-cupola | 1 | 14, 37, 35, 12 |
squippyal cube, K-4.16 | squippy atop gyro cube | 0.879465 | 13, 40, 47, 20 |
squippyp, K-4.12 | square-pyramidal prism, J1 prism, line || cube, digonal magnabicupolaic ring | 0.866025 | 10, 21, 18, 7 |
squipuf, K-4.105 | square pucofastegium, square - octagon-prismatic wedge, square magnabicupolaic ring, {4} || op, {8} || squacu, square-cap of srit | 1.847759 | 20, 44, 35, 11 |
squobcupe | square orthobicupola prism, J28 prism | ... | 32, 80, 68, 20 |
sradditdahix | small retroditetrahedronary dishecatonicosihexacosachoron | 2.288246 | 600, 3600, 5280, 840 |
sraghi | small rhombated grand hecatonicosachoron | 2.689994 | 3600, 10800, 8160, 960 |
srahi | small rhombated hecatonicosachoron, cantellated hecatonicosachoron | 6.735034 | 3600, 10800, 9120, 1920 |
srawv ditathi | small retrosphenoverted ditrigonary triakishecatonicosachoron | 3.294556 | 3600, 10800, 7680, 360 |
srawv hidy | small retrosphenoverted hecatonicosadishecatonicosachoron | 3.387054 | 3600, 10800, 6000, 360 |
srawv hixhi | small retrosphenoverted hecatonicosihexacosihecatonicosachoron | 6.073594 | 3600, 10800, 7440, 840 |
srawvathi | small retrosphenoverted triakishecatonicosachoron | 4.352502 | 3600, 10800, 5520, 360 |
srawvixady | small retrosphenoverted hexacosadishecatonicosachoron | 6.735034 | 3600, 10800, 6960, 840 |
srico | small rhombated icositetrachoron, cantellated icositetrachoron | 2.613126 | 288, 864, 720, 144 |
sricot | small rhombated demitesseractic tetracomb, small prismatodisicositetrachoric tetracomb | ||
..., xFoFx3ooooo5xofox&#xt (F=ff=x+f) | bilunabirotundic rhombicosidodecahedron prism, castellated rhombicosidodecahedral prism | 164, 492, 424, 96 | |
srida gridtum | bistratic srid-cap of prahi, (srid,grid)-based tutsachoron, (srid,grid)-based tutism | 8.278950 | 240, 540, 376, 76 |
sridaphi | small retroinverted dodecahedronary prismatohecatonicosachoron | 1 | 120, 1200, 4200, 1320 |
sridati, srid || ti, K-4.126 | small-rhombicosidodecahedron atop truncated-icosahedron | 2.485450 | 120, 330, 274, 64 |
sridatid, K-4.159 | small rhombicosidodecahedron atop truncated dodecahedron, small-rhombicosidodecahedral cap of small rhombated hecatonicosachoron | 6.735034 | 120, 330, 274, 64 |
sridatidu | expanded axially-icosahedral ursachoron, (srid,tid)-based ursulate | 3.077684 | 180, 450, 356, 76 |
sriddip, K-4.111 | small-rhombicosidodecahedron prism | 2.288246 | 120, 300, 244, 64 |
sridixhi | small retroinverted dodecahedronary hexacosahecatonicosachoron | 1 | 120, 1200, 3120, 720 |
sridtathi | small retroinverted ditetrahedronary trishecatonicosachoron | 2.288246 | 600, 3600, 4560, 360 |
srip | small rhombated pentachoron, cantellated pentachoron | 1.183216 | 30, 90, 80, 20 |
sripady | small rhombiprismic dishecatonicosachoron | 8.278950 | 7200, 18000, 11040, 1440 |
sriphi | small retropental hecatonicosachoron | 3.077684 | 720, 3600, 2520, 120 |
srit | small rhombated tesseract, cantellated tesseract | 1.847759 | 96, 288, 248, 56 |
srittit | small rhombitesseractic tetracomb, cantellated tesseractic tetracomb | ||
srix | small rhombated hexacosachoron, cantellated hexacosachoron | 6.073594 | 3600, 10800, 8640, 1440 |
stacupe | pentagrammic-cupola prism, stip atop 2pip | 0.874032 | 30, 65, 49, 14 |
stadidip | decagram-decagram duoprism | 0.874032 | 100, 200, 120, 20 |
stafe | stellar (pentagrammal) antifastegium, pentagram - stap wedge, {5/2} || gyro stip | 0.535857 | 15, 40, 38, 13 |
stapedit | ({5/2},{5})-duotegum, tegum product of a pentagon and a pentagram | 10, 35, 50, 25 | |
stapepy | pentagram-antiprismatical pyramid | 0.662791 | 11, 30, 32, 13 |
stappip | pentagramic-antiprism prism | 0.825168 | 20, 50, 44, 14 |
stappyp | pentagram-pyramidal prism, line || stip | 0.771681 | 12, 26, 22, 8 |
stardedip | pentagram - decagon duoprism | 1.701302 | 50, 100, 65, 15 |
stardip | pentagram-pentagram duoprism | 0.743496 | 25, 50, 35, 10 |
starodip | pentagram - octagon duoprism | 1.408368 | 40, 80, 53, 13 |
starpedip (old: stipdip, starpendip) | pentagram-pentagon duoprism, stellar (pentagonal) pentagonal diprism | 1 | 25, 50, 35, 10 |
starpglassit | pentagrammic-retroprismatic-hourglass tegum, pentagrammic-retroprismatic-hourglass bipyramid | 0.707107 | 12, 30, 27, 9 |
stasc (old: stappypy) | stellar scalene, pentagrammic scalene, pentagram-pyramidal pyramid, line atop fully orthogonal pentagram, 5 tet two-step rosette | 0.618034 | 7, 16, 16, 7 |
stastidedip | pentagram - decagram duoprism | 0.811393 | 50, 100, 65, 15 |
stastodip | pentagram - octagram duoprism | 0.754511 | 40, 80, 53, 13 |
staw | pentagrammic gyrobicupolaic ring, star antiwedge, {10/2} || stap | 0.870153 | 20, 50, 43, 13 |
stawros | pentagrammic ({10} || pip-)wedge rosette, bridge cyclopentaaugmented starpedip, ring-augmented starpedip | 35, 110, 130, 55 | |
sted | stellated decachoron, compound of 2 pen | 0.632456 | |
stefacoth | small tesseractifaceted cubitesseractihexadecachoron | 1.485633 | 64, 192, 208, 48 |
steth | small tesseractitesseractihexadecachoron | 1.485633 | 64, 192, 136, 32 |
stico (old: sico) | stellated icositetrachoron, stella tegmata, compound of 3 hex | 0.707107 | |
stidox | stellated dodecahedral hexacosachoron, compound of 75 hex in ex army, compound of 25 stico in ex army | 0.707107 | |
stippy | stellated-pentagonal prismatic pyramid, vertex pyramid of the rectified grand hexacosachoron | 0.726543 | 11, 25, 22, 8 |
stisaw | reduced pentagrammic gyrobicupolaic ring, star semiantiwedge, pseudo {10/2} || stap | 0.870153 | 15, 45, 42, 13 |
sto | small trisoctachoron, small triakisoctachoron | 1.224745 | 32, 96, 96, 24 |
... | sto+16tet (?) | 1.224745 | |
stoc | stellated tetracontoctachoron, compound of 2 ico | 1 | |
stodatixhi | small toroidoditrigonary hexacosihecatonicosachoron | 1.732051 | 1200, 7200, 5520, 720 |
stodip | octagram-octagram duoprism | 0.765367 | 64, 128, 80, 16 |
stoditpix | small toroidoditrigonary prismatohexacosichoron | 1.732051 | 1200, 7200, 8520, 1320 |
stut dixady | small tritrigonal dihexacosidihecatonicosachoron | 3.835128 | 2400, 10800, 8640, 1440 |
stut phiddix | small tritrigonal prismatohecatonicosidishexacosachoron | 3.835128 | 2400, 10800, 9840, 2040 |
stut pixady | small tritrigonal prismatohexacosidihecatonicosachoron | 3.835128 | 2400, 10800, 8880, 1560 |
stut thix | small tritrigonal trishecatonicosihexacosachoron | 3.835128 | 2400, 10800, 7680, 960 |
stut xethi | small tritrigonal hexacositrishecatonicosachoron | 3.835128 | 2400, 10800, 7680, 960 |
stuttixady | small tritrigonary hexacosidishecatonicosachoron | 3.835128 | 2400, 10800, 9840, 840 |
suti | small tetrakisicositetrachoron | 1.608038 | 576, 1440, 960, 96 |
swav ditathi | small sphenoverted ditrigonary triakishecatonicosachoron | 2.572554 | 3600, 10800, 6000, 360 |
swavathi | small sphenoverted triakishecatonicosachoron | 2.093315 | 3600, 10800, 6960, 360 |
swavixady | small sphenoverted hexacosadishecatonicosachoron | 3.294556 | 3600, 10800, 7440, 840 |
tabene | trigonal-bipyramidal enneacontahexachoron, joined icositetrachoron, rectified-icositetrachoron dual, surtegmated icositetrachoron | 48, 240, 288, 96 | |
tadeca | truncated decachoron | sqrt(2y2+7y+7) | 120, 240, 160, 40 |
taggix | truncated grand hexacosachoron | 1.199039 | 1440, 4320, 3600, 720 |
taghi | truncated grand hecatonicosachoron | 3.477092 | 1440, 4320, 3120, 240 |
tah | tesseractihexadecachoron, bitruncated tesseract, bitruncated hexadecachoron, runcicantic tesseract | 2.121320 | 96, 192, 120, 24 |
tahi | triakishecatonicosachoron | 2 | 2400, 7200, 4080, 360 |
tastic | truncated stellated tetracontoctachoron, compound of 2 truncated icositetrachora | 2.645751 | |
tat | truncated tesseract | 2.149726 | 64, 128, 88, 24 |
tatriddip | truncated triangular duoprism | sqrt[(2y2+5y+5)/3] | 36, 72, 51, 15 |
tattit | truncated tesseractic tetracomb | ||
tau ope | tetra-augmented ope | 16, 54, 64, 26 | |
tau tope | tetra-augmented tope | 60, 156, 140, 44 | |
tautipip | triaugmented-triangular-prism prism | 18, 51, 49, 16 | |
tautisdip | triaugmented 3,4-duoprism | ... | 15, 48, 55, 22 |
teddi adoe, teddi || doe, K-4.83 | tridiminished-icosahedron atop dodecahedron, triminished segment of vertex-first hexacosachoron | 1.618034 | 29, 90, 95, 34 |
teddi aid, teddi || id, K-4.147 | tridiminished icosahedron atop icosidodecahedron | 3.077684 | 39, 120, 115, 34 |
teddipe | tridiminished-icosahedron prism | 1.074481 | 18, 39, 31, 10 |
teddipy, K-4.88 | tridiminished-icosahedral pyramid | 1.618034 | 10, 24, 23, 9 |
tedope | tetra(hedrally) diminished octahedronal prism | 0.866025 | 8, 22, 26, 12 |
tehipau tuttip | hip-wise tetra-augmented tuttip | 36, 108, 110, 38 | |
telex | vertex first tele-elongated hexacosachoron | 138, 654, 800, 284 | |
tepe, K-4.9 (alt: dycuf) | tetrahedron prism, line || trip, square - square bi-wedge, digonal orthobicupolaic ring, vertex figure of rix, dyadic cupolafastegium, equatorial cross-section of tet-first hin | 0.790569 | 8, 16, 14, 6 |
teppix (old: dattix) | tripesic hexacosachoron, compound of 60 deca | 1.414214 | |
tes (alt.: squadip), K-4.20 | tesseract, octachoron, "hypercube", 4D measure-polytope (γ4), 8-cell, geoter(id), square duoprism, vertex figure of icot | 1 | 16, 32, 24, 8 |
test | tesseractic tetracomb, 4D hypercubical honeycomb (δ4), Voronoi complex of C4 lattice, Delone complex of C4 lattice | ||
tetacho | tetrahedron atop cubohemioctahedron | 1 | 16, 42, 38, 12 |
tetaco altut | tetrahedron atop cuboctahedron atop inverted truncated tetrahedron | ... | 28, 84, 80, 24 |
tetaco ausrip | tetaco-augmented srip | 34, 108, 102, 28 | |
tetaco, tet || co, K-4.23 | tetrahedron atop cuboctahedron, tetrahedral rotunda of small prismatodecachoron | 1 | 16, 42, 42, 16 |
tetacoa cube | tetrahedron atop cuboctahedron atop cube | ... | 24, 78, 84, 30 |
tetacoaoct | octahedron atop (pseudo) cuboctahedron atop tetrahedron | 1 | 22, 78, 86, 30 |
tetaltut, tet || inv. tut | (degenerate) tetrahedron atop inverted truncated tetrahedron, (degenerate) tetrahedron atop alternate truncated tetrahedron | ∞ i.e. flat in euclidean space | 16, 48, 48, 16 |
tetatricu, tet || tricu, K-4.24 | tetrahedron atop trigonal cupola, 0.290215-luna of small prismatodecachoron | 1 | 13, 30, 27, 10 |
tetatut, K-4.56 | tetrahedron atop truncated tetrahedron, tetrahedral cap of rectified tesseract | 1.224745 | 16, 36, 30, 10 |
tete (old: tedpy) | (line-)tetrahedron-tegum, tetrahedral bipyramid | 6, 14, 16, 8 | |
tetripau tuttip | trip-wise tetra-augmented tuttip | 28, 72, 70, 26 | |
tetu | axially-tetrahedral ursachoron ofx3xoo3ooo&#xt, tet-based ursulate, vertex figure of sadit | 1 | 14, 34, 30, 10 |
tewau thawrorh | tetra-augmented thawro rhombochoron | ... | 78, 342, 410, 146 |
tex | truncated hexacosachoron | 4.643523 | 1440, 4320, 3600, 720 |
thahp | tetrahemihexahedral prism, vertex figure of rhohid | 0.866025 | 12, 30, 26, 9 |
thaquitoth | tesseractihexadecaquasitruncated tesseractihexadecachoron | 1.338990 | 192, 384, 200, 32 |
thaquitpath | tesseractihexadecaquasitruncated prismatotesseractihexadecachoron | 1.608038 | 384, 768, 416, 56 |
thatgyt | triangular-hexagonal tiling gyrotrigonism | ||
thatoth | tesseractihexadecatruncated tesseractihexadecachoron | 1.790840 | 192, 384, 200, 32 |
thatpath | tesseractihexadecatruncated prismatotesseractihexadecachoron | 2.326846 | 384, 768, 416, 56 |
... | thawro pyrite, octa-diminishing of id - srid - F-ike - ti tower | ... | 138, 438, 418, 118 |
... | thawro wedge | ... | 21, 60, 60, 21 |
thawrorh | thawro rhombochoron | ... | 66, 246, 262, 82 |
... | thawro-wedged 1/6-luna of hexacosachoron | ... | 37, 150, 201, 88 |
... | thawro-wedged 2/6-luna of hexacosachoron | ... | 56, 264, 379, 171 |
thex | truncated hexadecachoron, cantic tesseract, equatorial cross-section of hex-first tot | 1.581139 | 48, 120, 96, 24 |
thext | truncated hexadecachoric tetracomb, truncated demitesseractic tetracomb, cantic tesseractic tetracomb | ||
thi | truncated hecatonicosachoron | 8.218334 | 2400, 4800, 3120, 720 |
thiddip, K-4.47 | triangle - hexagon duoprism, hexagon - hip wedge | 1.154701 | 18, 36, 27, 9 |
tho | tesseractihemioctachoron, octahemioctachoron, vertex figure of hehad | 0.707107 | 8, 24, 32, 12 |
thoot thibbit | tomohexagonal-omnitruncated-trihexagonal duoprismatic tetracomb | ||
thorahbit | tomohexagonal-rhombitrihexagonal duoprismatic tetracomb | ||
thot thibbit | trihexagonal-omnitruncated-trihexagonal duoprismatic tetracomb | ||
tiatid, ti || tid, K-4.151 | truncated icosahedron atop truncated dodecahedron | 3.835128 | 120, 300, 244, 64 |
tibbic | triangular-bipyramidal chilliadiacosichoron, rectified-hecatonicosachoron dual, surtegmated hexacosachoron | 720, 3120, 3600, 1200 | |
tibbid (alt.: durap) | triangular-bipyramidal decachoron, rectified-pentachoron dual, surtegmated pentachoron, joined pentachoron | 10, 30, 30, 10 | |
tibbit | triangular-bipyramidal triacontadichoron, rectified-tesseract dual, surtegmated hexadecachoron | 24, 88, 96, 32 | |
... | expanded augmented axially-octahedral ursachoron ofx3xoo4xxx&#xt | 80, 216, 196, 60 | |
tica gircobcu | ticagirco bicupola | 96, 240, 198, 54 | |
ticagirco, K-4.128 | truncated cube atop great rhombicuboctahedron, truncated-cubical cap of prismatorhombated hexadecachoron, cuboctahedral supra-cap of small rhombated icositetrachoron | 2.613126 | 72, 156, 112, 28 |
ticcup, K-4.99 | truncated-cube prism | 1.847759 | 48, 96, 64, 16 |
tico | truncated icositetrachoron, cantitruncated hexadecachoron | 2.645751 | 192, 384, 240, 48 |
ticont | truncated tetracontoctachoron | sqrt[(6+4 sqrt(2))y2+(23+16 sqrt(2))y+(23+16 sqrt(2))] | 1152, 2304, 1488, 336 |
ticot | truncated icositetrachoric tetracomb | ||
... | expanded augmented axially-icosahedral ursachoron ofxo3xooo5xxxx&#xt | 200, 540, 478, 138 | |
... | triaconta-sphenated id-first tristratic sub-cap of rahi | ... | 300, 840, 706, 166 |
tidagrid, tid || grid, K-4.173 | truncated dodecahedron atop great rhombicosidodecahedron, truncated-dodecahedral cap of prismatorhombated hexacosichoron | 9.744610 | 180, 390, 274, 64 |
tiddip, K-4.130 | truncated-dodecahedron prism | 3.011250 | 120, 240, 154, 34 |
tidimex (alt.: idimtex) | truncated icosidiminished hexacosachoron, icosidiminished truncated hexacosachoron | 4.643523 | 960, 2280, 1640, 320 |
tidox (old: togex) | truncated dodecahedronary-hexacosachoron (truncated great hexacosachoron), compound of 25 tico | 2.645751 | |
tidtes | tetra-diminished tesseract | 1 | 12, 36, 36, 12 |
tidtidohi | truncated ditrigonary dishecatonicosachoron | 2.645751 | 2400, 8400, 5280, 360 |
tiffix | truncated faceted hexacosichoron | 4.643523 | 1440, 4320, 2640, 240 |
tigaghi | truncated great grand hecatonicosachoron | 2 | 2400, 4800, 2160, 240 |
tigfix | truncated great faceted hexacosichoron | 1.199039 | 1440, 4320, 2640, 240 |
tiggia gaquatid | truncated great icosahedron atop great quasitruncated icosidodecahedron | 1.120533 | 180, 390, 274, 64 |
tiggidtixhi | truncated great ditrigonary hexacosihecatonicosachoron | 2.645751 | 2400, 8400, 6240, 840 |
tiggipe | truncated-great-icosahedron prism | 1.165943 | 120, 240, 154, 34 |
tighi | truncated great hecatonicosachoron | 3.477092 | 1440, 4320, 2160, 240 |
tigiddip | truncated-great-dodecahedron prism | 1.942303 | 120, 240, 138, 26 |
tigikaike | truncated gikaike | 2.645751 | 240, 600, 424, 76 |
... | vertex figure of triacontadipenteract | 0.935414 | 8, 24, 32, 12 |
tip (alt: tettum) | truncated pentachoron, tet-based tutsatope, tet-based tutism | 1.264911 | 20, 40, 30, 10 |
tipe, K-4.127 | truncated-icosahedron prism | 2.527959 | 120, 240, 154, 34 |
tisadi (alt.: idtex) | truncated snub icositetrachoron, icositetradiminished truncated hexacosachoron | 4.643523 | 864, 1872, 1248, 240 |
tiscsrix | tristratic icosidodecahedron-first cap of small rhombihexacosachoron | 6.073594 | 270, 690, 516, 96 |
tisdip, K-4.18 | triangle - square duoprism, square - cube wedge, vertex figure of nit | 0.912871 | 12, 24, 19, 7 |
tispic | truncated small prismated tetracontoctachoron | sqrt[(2+sqrt(2))y2+(7+4 sqrt(2))y+(7+4 sqrt(2))] | 1152, 2880, 2112, 384 |
tispid | truncated small prismated decachoron | sqrt(y2+3y+3) | 120, 300, 230, 50 |
tissidtixhi | truncated small ditrigonary hexacosihecatonicosachoron | 2.645751 | 2400, 8400, 6240, 840 |
tistadip | triangle - pentagram duoprism, pentagram - stip wedge | 0.780850 | 15, 30, 23, 8 |
tisted | truncated stellated decachoron, compound of 2 truncated pentachora | 1.264911 | |
tisthit | triangular-simotrihexagonal tetracomb | ||
tistodip | triangle - octagram duoprism, octagram - stop wedge | 0.791345 | 24, 48, 35, 11 |
titepe | truncated tetrahedral prism | sqrt[(5y2+12y+12)/8] | 32, 64, 46, 14 |
titho | truncated tesseractihemioctachoron | 1.581139 | 48, 120, 88, 20 |
titwadip | triangle - dodecagon duoprism, dodecagon - twip wedge | 2.016280 | 36, 72, 51, 15 |
toagirco, toe || girco, K-4.149 | truncated octahedron atop great rhombicuboctahedron, truncated octahedral cap of prismatorhombated icositetrachoron | 3.498949 | 72, 156, 112, 28 |
toagircoatic | toe atop girco atop tic | 96, 240, 198, 54 | |
toatic, toe || tic, K-4.98 | truncated octahedron atop truncated cube | 1.785406 | 48, 120, 100, 28 |
tobcuatut, tobcu || tut, K-4.49 | triangular-orthobicupola atop truncated-tetrahedron | 1.183216 | 24, 66, 61, 19 |
tobcupe, K-4.44 | triangular-orthobicupola prism | 1.118034 | 24, 60, 52, 16 |
tocap | toroidal cycloantiprism | 1 | 50, 200, 260, 110 |
todip, K-4.59 | triangle - octagon duoprism, octagon - op wedge | 1.428440 | 24, 48, 35, 11 |
todithix | toroidoditrigonary hecatonicosihexacosichoron | 1.732051 | 1200, 7200, 7440, 720 |
todtixhi | toroidal ditrigonal hexacosihecatonicosachoron | 1.732051 | 1200, 7200, 6600, 720 |
... | vertex figure of topax | 0.907485 | 9, 24, 24, 9 |
tope, K-4.89 | truncated-octahedron prism | 1.658312 | 48, 96, 64, 16 |
tosot thibbit | tomosquare-omnitruncated-trihexagonal duoprismatic tetracomb | ||
tracufbil | triangular-cupofastegia biluna, {3} || tricu || {3}, 0.419569-luna of gyspid | 1 | 15, 39, 40, 16 |
traddet | triangular antiditetragoltriate | sqrt[(a22+b22)/3] | 18, 72, 96, 42 |
tradedip, K-4.94 | triangle - decagon duoprism, decagon - dip wedge | 1.717954 | 30, 60, 43, 13 |
traf, K-4.6 | triangular antifastegium, triangle oct wedge, {3} || gyro trip, {3} || oct, (vertex-) diminished rap | 0.774597 | 9, 24, 24, 9 |
... | icosaswirlic hexacosachoron, thirtyfold dissected icosahedral polytwister, thirtyfold dissected ikter | ... | 360, 2160, 2400, 600 |
... | octaswirlic enneacontahexachoron, twelvefold dissected octahedral polytwister, twelvefold dissected octer | 1.255926 | 72, 360, 384, 96 |
trapedip, K-4.34 | triangle - pentagon duoprism, pentagon - pip wedge | 1.028076 | 15, 30, 23, 8 |
trateddi, {3} || teddi, K-4.33 | {3} atop teddi, teddi based wedge | 1 | 12, 33, 33, 12 |
tratgyt | triangular tiling gyrotrigonism | ||
traw, K-4.27 | trigonal antitriwedge, hexagon - octahedral wedge, triangular gyrobicupolaic ring, {6} || oct, {3} || gyrated tricu, 1/6-luna of ico | 1 | 12, 30, 27, 9 |
tribbit | triangular duoprismatic tetracomb, triangular biprismated tetracomb, Delone complex of bihexagonal lattice A2×A2 | ||
tricuatut, tricu || tut, K-4.50 | triangular-cupola atop truncated-tetrahedron | 1.183216 | 21, 51, 43, 13 |
tricuf, K-4.25 | trigonal cupofastegium, hexagon - triangle-prismatic wedge, triangle orthobicupolaic ring, {6} || trip, {3} || tricu, 0.209785-luna of small prismatodecachoron | 1 | 12, 27, 24, 9 |
tricupe, K-4.45 | triangular-cupola prism, triangular prism atop hexagonal prism | 1.118034 | 18, 39, 31, 10 |
triddap | triangle duoantiprism, hemiated hiddip | 1.414214 | 18, 72, 84, 30 |
triddep | triangular duoexpandoprism, expanded triddip, tegum sum of 2 alternated thiddips | 1.154701 | 36, 108, 120, 48 |
triddet | triangular ditetragoltriate | sqrt[(a2+b2)/3] | 18, 45, 42, 15 |
triddip, K-4.10 | triangle-triangle duoprism, triangle - trip wedge, vertex figure of dot, Delone cell of lattice A2×A2, equatorial cross-section of trig-first rix | 0.816497 | 9, 18, 15, 6 |
triddit | triangle duotegum, dual of triangle duoprism, 6-2-stepprism | 0.707107 | 6, 15, 18, 9 |
tridex | tri-icositetradiminished hexacosachoron, tetragonal-antiwedge heptacontadichoron | 1.618034 | 48, 192, 216, 72 |
tridico (alt.: cytid ico) | (cyclo)tridiminished ico | 1 | 21, 72, 78, 27 |
tridpyp | triangular-bipyramid prism, tetrahedral prism bicupola, external blend of 2 tetrahedral prisms | 10, 23, 21, 8 | |
..., trip || gybef | triangular prism || gyrobifastegium | ... | 14, 37, 38, 15 |
trippy, K-4.7 | trigonal-prismatic pyramid, vertex pyramid of the rectified pentachoron | 0.774597 | 7, 15, 14, 6 |
tript | trigonal-prismatic (line-)tegum, trigonal-prismatic dipyramid | ... | 8, 21, 23, 10 |
tripuf, K-4.51 | trigonal pucofastegium, triangle - hexagon-prismatic wedge, trigonal magnabicupolaic ring, {3} || hip, {6} || tricu, {3}-first cap of srip | 1.183216 | 15, 33, 27, 9 |
trisqdip | trisquare duoprism, compound of 9 tes in twaddip army | 1 | |
tritep (alt: dycufbil) | (line-)triangle-tegum prism, triangular-bipyramidal prism, dyadic cupofastegia biluna | 10, 23, 21, 8 | |
... | truncated generalized Shephard hexadecachoron, complex polychoron op-4-o2-3-x2-3-x2 | 12p2, 6p2(2p+1), 4p3(p+1), p(p3+4) | |
... | truncated Witting polychoron, complex polychoron x3-3-x3-3-o3-3-o3 | 6480, 19440, 8640, 480 | |
... | truncated hyperbolic o4x4o3*a4x4o3*a tetracomb | ... | |
... | truncated generalized Shephard tesseract, complex polychoron xp-4-x2-3-o2-3-o2 | 4p4, 2p3(3p+2), 2p2(2p2+3), p(p3+4) | |
tubidrap | blend of 2 bidraps | 0.774597 | 12, 32, 32, 11 |
turap | two rectified-pentachoron cupolaic blend | 0.774597 | |
... | expanded augmented axially-tetrahedral ursachoron ofxo3xooo3xxxx&#xt | 40, 108, 102, 34 | |
tuta (alt.: pabdirit, tutcup, tutaltut), tut || inv tut, K-4.55 | truncated tetrahedral alterprism, truncated tetrahedral cupoliprism, runcic snub cubic hosochoron, truncated tetrahedron atop inverted truncated tetrahedron, truncated tetrahedron atop alternate truncated tetrahedron, tetrahedrally medial part of rectified tesseract, parabidiminished rectified tesseract | 1.224745 | 24, 60, 52, 16 |
tutatoa sirco | truncated tetrahedron atop truncated octahedron atop small rhombicuboctahedron | ... | 60, 174, 158, 42 |
tutatobcu | tutatoe orthobicupola | 48, 120, 102, 30 | |
tutatoe augrip | tutatoe-augmented grip | 72, 162, 118, 28 | |
tutatoe gybcu | tutatoe gyrobicupola | 48, 120, 102, 30 | |
tutatoe, tut || toe, K-4.76 | truncated tetrahedron atop truncated octahedron, truncated-tetrahedral cap of prismatorhombated pentachoron, tetrahedral canticupola | 1.612452 | 36, 78, 58, 16 |
tutepe | blend of 2 tepes | 0.790569 | 12, 28, 26, 10 |
tutrippapy | tutrip pyramid, internal blend of 2 trippies | 0.774597 | 9, 22, 22, 9 |
tutrippy | external blend of 2 trippies | ... | 10, 26, 27, 11 |
tuttip, K-4.57 | truncated-tetrahedron prism | 1.274755 | 24, 48, 34, 10 |
twaddip | dodecagonal-dodecagonal duoprism | 2.732051 | 144, 288, 168, 24 |
twagy griddip | twelve-gyro-augmented great-rhombated-icosidodecahedral prism | 300, 780, 676, 196 | |
twagy tiddip | twelve-gyro-augmented truncated-icosidodecahedral prism | 180, 540, 526, 166 | |
twau doaid | deep mono-diminished rotunda of ex, 12-augmented doe || id | 1.618034 | 62, 270, 374, 166 |
twau griddip | twelve-(ortho-)augmented great-rhombated-icosidodecahedral prism | 300, 780, 676, 196 | |
twau iddip | twelve-augmented icosidodecahedral-prism | 72, 270, 304, 106 | |
twau sridati | twelve-augmented sridati | 132, 450, 514, 196 | |
twau sriddip | twelve-augmented sriddip | 132, 420, 424, 136 | |
twau tiddip | twelve-(ortho-)augmented truncated-icosidodecahedral prism | 180, 540, 526, 166 | |
twau tipe | twelve-augmented truncated-icosahedral prism | 132, 360, 334, 106 | |
twausniddip | twelve-augmented sniddip | 132, 480, 514, 166 | |
... | Waterman polychoron number 3 wrt. cyclo-pentachoric lattice A4 centered at a lattice point | 1.732051 | 60, 240, 230, 50 |
... | external blend of the sphenocorona-prism and a cube-pyramid, cubic-pyramid-augmented sphenocorona-prism | 21, 62, 62, 21 | |
wavathi | sphenoverted triakishecatonicosachoron | 1.662508 | 3600, 10800, 6000, 360 |
wavaty | sphenoverted triakisicositetrachoron | 1.082392 | 288, 864, 576, 72 |
wavdatixady | sphenoverted ditrigonary hexacosadishecatonicosachoron | 1.258409 | 3600, 10800, 6960, 840 |
wavhiddix | sphenoverted hecatonicosadishexacosachoron | 5.330704 | 3600, 10800, 7920, 1320 |
wavitoth | sphenoverted tesseractitesseractihexadecachoron | 0.765367 | 96, 288, 200, 32 |
... | wx ox3xx4oo&#zx | 72, 192, 164, 44 | |
... | wx ox3xx4xx&#zx | 144, 360, 296, 80 | |
... | tricupe variant wx xx3oq&#q | 1.402029039 | 18, 39, 31, 10 |
... | hyperbolic x3o3o3o *b3o3*c tesselation | 0.387298 | |
... | x3o3o4q, variation of sidpith | 1.870829 | 64, 192, 208, 80 |
... | hyperbolic pentagrammic-order hexacontachoric tetracomb | 0.393076 i | |
... | x3o3o5v, variation of small disprismatohexacosihecatonicosachoron | 3.835128 | 2400, 7200, 7440, 2640 |
... | hyperbolic hex-ex tetracomb | 0.171780 i | |
... | x3o3β4o (?) | ... | 96, 384, 304, 56 |
... | x3o3β4x (?) | ... | 192, 672, 576, 136 |
... | x3o3β5o (?) | ... | 3600, 18000, 14640, 2640 |
... | x3o3β5x (?) | ... | 7200, 25200, 19440, 3840 |
... | hyperbolic order 4 icositetrachoral tetracomb | 0 i | |
... | x3o4β3o (?) | ... | 288, 1152, 1056, 264 |
... | x3o4s4o (?) | ... | |
... | hyperbolic order 5 faceted-hexacosichoral tetracomb, hyperbolic order 5 icosahedral-hecatonicosachoral tetracomb, hyperbolic ridged pentachoric tetracomb | 0.393076 i | |
... | x3β3o3o (?) | ... | 20, 100, 80, 20 |
... | x3β3o3β (?) | ... | 60, 270, 240, 60 |
... | x3β3o3x (?) | ... | 60, 210, 170, 40 |
... | x3β3o4o (?) | ... | 48, 312, 240, 48 |
... | x3β3o4β (?) | ... | 192, 768, 656, 152 |
... | x3β3o4x (?) | ... | 192, 672, 512, 104 |
... | x3β3o5o (?) | ... | 1440, 11520, 8640, 1440 |
... | x3β3o5β (?) | ... | 7200, 32400, 27840, 6240 |
... | x3β3o5x (?) | ... | 7200, 25200, 18480, 3360 |
... | x3β3β3x (?) | ... | 120, 360, 290, 60 |
... | x3β3β4o (?) | ... | 192, 672, 592, 128 |
... | x3β3β4β (?) | ... | 384, 1344, 1248, 304 |
... | x3β3β4x (?) | ... | 384, 1152, 960, 208 |
... | x3β3β5o (?) | ... | 7200, 28800, 25440, 5040 |
... | x3β3β5β (?) | ... | 14400, 50400, 46080, 10680 |
... | x3β3β5x (?) | ... | 14400, 50400, 33840, 6240 |
... | x3β3x4β (?) | ... | 384, 1152, 896, 200 |
... | x3β3x5β (?) | ... | 14400, 43200, 31440, 6240 |
... | x3β4o3o (?) | ... | 192, 672, 576, 168 |
... | x3β4o3β (?) | ... | 576, 2304, 2112, 528 |
... | x3β4o3x (?) | ... | 576, 1728, 1430, 360 |
... | x3β4β3x (?) | ... | 1152, 3456, 2688, 528 |
... | x3x3β3o (?) | ... | 60, 180, 130, 30 |
... | x3x3β4o (?) | ... | 192, 480, 304, 56 |
... | x3x3β5o (?) | ... | 7200, 21600, 14640, 2640 |
... | truncated hyperbolic order 4 icositetrachoral tetracomb | 1.414214 i | |
... | x3x4β3o (?) | ... | 576, 1728, 1344, 264 |
... | hyperbolic x3x4x3x8o tesselation | 1.864101 i | |
... | tesseractic tetracomb | ||
... | hyperbolic small cellated dishecatonicosachoral honeycomb, hyperbolic cellated order 5 hecatonicosachoral honeycomb | 1.272020 i | |
... | xAFxx3ooxxF3Fxoxo3ooffx&#zx | 300, 960, 910, 250 | |
... | xFfoo3xoxxF3fxoxo3ooffx&#zx | 240, 1080, 1320, 480 | |
... | xFfxo3xoxoF3fxooo3oofFx&#zx | 200, 780, 760, 180 | |
... | Fxo xfo3oox5xxx&#zxt | 300, 840, 828, 258 | |
... | xfofxxfoFxfxo3ooxxoFxFoxxoo3oxfxFofxxfofx&xt (F=ff=x+f) | 176, 636, 592, 132 | |
... | xfooo5xofxo oxofx5ooxox&#zx, icosapentadiminished ex | 95, 445, 600, 250 | |
... | trigonal mibdi-laced wedge | 1 | 17, 52, 52, 17 |
xhi | hexacosihecatonicosachoron, bitruncated hecatonicosachoron, bitruncated hexacosachoron | 7.579634 | 3600, 7200, 4320, 720 |
xhidy | hexacosihecatonicosadishecatonicosachoron | 3 | 7200, 18000, 10080, 960 |
xithi | hexacositriakishecatonicosachoron | 3.872983 | 14400, 28800, 14880, 960 |
... | xo3oo ox&#q, q-laced trigonal scalene | 0.804400 | 5, 10, 10, 5 |
... | xo3oo3oo&#q, taller variant of tetrahedral pyramid | 0.784465 | 5, 10, 10, 5 |
... | xo3oo3ox&#q, longer variant of tetrahedral antiprism, vertex figure of scad | 0.866025 | 8, 24, 32, 16 |
... | cyclo-hexagonally diminished ico, tegum sum of 2 bi-dual (x,q)-triddips | 1 | 18, 72, 84, 30 |
... | tegum sum of 2 mutually inverted (x,u)-tips | 2 | 40, 200, 280, 120 |
... | tetra-augmented axially-octahedral ursachoron xoBo3ofox3xooo&#xt | ... | 28, 102, 118, 44 |
... | xofo3ofox5xoxx&#xt | 3.077684 | 210, 750, 736, 196 |
... | tetra-augmented axially-tetrahedral ursachoron xofo3ooox3oxoo&#xt | ... | 18, 70, 90, 38 |
... | triaugmented trigonal mibdi-laced wedge | ... | 20, 82, 112, 50 |
... | xofxxFfooFxfo3xxxoFxxxFoxxx3ofxFoofFxxfox&#xt | 192, 804, 888, 276 | |
... | xoo3ofx5xox&#xt | 3.077684 | 150, 390, 304, 64 |
... | xoofoox3ofxoxfo5xoxxxox&#xt | 360, 1140, 1046, 266 | |
... | xooFxxFfooFoofo3xxFooFxxxFooFxx3ofooFoofFxxFoox&#xt | 164, 588, 568, 144 | |
... | xoofxxFfooFxofo3xxFxoFxxxFoxFxx3ofoxFoofFxxfoox&#xt | 204, 924, 1104, 384 | |
... | :xoqo:4:xxox:3:oooo:4:oxxx:&##x | ||
... | hexastratic ike-first cap of rectified hexacosachoron | 3.077684 | 264, 1140, 1124, 248 |
... | xoxFoFxox3oxoooooxo5ooxofoxoo&#xt | 248, 1032, 1020, 236 | |
... | xoxFxFxox3oxfoxofxo5xxoxxxoxx&#xt | 600, 2040, 1978, 538 | |
... | ike atop id atop srid atop ti | 162, 600, 584, 146 | |
... | xoxxFxxox3oxoxoxoxo5ooxoooxoo&#xt | 336, 1380, 1414, 370 | |
... | decachoron-derived Gévay polychoron, Waterman polychoron number 4 wrt. cyclo-pentachoric lattice A4 centered at a lattice point | 2 | 60, 260, 300, 100 |
... | Powertope {p}{8} | sqrt[1+1/sqrt(2)]/sin(π/p) | |
... | xxfoF3oxxFx3xFxxo3Fofxx&#zx | 360, 1080, 900, 180 | |
... | magnaursachoron, cell-expanded tetrahedral ursachoron | ... | 132, 342, 272, 62 |
xxo ooo3oxx&#xt | line || trip || {3}, stack of tepe and triddip | 11, 25, 24, 10 | |
... | xxxFooAFxxAxxFx3oxFxxAxxxFooFxx3xfoxFoofFxxFoox&#xt | 246, 768, 696, 174 | |
... | xxxoooFFFAAA 2 FxfoFfxFofxo 2 xfFFfoFoxxof 2 fFxfoFoxFofx &#zx | 108, 384, 404, 128 | |
... | xxxoooFFFAAABxxxF FxfoFfxFofxooVoof xfFFfoFoxxofooVof FAoFxAxoAxFoxxxBF&#zx | 152, 564, 572, 160 | |
... | xxxoooFFFAAAxxF FxfoFfxFofxoVof xfFFfoFoxxofoVf FAoFxAxoAxFoxxF&#zx | 144, 496, 476, 124 |
Count of actually available polytopes: 1850
---- 5D ----
Acronym | Name | Circumradius | Face vector |
(n,m-ap)-dip | n-gon - m-antiprism - duoprism | sqrt[1/(4 sin2(π/n))+(3-2 cos(π/m))/(8-8 cos(π/m))] | 2nm, 6nm, 6nm+2n+2m, 2nm+3n+4m, n+2m+2 |
(n/d, m/b)-dow | n/d-grammal m/b-grammal disphenoid, {n/d} || perp {m/b} | sqrt[1+1/(4 sin2(π d/n))]+1/(4 sin2(π b7m))/2 | n+m, nm+n+m, 2nm+2, nm+n+m, n+m |
..., 02,1,1,1 | hyperbolic Gosset pentacomb 02,1,1,1 | 1.732051 i | |
..., 11,1,1,1 | hyperbolic hexachoric-tetracomb pentacomb, hyperbolic Gosset pentacomb 11,1,1,1 | 0 i | |
..., 12,1,1 | hyperbolic Gosset pentacomb 12,1,1 | 0.707107 i | |
... | 2dah (?) | 0.790569 | |
... | 2firx (?) | 0.816497 | |
... | 2hehad (?) | 0.707107 | |
... | 2howoh (?) | 1.732051 | |
... | 2rhohid (?) | 1 | |
2sophip | 2sophi prism | 3.118034 | |
3,n-dippip | triangle - n-gon duoprismatic prism | sqrt[7/12+1/(4 sin2(π/n))] | 6n, 15n, 14n+6, 6n+9, n+5 |
..., {4} || perp {4} | (degenerate) square atop fully orthogonal square, square disphenoid | ∞ i.e. flat in euclidean space | 8, 24, 34, 24, 8 |
5,n-dippip | pentagon - n-gon duoprismatic prism | sqrt[(15+2 sqrt(5))/20+1/(4 sin2(π/n))] | 10n, 25n, 22n+10, 8n+15, n+7 |
..., {5} || perp {5/2} | (degenerate) pentagon atop fully perpendicular pentagram | ∞ i.e. flat in euclidean space | 10, 35, 52, 35, 10 |
..., {5} || gyro pedip | (degenerate) pentagon atop gyrated pedip | ∞ i.e. flat in euclidean space | 30, 105, 136, 75, 16 |
bacox | biprismatocellihexateron | 1 | 30, 120, 210, 165, 41 |
bad | biprismatododecateron | 0.866025 | 20, 90, 210, 150, 32 |
bend | biprismatointercepted dodecateron | 0.866025 | 20, 90, 210, 150, 32 |
bidhin (alt.: octahex, tetalrap, tetaltet octtric) | bidiminished hemipenteract, oct || hex, tet || inverted rap, (tet,dual tet,oct)-trigonic | 0.790569 | 14, 60, 100, 69, 17 |
bidot | bidodecateron, triangular duotegmatic icosateron, triangular duotegmatic alterprism, dodecateron dual | 0.790569 | 12, 60, 120, 90, 20 |
bidrappy | bidrap pyramid | 0.790569 | 9, 26, 35, 24, 8 |
bidrix | bidiminished rectified hexateron | 0.816497 | 13, 44, 59, 36, 10 |
bittin | bitruncated penteract | 2.549510 | 320, 800, 720, 280, 42 |
bittit | bitruncated triacontiditeron, Voronoi cell of lattice D5* | 2.121320 | 240, 720, 720, 280, 42 |
bittix (old: dittox) | bitruncated hexateron | 1.554563 | 60, 150, 140, 60, 12 |
bodnit | bi-octa-diminished penteractitriacontiditeron | 1.224745 | 64, 288, 440, 272, 58 |
bostarpglassdit | bowtie - pentagrammic-retroprismatic-hourglass duotegum | 0.707107 | 14, 52, 72, 43, 11 |
brinoh | birectified penteractic pentacomb | ||
cabbix | cellibiprismatohexateron | 0.866025 | 20, 90, 210, 165, 41 |
caddix | cellidishexateron | 0.866025 | 20, 90, 210, 165, 27 |
cappin | celliprismated penteract, steritruncated pentacross | 2.423081 | 640, 2240, 2880, 1520, 242 |
cappix (old: happix) | celliprismated hexateron, cellitruncated hexateron, hedratoprismated hexateron, steritruncated hexateron | 1.632993 | 120, 420, 570, 330, 62 |
capt | celliprismated triacontiditeron, steritruncated penteract | 2.878460 | 640, 2240, 2960, 1600, 242 |
captid (old: hiptid) | celliprismatotruncated dodecateron, hedratoprismatotruncated dodecateron, steriruncitruncated hexateron | 2.236068 | 360, 1080, 1110, 450, 62 |
captint | celliprismatotruncated penteractitriacontiditeron, steriruncitruncated penteract, steriruncitruncated pentacross | 3.701317 | 1920, 5760, 5760, 2160, 242 |
caquapin | celliquasiprismated penteract | 1.276197 | 640, 2240, 2880, 1520, 242 |
card (old: scard, shard) | (small) cellirhombated dodecateron, small hedratorhombated dodecateron, stericantellated hexateron | 1.658312 | 180, 720, 900, 420, 62 |
carnit (old: scarnit) | (small) cellirhombated penteractitriacontiditeron, stericantellated penteract, stericantellated pentacross | 2.660531 | 960, 3840, 4720, 2080, 242 |
chad | cellihemidodecateron | 1 | 30, 120, 210, 180, 36 |
coa tutcup, co || tutcup | co atop tuta | 1.224745 | 36, 132, 162, 81, 17 |
coarit | co atop rit | 1.224745 | 44, 168, 222, 121, 25 |
coasircope | cuboctahedron atop small-rhombicuboctahedron prism | 1.847759 | 60, 240, 306, 153, 29 |
coates | cuboctahedron atop tesseract | 1.050501 | 28, 104, 134, 73, 17 |
coatope (alt.: cotoe totric) | co atop tope, (co,toe,toe)-trigonic, co-first cap of sibrant at (rico,rico)-margin | 2.236068 | 60, 168, 174, 81, 17 |
coatuttip | co atop tuttip, co-first cap of sarx | 1.290994 | 36, 120, 144, 75, 17 |
cogart (old: gocart) | celligreatorhombated triacontiditeron, (great cellirhombated triacontiditeron), stericantitruncated pentacross | 3.534493 | 1920, 5760, 5920, 2320, 242 |
cograx (old: gocrax, goharx) | celligreatorhombated hexateron (great cellirhombated hexateron, great hedratorhombated hexateron), stericanitruncated hexateron | 2.327373 | 360, 1080, 1140, 480, 62 |
cogrin (old: gocrin) | celligreatorhombated penteract (great cellirhombated penteract), stericantitruncated penteract | 3.988340 | 1920, 5760, 6000, 2400, 242 |
..., cont || grico | (degenerate) cont atop grico | ∞ i.e. flat in euclidean space | 864, 2304, 2208, 912, 146 |
contip | tetracontoctachoron prism, bitruncated-icositetrachoron prism | 3.450631 | 576, 1440, 1248, 432, 50 |
copatoe (alt.: coco totric) | cope atop toe, (co,co,toe)-trigonic | 1.870829 | 48, 144, 162, 81, 17 |
copatope | cope atop tope, coatoe prism, cope-first monostratic cap of ricope | 1.802776 | 72, 204, 212, 96, 18 |
copatut | cope atop tut | 1.190238 | 36, 126, 156, 81, 17 |
copea tuttip | cope atop tuttip, cope-first monostratic cap of srippip | 1.284523 | 48, 156, 182, 90, 18 |
copeatope | cope atop tope, coatoe-prism | 1.802776 | 72, 204, 212, 96, 18 |
cotut totric | (co,tut,toe)-trigonic | 1.732051 | 48, 150, 168, 81, 17 |
cuba sircope | cube atop small-rhombicuboctahedron-prism | 1.695040 | 56, 180, 226, 129, 29 |
cubacope | cube atop cuboctahedron-prism | 1.120019 | 32, 120, 154, 81, 17 |
cubaope | cube atop octahedral-prism | 0.895420 | 20, 90, 154, 111, 29 |
cubasc | (degenerate) cubical scalene, line atop fully orthogonal cube | ∞ i.e. flat in euclidean space | 10, 29, 38, 25, 8 |
cubasquasc | cube atop squasc | 1 | 14, 41, 51, 31, 9 |
cubpyp | cubpy prism | 1.118034 | 18, 49, 56, 32, 9 |
cutep | cubical-tegum prism, prism of tepepy | ... | 20, 66, 88, 54, 14 |
cydispan | cubically cyclodiminished small-prismated-penteract | 1.914214 | 288, 1200, 1752, 1020, 182 |
cypropit | cycloprismatorhombated pentachoric tetrachomb, great prismatodispentachoric tetracomb, runcitruncated pentachoric tetrachomb | ||
cytaxh | cyclotruncated hexateric honeycomb | ||
cyxh | cyclohexateric honeycomb, Delone complex of lattice A5 | ||
dacox | dodecacellihexateron | 1 | 30, 120, 210, 135, 33 |
dah | dishexadecateron, vertex figure of kaje | 0.790569 | 16, 80, 160, 120, 32 |
danbitot | dispenteractibitruncated triacontaditeron | 1.802776 | 960, 2400, 1760, 480, 52 |
danpit | dispenteractiprismated triacontaditeron | 2.5 | 3840, 9600, 7680, 2160, 132 |
deca agrip | deca atop grip, deca-first cap of pirx | 1.914854 | 90, 240, 240, 110, 22 |
deca aprip | deca atop prip | 1.620185 | 90, 330, 400, 190, 32 |
..., deca || gippid | (degenerate) deca atop gippid | ∞ i.e. flat in euclidean space | 150, 420, 430, 190, 32 |
decap | decachoron prism | 1.5 | 60, 150, 140, 60, 12 |
dehad | dodecahemidodecateron | 1 | 30, 120, 140, 75, 18 |
dibhid | dodecabiprismatohemidodecateron | 1 | 30, 120, 210, 180, 38 |
dihin (alt.: penalrap) | (vertex-)diminished hemipenteract, pentachoron atop alternate rectified pentachoron | 0.790569 | 15, 70, 130, 95, 22 |
ditdia | disicositetratruncated-disicositetrachoron alterprism | 2.352869 | 1152, 4032, 3936, 1296, 98 |
ditetaf (alt.: traltepe, penaltrip) | diminished tetaf, triangle atop gyrated tepe, pen atop gyrated trip, (edge,perp triangle,gyro trip)-trigonic | 0.790569 | 11, 37, 54, 37, 11 |
dittadiu | dittady-based ursateron | 1.008123 | 1440, 10920, 16080, 5880, 362 |
doa iddip | dodecahedron atop icosidodecahedron-prism | 1.738546 | 80, 300, 376, 189, 35 |
..., doe || ipe | (degenerate) doe atop ipe | ∞ i.e. flat in euclidean space | 44, 222, 382, 267, 65 |
dot (alt.: rapa) | dodecateron, birectified hexateron, equatorial cross-section of (vertex first) 1/q-ax, rap alterprism, rap atop inverted rap, vertex figure of mo, Gosset polytope 02,2, equatorial cross-section of hix-first hax | 0.866025 | 20, 90, 120, 60, 12 |
durat | rectified-triacontiditeron dual, joined penteract | 42, 240, 400, 240, 40 | |
... | point || hex || gyro hex, Dutour polyteron type A | 17, 88, 184, 144, 33 | |
ecypit | elongated cyclopentachoric tetracomb, elongated pentachoric-dispentachoric tetracomb | ||
editetaf | edge-diminished tetaf, (top base) edge-diminishing of tet-first rotunda of hin | 0.790569 | 10, 29, 38, 25, 8 |
exip | hexacosachoron prism | 1.693527 | 240, 1560, 3120, 2400, 602 |
exu | (degenerate) ex-based ursateron | ∞ i.e. flat in euclidean space | 960, 5880, 9120, 4920, 722 |
fawdint | frustisphenary dispenteractitriacontaditeron, fastegiverted dispenteractitriacontaditeron | 0.914214 | 320, 1440, 1440, 480, 52 |
fenandoh | facetospinopenteractidishexadecateron | 1.274755 | 80, 400, 620, 280, 42 |
fidoh | facetoinverted decahexadecateron | 1.274755 | 80, 400, 940, 320, 26 |
firn | facetorectified penteract | 1.414214 | 80, 320, 480, 320, 80 |
firx | facetorectified hexateron | 0.816497 | 15, 60, 105, 90, 31 |
..., fix || padohi | (degenerate) fix atop padohi | ∞ i.e. flat in euclidean space | 1560, 9360, 15840, 9720, 2162 |
gabdacan | great biprismatodiscellipenteract | 1.021221 | 160, 640, 1120, 840, 210 |
gacnet | great cellated penteractitriacontiditeron, omnitruncated penteract, omnitruncated pentacross | 4.829189 | 3840, 9600, 8160, 2640, 242 |
gadencorn | great dispinocellirhombated penteract | 1.192297 | 960, 3840, 4480, 1600, 132 |
gadinnert | great dispenteractirhombated triacontaditeron | 2.336045 | 1920, 4800, 3760, 1080, 92 |
gadtaxadiap | grand ditetrahedronary hexacosadishecatonicosachoron atop alternate grand ditetrahedronary hexacosadishecatonicosachoron, grand ditetrahedronary hexacosadishecatonicosachoron alterprism | 0.951057 | 1200, 9600, 14880, 7920, 1442 |
gadtaxhiap | grand ditetrahedrary hexacontahecatonicosachoron antiprism | 0.951057 | 1200, 9600, 13440, 6960, 1322 |
gafwan | great facetosphenary penteract | 0.792893 | 320, 1280, 1840, 1120, 210 |
..., gaghi || gofix | (degenerate) gaghi atop gofix, (degenerate) gaghi antiprism, (degenerate) gofix antiprism | ∞ i.e. flat in euclidean space | 240, 3360, 9120, 7680, 2162 |
gaghipy, pt || gaghi | (degenerate) gaghi pyramid | ∞ i.e. flat in euclidean space | 121, 1320, 1920, 840, 121 |
gancpan | great spinocelliprismated penteract | 1.276197 | 640, 2240, 2640, 1080, 132 |
gapcyxh | great prismated cyclohexateric honeycomb, Voronoi complex of lattice A5* | ||
gappip | great-antiprism prism | 1.693527 | 200, 1100, 1940, 1360, 322 |
gapquinoh | great prismated quarterpenteractic pentacomb | ||
gaqrin | great quasirhombated penteract | 1.673396 | 640, 1600, 1520, 680, 122 |
gaquacint | great quasicellated penteractitriacontiditeron | 3.029675 | 3840, 9600, 8160, 2640, 242 |
gaquapan | great quasiprismated penteract | 2.527061 | 1920, 4800, 4240, 1530, 202 |
gaquidpothip | great-quasidisprismatotesseractihexadecachoric prism, great-quasiprismated-tesseract prism | 2.001839 | 768, 1920, 1696, 624, 82 |
garcornit | great retrocellirhombated penteractitriacontaditeron | 1.192297 | 960, 3840, 3920, 1280, 142 |
gart | great rhombated triacontiditeron, cantitruncated pentacross | 2.645751 | 480, 1440, 1520, 640, 82 |
garx | great rhombated hexateron, cantitruncated hexateron | 2 | 120, 300, 290, 135, 27 |
gashia | grand stellated hecatonicosachoron antiprism, grand stellated hecatonicosachoron alterprism, grand stellated hecatonicosachoron atop dual grand stellated hecatonicosachoron | 0.707107 | 240, 2880, 8640, 6720, 1682 |
gatopin | great pteroprismated penteract | 0.914214 | 320, 1440, 1680, 560, 50 |
gaxu | gax-based ursateron | 1.008123 | 960, 5880, 9120, 4920, 722 |
gektabcadont (old: giktabacadint) | great skewtrigonary biprismatocellidispenteractitriacontiditeron | 1.5 | 640, 2880, 3920, 1920, 172 |
getitdin | great tesseractitriacontidiadispenteract | 1.276197 | 640, 2240, 2160, 760, 92 |
gibcotdin | great biprismatocellitriacontadiadispenteract | 2.001839 | 1920, 5760, 5440, 1840, 172 |
gibrant | great birhombated penteractitriacontiditeron, bicantitruncated penteract | 3.391165 | 960, 2400, 2160, 840, 122 |
gibrid (old: gadrid) | great birhombated dodecateron, bicantitruncated hexateron | 2.179449 | 180, 450, 420, 180, 32 |
gibtadin | great biprismatotriacontadiadispenteract | 1.488108 | 960, 2880, 2720, 1000, 132 |
gicalico | great icositetrachoron atop dual icositetrachoron, blend of 3 icateses | 1.050501 | 48, 336, 744, 600, 122 |
gidpithip | great-disprismatotesseractihexadecachoric prism, great-prismated-tesseract prism, central segment of cogart | 3.534493 | 768, 1920, 1696, 624, 82 |
gidpixhip | great-disprismatohexacosihecatonicosachoron prism, omnitruncated-hexacosachoron prism | 12.796423 | 28800, 72000, 62880, 22320, 2642 |
gidtixhipy, pt || gidtixhi | (degenerate) gidtixhi pyramid | ∞ i.e. flat in euclidean space | 121, 1320, 3600, 3120, 721 |
gidtixhiu | gidtixhi-based ursateron | 1.008123 | 1440, 10920, 17040, 7800, 842 |
ginnont | great penteractipenteractitriacontiditeron | 1.021221 | 160, 640, 640, 280, 52 |
gipbin | great prismated biprismatopenteract | 0.914214 | 320, 1440, 2880, 1880, 322 |
giphin | great prismated hemipenteract, steriruncicantic penteract | 3.259601 | 960, 2400, 2080, 720, 82 |
gippiccup | great-prismatotetracontoctachoron prism, omnitruncated-icositetrachoron prism | 5.194028 | 2304, 5760, 5088, 1872, 242 |
gippiddip | great-prismatodecachoron prism | 2.291288 | 240, 600, 540, 210, 32 |
gippin | great prismated penteract, runcicantitruncated penteract | 4.371952 | 1920, 4800, 4240, 1560, 202 |
gippit | great prismated triacontiditeron, omnitruncated hemipenteract | 3.872983 | 1920, 4800, 4160, 1440, 162 |
gippix | great prismated hexateron, runcicantitruncated hexateron | 2.581989 | 360, 900, 810, 315, 47 |
gircaptint (old: grecaptint) | great retrocelliprismatotruncated penteractitriacontaditeron | 1.949424 | 1920, 5760, 5440, 1840, 172 |
girhin | great rhombated hemipenteract, cantitruncated demipenteract, runcicantic penteract | 2.761340 | 480, 1200, 1040, 360, 42 |
girn | great rhombated penteract, cantitruncated penteract | 3.563671 | 640, 1600, 1520, 680, 122 |
gittithip | great-tesseractitesseractihexadecachoron prism | 1.021221 | 128, 448, 464, 200, 34 |
gloptin | great lapidoprismatotruncated penteract | 1.416813 | 960, 3260, 3440, 1280, 132 |
gocad (old: gohad) | great cellated dodecateron (great hedrated dodecateron), omnitruncated hexateron, Voronoi cell of lattice A5*, permutoteron of 6 elements | 2.958040 | 720, 1800, 1560, 560, 62 |
gocypapit | bitruncated pentachoric tetracomb, great cycloprismated pentachoric tetrachomb, grand prismatodispentachoric tetracomb | ||
gofixa quipdohi | (degenerate) gofix atop quipdohi | ∞ i.e. flat in euclidean space | 1560, 9360, 15840, 9720, 2162 |
gofixu | gax-based ursateron | 1.008123 | 960, 5880, 8160, 3000, 242 |
gogishiagax | great grand stellated hecatonicosachoron antiprism, grand hexacosachoron antiprism, taller great grand stellated hecatonicosachoron atop grand hexacosachoron | 0.667731 | 720, 4320, 9120, 8160, 2642 |
gogiship | great-grand-stellated-hecatonicosachoron prism | 0.736068 | 1200, 3000, 2640, 960, 122 |
gogishiragax | great grand stellated hecatonicosachoron retroprism, grand hexacosachoron retroprism, narrower great grand stellated hecatonicosachoron atop grand hexacosachoron | 0.636010 | 720, 4320, 91420, 8160, 2642 |
gohip | great hexacosachoron prism | 1.693527 | 240, 1560, 2160, 960, 122 |
gorcrin | great retrocelligreat rhombated penteract | 2.143163 | 1920, 5760, 5680, 2080, 212 |
grahip (old: grahipe) | great-rhombated-hecatonicosachoron prism, cantitruncated-hecatonicosachoron prism | 11.263210 | 14400, 36000, 32640, 12960, 1922 |
..., grico || gippic | (degenerate) grico atop gippic | ∞ i.e. flat in euclidean space | 1728, 4608, 4416, 1776, 242 |
gricoa (old: gricoalgrico) | great-rhombated-icositetrachoron alterprism, great-rhombated-icositetrachoron atop alternate great-rhombated-icositetrachoron | 4.311477 | 1152, 3456, 3744, 1680, 242 |
gricope (old: gripe) | great-rhombated-icositetrachoron prism, cantitruncated-icositetrachoron prism | 4.328427 | 1152, 2880, 2592, 1008, 146 |
gripa (old: gripalgrip) | grip alterprism, grip atop inverted grip, medial spid-first segment of spat | 1.870829 | 120, 360, 400, 190, 32 |
gripagippid | grip atop gippid, grip-first cap of cograx | 2.327373 | 180, 480, 470, 200, 32 |
grippip | great-rhombated-pentachoron prism | 1.910497 | 120, 300, 280, 120, 22 |
gritta gidpith | grit atop gidpith, grit-first segment of cogrin | 3.988340 | 576, 1536, 1480, 600, 82 |
grittip | truncated-tesseract prism, central segment of prin | 3.047217 | 384, 960, 880, 360, 58 |
..., grix || prix | (degenerate) grix atop prix | ∞ i.e. flat in euclidean space | 14400, 46800, 50880, 21120, 2642 |
grixip | great-rhombated-hexacosachoron prism | 9.137791 | 14400, 36000, 31680, 11520, 1442 |
gyetac | gyroelongated triacontaditeron, parabiapiculated demipenteract | ... | 18, 96, 208, 168, 40 |
haco (old: hicco) | hexagon cuboctahedron duoprism | 1.414214 | 72, 216, 240, 114, 20 |
hacube (old: hiccube) | hexagon cube duoprism | 1.322876 | 48, 120, 116, 54, 12 |
hadoe | hexagon - dodecahedron duoprism | 1.721489 | 120, 300, 272, 108, 18 |
hagirco (old: higgirco) | hexagon great-rhombicuboctahedron duoprism | 2.524147 | 288, 720, 636, 234, 32 |
hagrid | hexagon - great-rhombicosidodecahedron duoprism | 3.931692 | 720, 1800, 1572, 558, 68 |
hahip (old: hiddippip) | hexagon hexagonal-prism duoprism, hexagon-hexagon duoprismatic prism | 1.5 | 72, 180, 168, 72, 14 |
han | hexadecapenteract, vertex figure of daj | 0.790569 | 16, 80, 160, 160, 26 |
haop (old: hodippip) | hexagon octagonal-prism duoprism, hexagon-octagon duoprismatic prism | 1.719624 | 96, 240, 220, 90, 16 |
haquitco | hexagon - quasitruncated-cuboctahedron duoprism | 1.459000 | 288, 720, 636, 234, 32 |
hasirco (old: hissirco) | hexagon small-rhombicuboctahedron duoprism | 1.719624 | 144, 432, 468, 210, 32 |
hasrid | hexagon - small-rhombicosidodecahedron duoprism | 2.446644 | 360, 1080, 1152, 498, 68 |
hatet (old: hittet, alt. hipdaw) | hexagon-tetrahedron duoprism, hexagon duofastegium, hip disphenoid | 1.172604 | 24, 60, 64, 36, 10 |
hati | hexagon - truncated-icosahedron duoprism | 2.672186 | 360, 900, 792, 288, 38 |
hatic (old: hittic) | hexagon truncated-cube duoprism | 2.040640 | 144, 360, 324, 126, 20 |
hatid | hexagon - truncated-dodecahedron duoprism | 3.133309 | 360, 900, 792, 288, 38 |
hatoe (old: hittoe) | hexagon truncated-octahedron duoprism | 1.870829 | 144, 360, 324, 126, 20 |
hatricu | hexagon-tricu duoprism, trip-first half of haco | 1.414214 | 54, 144, 147, 69, 14 |
hatut (old: hittut) | hexagon truncatet-tetrahedron duoprism | 1.541104 | 72, 180, 168, 72, 14 |
hehad | hexadecahemidecateron, vertex figure of thox | 0.707107 | 10, 40, 80, 80, 21 |
hexaco | hexadecachoron atop cuboctahedron, 0.147584-luna of rectified triacontiditeron | 1 | 20, 72, 106, 68, 17 |
hexaico, hex || ico | hexadecachoron-first rotunda of rectified triacontiditeron, hexadecachoron atop icositetrachoron, rectified hexadecachoron-pyramid | 1 | 32, 168, 248, 136, 26 |
hexalrit | hex atop gyrated rit, hex-first cap of siphin | 1.274755 | 40, 152, 216, 128, 26 |
hexarit | (degenerate) hex atop rit | ∞ i.e. flat in euclidean space | 40, 216, 408, 280, 50 |
hexasidpith | (degenerate) hex atop sidpith | ∞ i.e. flat in euclidean space | 72, 280 ,432, 304, 82 |
hexathex | (degenerate) hex atop thex | ∞ i.e. flat in euclidean space | 56, 192, 248, 136, 26 |
hexip | hexadecachoron prism, vertex figure of rag, equatorial cross-section of hex-first hax | 0.866025 | 16, 56, 88, 64, 18 |
hexpy | hexadecachoral pyramid, vertex-first rotunda of triacontiditeron | 0.707107 | 9, 32, 56, 48, 17 |
hextum | hex-based tutsatope, hex-based tutism, hex-first rotunda of tot, truncation of hexpy | 1.581139 | 64, 200, 248, 136, 26 |
hexu | hexadecachoron-based ursateron, hex-based ursulate, vertex figure of s3s4o3o3o4o | 1.144123 | 40, 176, 248, 136, 26 |
hiarahi, hi || rahi | (degenerate) hi atop rahi | ∞ i.e. flat in euclidean space | 1800, 7200, 8640, 3960, 722 |
hid | hexagon icosidodecahedron duoprism | 1.902113 | 180, 540, 582,258, 38 |
hike | hexagon icosahedron duoprism | 1.380039 | 72, 252, 312, 156, 26 |
hin | hemipenteract, demipenteract, hemitesseractic gyroprism, tetrahedral altersquarism, vertex figure of jak, Gosset polytope 12,1 | 0.790569 | 16, 80, 160, 120, 26 |
hinoh | hemipenteractic pentacomb, Delone complex of lattice D5 | ||
hipe | hecatonicosachoron prism | 3.736068 | 1200, 3000, 2640, 960, 122 |
hisquippy | hexagon-squippy douprism, half of hoct | 1.224745 | 30, 78, 83, 44, 11 |
hit | hexadecateron | 0.790569 | 16, 80, 220, 120, 16 |
hix | hexateron, 5D simplex (α5), pyropet(id), pentachoral pyramid, regular tet-scalene, regular triangle-tettene, regular line-pennene, regular (point-)hixene, digonal gyrotrigonism, vertex figure of hop, Gosset polytope 04 | 0.645497 | 6, 15, 20, 15, 6 |
hoct | hexagon octahedron duoprism | 1.224745 | 36, 108, 126, 66, 14 |
hodidgyt | hollow dodecadodecahedral gyrotrigonism | 1.098185 | 90, 540, 696, 288, 39 |
... | 2did gyrotrigonism | 1.098185 | |
horico adisti | hollow rectified icositetrachoron atop disnub tetrakisicositetrachoron, snub disicositetrachoric cupolaic blend | 1.738546 | 288, 1728, 2688, 1440, 241 |
hosiap | hollow stellated icosatetrachoric antiprism, pseudo stico atop pseudo stico | 0.790569 | 48, 336, 768, 624, 144 |
hossidgyt | hollow small-stellated-dodecahedral gyrotrigonism | 0.742632 | 36, 270, 516, 288, 39 |
... | 2sissid gyrotrigonism | 0.742632 | |
howoh | hexadecasphenohexadecateron, cantellated hexadecahemidecateron | 1.732051 | 240, 1200, 1440, 560, 71 |
ica sidpith, ico || sidpith | icositetrachoron atop small disprismatotesseractihexadecachoron | 1.847759 | 88, 480, 784, 472, 82 |
ica tutcup, ico || tutcup | icositetrachoron atop truncated-tetrahedral-cupoliprism | 1.224745 | 48, 228, 304, 148, 26 |
icarico | (degenerate) ico atop rico | ∞ i.e. flat in euclidean space | 120, 576, 720, 312, 50 |
icarit, ico || rit | icositetrachoron atop rectified tesseract, ico-first half of nit | 1.224745 | 56, 288, 376, 168, 26 |
icates, ico || tes | icositetrachoron atop tesseract | 1.050501 | 40, 216, 408, 288, 58 |
icathex | ico atop thex, ico-first segment of sart | 1.732051 | 72, 264, 312, 144, 26 |
..., ico || sadi | ico atop sadi | ∞ i.e. flat in euclidean space | 120, 816, 1584, 1128, 242 |
..., ico || spic | (degenerate) ico atop spic | ∞ i.e. flat in euclidean space | 168, 816, 1344, 936, 242 |
..., ico || srit | (degenerate) ico atop srit | ∞ i.e. flat in euclidean space | 120, 480, 632, 328, 58 |
icoap (alt.: icoalico) | icositetrachoral antiprism, icositetrachoron atop dual icositetrachoron | 1.050501 | 48, 336, 768, 720, 242 |
icope | icositetrachoron prism | 1.118034 | 48, 216, 288, 144, 26 |
icopy | (degenerate) ico pyramid | ∞ i.e. flat in euclidean space | 25, 120, 192, 120, 25 |
icou | icositetrachoron-based ursateron, ico-based ursulate, vertex figure of s3s4o3o4o3o | 1.738546 | 144, 600, 720, 312, 50 |
ictum | (degenerate) ico-based tutsateron, ico-first bistratic "cap" of thext | ∞ i.e. flat in euclidean space | 240, 696, 720, 312, 50 |
idadope | icosidodecahedron atop dodecahedron-prism | 1.618034 | 70, 260, 326, 169, 35 |
..., ike || dope | (degenerate) ike atop dope | ∞ i.e. flat in euclidean space | 52, 230, 374, 259, 65 |
irl | invertiretrolepidoteron | 1.224745 | 80, 480, 880, 400, 48 |
irohlohn | invertiretrohexadecalepidohemipenteract | 1.224745 | 80, 480, 1120, 640, 69 |
kafandoh | spikifacetospinodishexadecateron | 1.620185 | 160, 720, 800, 280, 32 |
lawx | lepidosphenary hexateron | 1.290994 | 60, 240, 270, 135, 27 |
mibdinit | metabidiminished nit, rectified bidhin | 1.224745 | 60, 300, 394, 183, 31 |
n,co-dip | n-gon - cuboctahedron duoprism | sqrt[1+1/(4 sin2(π/n))] | 12n, 36n, 38n+12, 15n+24, n+14 |
n,cube-dip | n-gon - cube duoprism | sqrt[3/4+1/(4 sin2(π/n))] | 8n, 20n, 18n+8, 7n+12, n+6 |
n,doe-dip | n-gon - dodecahedron duoprism | sqrt[(9+3 sqrt(5))/8+1/(4 sin2(π/n))] | 20n, 50n, 42n+20, 13n+30, n+12 |
n,girco-dip | n-gon - great-rhombicuboctahedron duoprism | sqrt[(13+6 sqrt(2))/4+1/(4 sin2(π/n))] | 48n, 120n, 98n+48, 27n+72, n+26 |
n,grid-dip | n-gon - great-rhombicosidodecahedron duoprism | sqrt[(31+12 sqrt(5))/4+1/(4 sin2(π/n))] | 120n, 300n, 242n+120, 63n+180, n+62 |
n,id-dip | n-gon - icosidodecahedron duoprism | sqrt[(3+sqrt(5))/2+1/(4 sin2(π/n))] | 30n, 90n, 92n+30, 33n+60, n+32 |
n,ike-dip | n-gon - icosahedron duoprism | sqrt[(5+sqrt(5))/8+1/(4 sin2(π/n))] | 12n, 42n, 50n+12, 21n+30, n+20 |
n,m-dafup | (n,m)-duoantifastegiaprism, (n,m)-duoantiwedge, (n,m)-dip atop bidual (n,m)-dip | sqrt([2+1/(1-cos(π/n))+1/(1-cos(π/m))]/8) | 2nm, 8nm, 10nm+2n+2m, 4nm+4n+4m, 2n+2m+2 |
n,m-dippip | n-gon - m-gon duoprismatic prism | sqrt[1/4+1/(4 sin2(π/n))+1/(4 sin2(π/m))] | 2nm, 5nm, 4nm+2n+2m, nm+3n+3m, n+m+2 |
n,n-dippip | n-gon - n-gon duoprismatic prism | sqrt[1/4+1/(2 sin2(π/n))] | 2n2, 5n2, 4n2+4n, n2+6n, 2n+2 |
n,oct-dip | n-gon - octahedron duoprism | sqrt[1/2+1/(4 sin2(π/n))] | 6n, 18n, 20n+6, 9n+12, n+8 |
n,sirco-dip | n-gon small-rhombicuboctahedron duoprism | sqrt[(5+2 sqrt(2))/4+1/(4 sin2(π/n))] | 24n, 72n, 74n+24, 27n+48, n+26 |
n,srid-dip | n-gon - small-rhombicosidodecahedron duoprism | sqrt[sqrt(5)+11/4+1/(4 sin2(π/n))] | 60n, 180n, 182n+60, 63n+120, n+62 |
n,tet-dip | n-gon - tetrahedron duoprism, n-gonal duofastegium, n-gonal prism disphenoid | sqrt[3/8+1/(4 sin2(π/n))] | 4n, 10n, 10n+4, 5n+6, n+4 |
n,ti-dip | n-gon - truncated-icosahedron duoprism | sqrt[(29+9 sqrt(5))/8+1/(4 sin2(π/n))] | 60n, 150n, 122n+60, 33n+90, n+32 |
n,tic-dip | n-gon - truncated-cube duoprism | sqrt[sqrt(2)+7/4+1/(4 sin2(π/n))] | 24n, 60n, 50n+24, 15n+36, n+14 |
n,tid-dip | n-gon - truncated-dodecahedron duoprism | sqrt[(37+15 sqrt(5))/8+1/(4 sin2(π/n))] | 60n, 150n, 122n+60, 33n+90, n+32 |
n,toe-dip | n-gon truncated-octahedron duoprism | sqrt[5/2+1/(4 sin2(π/n))] | 24n, 60n, 50n+24, 15n+36, n+14 |
n,tut-dip | n-gon - truncated-tetrahedron duoprism | sqrt[11/8+1/(4 sin2(π/n))] | 12n, 30n, 26n+12, 9n+18, n+8 |
..., N-g || N-appip | N-gon atop N-appip, (N-gon, N-p, gyro N-p)-trigonic | ... | 5n, 17n, 21n+5, 11n+8, 2n+5 |
n/d,2n/d-dipcup | n/d,2n/d-dip cupoliprism | sqrt([7+4 cos(π d/n)-2 cos2(π d/n)]/[8-8 cos2(π d/n)]) | 4n2, 12n2, 12n2+6n, 4n2+10n, 4n+2 |
n/d-daf | n/d-duoantifastegium, (2,n)-duoantiwedge, n/d-p atop bidual n/d-p | sqrt([3+1/(1-cos(pi d/n))]/8) | 4n, 14n, 18n+4, 10n+6, 2n+4 |
n/d-dow | n/d-grammal disphenoid, n/d-grammal biwedge, {n/d} || perp {n/d} | sqrt[1+1/(2 sin2(π d/n))]/2 | 2n, n2+2n, 2n2+2, n2+2n, 2n |
... | {N} atop gyrated 3,N-dip, (N-g, dual N-g, N-p)-trigonic | ... | 4n, 13n, 16n+4, 9n+6, 2n+4 |
naquiptant | penteractiquasiprismatotruncated penteractitriacontaditeron | 1.621320 | 1920, 5760, 5520, 1920, 172 |
naquitant | penteractiquasitruncated penteractitriacontaditeron | 1.354911 | 640, 1600, 1280, 440, 52 |
narptint | penteractiretroprismatotruncated penteractitriacontaditeron | 2.621320 | 1920, 5760, 5200, 1600, 142 |
nat | spinotriacontaditeron | 1.224745 | 80, 480, 640, 240, 32 |
nippant | penteractiprismated penteractitriacontaditeron | 3.505073 | 3840, 9600, 7680, 2160, 172 |
niptant | penteractiprismatotruncated penteractitriacontaditeron | 2.621320 | 1920, 5760, 5520, 1920, 172 |
nit | penteractitriacontiditeron, birectified penteract, birectified triacontiditeron, birectified pentacross, Gosset polytope 02,1,1, equatorial cross-section of rat-first brag | 1.224745 | 80, 480, 640, 280, 42 |
nophap | spinopentachoric hemiantiprism, pseudo pentachoric hemiantiprism | 0.707107 | 10, 40, 80, 80, 25 |
noqrant | penteractiquasirhombated penteractitriacontaditeron | 1.849749 | 1920, 4800, 4000, 1320, 132 |
noqraptant | penteractiquasiretroprismatotruncated penteractitriacontaditeron | 1.621320 | 1920, 5760, 5200, 1600, 142 |
noquapant | penteractiquasiprismated penteractitriacontaditeron | 2.283521 | 3840, 9600, 7680, 2160, 172 |
nottant | penteractitruncated penteractitriacontaditeron | 2.159679 | 640, 1600, 1280, 440, 52 |
nurrant | penteractirhombated penteractitriacontaditeron | 3.013043 | 1920, 4800, 4000, 1320, 132 |
... | hyperbolic order 3 icositetrachoric-tetracomb pentacomb, hyperbolic Gosset pentacomb 01,1,1,1,1 | 1 i | |
... | hyperbolic o3o3o3o4s3s pentacomb | 2.058171 i | |
... | hyperbolic truncated order 3 icositetrachoric-tetracomb pentacomb | 3.316625 i | |
oco (old: occo) | octagon cuboctahedron duoprism | 1.645329 | 96, 288, 316, 144, 22 |
octa tutcup, oct || tutcup | oct atop tuta | 1.274755 | 30, 96, 120, 69, 17 |
octacope | oct atop cope, oct-first cap of nit | 1.224745 | 30, 120, 156, 81, 17 |
octasc | octahedral scalene, octahedron-pyramid pyramid, line atop fully orthogonal octahedron, 1/4-lune of triacontiditeron | 0.707107 | 8, 25, 38, 29, 10 |
octatepe (alt.: tettet octtric) | oct atop tepe, diminished rix, (tet,tet,oct)-trigonic | 0.816497 | 14, 52, 70, 41, 11 |
octatuttip (alt.: octtut tuttric) | oct atop tuttip, (oct,tut,tut)-trigonic | 1.414214 | 30, 84, 90, 45, 11 |
octco tuttric | (oct,co,tut)-trigonic | 1.224745 | 30, 114, 144, 75, 17 |
octhipdaw (alt.: traporhip) | (oct,hip)-disphenoid, trigonal antiprism atop axis-orthogonal hexagonal prism | 1.224745 | 18, 54, 64, 36, 10 |
octpy || octaco | 1/4-lune of rectified triacontiditeron, octahedron-pyramid atop octhedron-first-rotunda-of-icositetrachoron | 1 | 25, 114, 156, 83, 18 |
octpyp, line||ope | octahedron-prismatic wedge, line atop ope, octahedral-pyramid prism, half of hexip | 0.866025 | 14, 43, 58, 38, 11 |
ocube | octagon - cube duoprism | 1.567516 | 64, 160, 152, 68, 14 |
odnit | octadiminished penteractitriacontiditeron | 1.224745 | 72, 384, 556, 292, 50 |
odoe | octagon - dodecahedron duoprism | 1.915889 | 160, 400, 356, 134, 20 |
..., ofx3xoo4ooo&#xt || o3o4x | cube atop (oct,co)-ursachoron, (oct,co)-ursachoron based wedge | 1.994779 | 32, 150, 244, 159, 35 |
ogdow | octagrammic disphenoid, octagram atop fully orthogonal octagram | 0.629640 | 16, 80, 130, 80, 16 |
ogirco | octagon - great-rhombicuboctahedron duoprism | 2.660531 | 384, 960, 832, 288, 34 |
ogrid | octagon - great-rhombicosidodecahedron duoprism | 4.020611 | 960, 2400, 2056, 684, 70 |
oid | octagon-icosidodecahedron duoprism | 2.079697 | 240, 720, 766, 324, 40 |
oike | octagon-icosahedron duoprism | 1.616049 | 96, 336, 412, 198, 28 |
opeaco | octahedron-prism atop cuboctahedron, diminished 1/4-lune of rat | 1 | 24, 102, 138, 75, 17 |
opeacope | ope atop cope, octaco-prism, ope-first half of icope | 1.118034 | 36, 138, 176, 90, 18 |
opeah | ope atop hexagon, (trip,gyro trip,hexagon)-trigonic | 1 | 18, 60, 77, 44, 11 |
opeatut (alt.: octoct tuttric) | ope atop tut, (oct,oct,tut)-trigonic | 1.190238 | 24, 72, 84, 45, 11 |
opeatuttip | ope atop tuttip, octatut-prism, ope-first cap of srippip | 1.284523 | 36, 102, 110, 54, 12 |
opepy | octahedral-prismatic pyramid, vertex pyramid of rectified triacontiditeron | 1 | 13, 42, 58, 38, 11 |
opet | octahedral-prism tegum, (line, octahedral prism) duotegum | ... | 14, 54, 88, 66, 20 |
osirco | octagon small-rhombicuboctahedron duoprism | 1.914214 | 192, 576, 616, 264, 34 |
osrid | octagon - small-rhombicosidodecahedron duoprism | 2.587117 | 480, 1440, 1516, 624, 70 |
otet | octagon-tetrahedron duoprism, octagon duofastegium | 1.442951 | 32, 80, 84, 46, 12 |
oti | octagon - truncated-icosahedron duoprism | 2.801372 | 480, 1200, 1036, 354, 40 |
otic (old: ottic) | octagon - truncated-cube duoprism | 2.207107 | 192, 480, 424, 156, 22 |
otid | octagon - truncated-dodecahedron duoprism | 3.244185 | 480, 1200, 1036, 354, 40 |
otoe (old: otto) | octagon truncated-octahedron duoprism | 2.051123 | 192, 480, 424, 156, 22 |
otut | octagon - truncated-tetrahedron duoprism | 1.755593 | 96, 240, 220, 90, 16 |
owoct | octagon octahedron duoprism | 1.485633 | 48, 144, 166, 84, 16 |
pabac carnit | partially bicontracted cellirhombated penteractitriacontiditeron | ... | 600, 2568, 3200, 1384, 154 |
pabac scant | partially bicontracted small cellated penteractitriacontiditeron | ... | 56, 224, 386, 324, 108 |
pabac sirn | partially bicontracted small rhombated penteract | ... | 200, 912, 1144, 520, 90 |
pabac span | partially bicontracted small prismated penteract | ... | 152, 756, 1192, 700, 114 |
pabacca pin | partially bicontracted celliprismated penteract | ... | 304, 1064, 1396, 752, 118 |
pabex gyetac | partially bi-expanded gyroelongated-triacontaditeron | ... | 288, 1008, 1200, 560, 82 |
pabex hix (alt.: thiddipcup) | partially bi-expanded hexateron, thiddip cupoliprism | 1.190238 | 36, 108, 126, 66, 14 |
pabex rat | partially biexpanded rectified triacontiditeron | ... | 100, 528, 852, 504, 82 |
pabex sart | partially biexpanded small rhombated triacontiditeron | ... | 456, 2040, 2560, 1096, 122 |
pabex tac | partially biexpanded triacontaditeron | ... | 32, 128, 230, 204, 72 |
pabexnit | partially biexpanded penteractitriacontiditeron | ... | 152, 752, 968, 440, 74 |
pabextot | partially biexpanded truncated triacontaditeron | ... | 200, 700, 936, 516, 82 |
pabgysiphin | parabigyrated small-prismated-hemipenteract | 1.274755 | 80, 400, 720, 480, 82 |
pac scant | partially contracted small cellated penteractitriacontiditeron | ... | 96, 384, 640, 512, 162 |
pac span | partially contracted small prismated penteract | ... | 224, 1056, 1624, 944, 154 |
pacca pin | partially contracted celliprismated penteract | ... | 448, 1568, 2032, 1080, 170 |
paccarnit | partially contracted cellirhombated penteractitriacontiditeron | ... | 768, 3168, 3920, 1712, 194 |
pacsirn | partially contracted small rhombated penteract | ... | 256, 1088, 1328, 600, 106 |
..., padohi || rofix | (degenerate) padohi atop rofix | ∞ i.e. flat in euclidean space | 2160, 18000, 28080, 14880, 2162 |
pattin | prismatotruncated penteract, runcitruncated penteract | 3.239235 | 960, 3360, 3760, 1560, 202 |
pattit | prismatotruncated triacontiditeron, runcitruncated pentacross | 2.738613 | 960, 3360, 3680, 1440, 162 |
pattix | prismatotruncated hexateron, runcitruncated hexateron | 1.848423 | 180, 630, 720, 315, 47 |
peco | pentagon-cuboctahedron duoprism | 1.312862 | 60, 180, 202, 99, 19 |
pecube | pentagon-cube duoprism | 1.213922 | 40, 100, 98, 47, 11 |
pedoe | pentagon-dodecahedron duoprism | 1.639247 | 100, 250, 230, 95, 17 |
penalsrip, pen || inv srip | (degenerate) pen atop inverted srip | ∞ i.e. flat in euclidean space | 35, 160, 240, 145, 32 |
penaspid | pentachoron atop small prismated decachoron, pen-first rotunda of scad | 1 | 25, 90, 140, 105, 32 |
penasrip | pen atop srip | 1.274755 | 35, 130, 180, 105, 22 |
penatrip | pentachoron atop trigonal prism, (edge,perp triangle,trip)-trigonic | 1 | 11, 31, 39, 25, 8 |
penit (old: pendpy) | pentachoral (line-)tegum, pentachoral dipyramid | 7, 20, 30, 25, 10 | |
pennatip | pen atop tip, pen-first cap of rin | 1.414214 | 25, 70, 80, 45, 12 |
penp | pentachoron prism, vertex figure of ril | 0.806226 | 10, 25, 30, 20, 7 |
pent | penteract, decateron, 5D measure-polytope (γ5), geopet(id) | 1.118034 | 32, 80, 80, 40, 10 |
penth (alt.: stenoh) | penteractic pentacomb, 5D hypercubical honeycomb (δ5), (alt.: small terated penteractic pentacomb) | ||
penu | pentachoron-based ursateron, pen-based ursulate, vertex figure of o3o3o3o4s3s | 1.029086 | 20, 65, 80, 45, 12 |
pepip | pentagon duoprismatic prism | 1.302772 | 50, 125, 120, 55, 12 |
petet | pentagon-tetrahedron duoprism, pentagon duofastegium | 1.048144 | 20, 50, 54, 31, 9 |
pex rat | partially expanded rectified triacontiditeron | ... | 64, 360, 592, 352, 58 |
pex sart | partially expanded small rhombated triacontiditeron | ... | 336, 1584, 2000, 848, 98 |
pex tac | partially expanded triacontaditeron | ... | 18, 72, 136, 128, 48 |
pexgyetac | partially expanded gyroelongated-triacontaditeron | ... | 144, 624, 816, 392, 58 |
pexhin (old: tutas) | partially expanded hemipenteract, truncated tetrahedron altersquarism, tuta alterprism, cyclodiminished siphin | 1.274755 | 48, 192, 296, 188, 38 |
pexhix (alt.: triddipah, tripotricudaw) | partially expanded hexateron, triangle-triangle duoprism atop hexagon, (trip, ortho tricu)-disphenoid | 1 | 15, 42, 52, 33, 10 |
pexnit | partially expanded penteractitriacontiditeron | ... | 112, 608, 800, 360, 58 |
pextot | partially expanded truncated triacontaditeron | ... | 128, 448, 616, 352, 58 |
phap | pentachoric hemiantiprism | 0.707107 | 10, 40, 80, 60, 17 |
pid | pentagon - icosidodecahedron duoprism | 1.828016 | 150, 450, 490, 225, 37 |
pike | pentagon-icosahedron duoprism | 1.275976 | 60, 210, 262, 135, 25 |
pirgadia | pirgady alterprism | 1.125151 | 7200, 36000, 45120, 15840, 1082 |
pirghia | prismatorhombated great hecatonicosachoron alterprism | 4.923348 | 14400, 50400, 51840, 18480, 1682 |
pirhin | prismatorhombated hemipenteract, runcicantellated demipenteract, steriruncic penteract | 2.150581 | 320, 1120, 1280, 560, 82 |
pirt | prismatorhombated triacontiditeron, runcicantellated pentacross | 3 | 960, 2880, 2960, 1200, 162 |
pirx | prismatorhombated hexateron, runcicantellated hexateron | 1.914854 | 180, 540, 570, 255, 47 |
pithin | prismatotruncated hemipenteract, runcitruncated demipenteract, stericantic penteract | 2.371708 | 480, 1680, 1840, 720, 82 |
poct | pentagon - octahedron duoprism | 1.106168 | 30, 90, 106, 57, 13 |
..., prahi || grix | (degenerate) prahi atop grix | ∞ i.e. flat in euclidean space | 14400, 46800, 50880, 21120, 2642 |
prahip (old: prahipe) | prismatorhombated-hexacosachoron prism, runcitruncated-hexacosachoron prism | 8.294035 | 14400, 43200, 44880, 18720, 2642 |
praquinoh | prismatorhombated quarterpenteractic pentacomb | ||
..., prico || gyro grico | (degenerate) prico atop gyrated grico | ∞ i.e. flat in euclidean space | 1152, 3744, 4128, 1776, 242 |
pricoa (old: pricoalprico) | prismatorhombated-icositetrachoron alterprism, prismatorhombated-icositetrachoron atop alternate prismatorhombated-icositetrachoron | 3.522336 | 1152, 4032, 4512, 1872, 242 |
pricope (old: pripe) | prismatorhombated-icositetrachoron prism, runcitruncated-icositetrachoron prism | 3.534493 | 1152, 3456, 3648, 1584, 242 |
prin | prismatorhombated penteract, runcicantellated penteract | 3.047217 | 960, 2880, 2960, 1240, 202 |
pripa (old: pripalprip) | prip alterprism, prip atop inverted prip, medial segment of card | 1.658312 | 120, 420, 480, 210, 32 |
pripa gippid | prip atop gippid, prip-first cap of pattit | 2.738613 | 180, 510, 510, 210, 32 |
pripagrip | prip atop grip | 1.870829 | 120, 390, 440, 200, 32 |
pripal gripu | (prip,grip)-based ursateron | 1.904375 | 180, 540, 570, 245, 37 |
pripalgrip | prip atop alternate grip | 1.848423 | 120, 390, 440, 200, 32 |
prippip | prismatorhombated-pentachoron prism | 1.688194 | 120, 360, 390, 180, 32 |
pripro | prip-first rotunda of captid | 2.236068 | 240, 660, 640, 255, 37 |
prissia | prismatorhombisnub icositetrachoric alterprism, triangle-alternation of prismatorhombated icositetrachoric prism | 3.534493 | 576, 2880, 4224, 2256, 338 |
..., prit || grit | (degenerate) prit atop grit | ∞ i.e. flat in euclidean space | 384, 1248, 1384, 600, 82 |
prittip | prismatorhombated-tesseract prism, prismatotruncated-hexadecachoron prism, runcitruncated-hexadecachoron prism, central segment of cappin | 2.423081 | 384, 1152, 1216, 528, 82 |
prixip | prismatorhombated-hexacosachoron prism, runcitruncated-hexacosachoron prism | 9.757429 | 14400, 43200, 44880, 18720, 2642 |
..., proh || gidpith | (degenerate) proh atop gidpith | ∞ i.e. flat in euclidean space | 576, 1632, 1600, 624, 82 |
prohagrit | proh atop grit, proh-first segment of pattin | 3.239235 | 384, 1248, 1384, 600, 82 |
prohalsrico | proh atop srico | 2.632865 | 480, 2112, 2624, 1168, 178 |
prohp | prismatorhombated-hexadecachoron prism, prismatotruncated-tesseract prism, runcitruncated-tesseract prism, central segment of carnit | 2.660531 | 384, 1152, 1216, 528, 82 |
pysnan | pyritosnub penteract, edge-alternation of great cellated penteractitriacontiditeron | ... | 1920, 10560, 15360, 7920, 1202 |
pysneta | pyritosnub tesseractic alterprism, edge-snub hexadecachoric hosoteron | ... | 384, 1920, 2848, 1584, 274 |
... | q x3o3o3o, variation of pentachoron prism, vertex figure of rectified hexeract | 0.948683 | 10, 25, 30, 20, 7 |
quacant | quasicellated penteractitriacontiditeron | 1.021221 | 160, 640, 1040, 800, 242 |
quacgarn | quasicelligreatorhombated penteract | 2.143163 | 1920, 5760, 6000, 2400, 242 |
quacpot | quasicelliprismated triacontiditeron | 1.102028 | 640, 2240, 2960, 1600, 242 |
quacrant | quasicellirhombipenteractitriacontiditeron | 1.192297 | 960, 3840, 4720, 2080, 242 |
quappin | quasiprismated penteract | 0.914214 | 320, 1440, 2160, 1240, 202 |
quarn | quasirhombated penteract | 0.792893 | 320, 1280, 1520, 680, 122 |
quicgrat (old: cogqrit) | quasicelligreat rhombated triacontiditeron, (celligreat quasirhombated triacontiditeron) | 2.001839 | 1920, 5760, 5920, 2320, 242 |
quicpatint | quasicelliprismatotruncated penteractitriacontiditeron | 1.949424 | 1920, 5760, 5760, 2160, 242 |
quiprin | quasiprismatorhombated penteract | 1.488108 | 960, 2880, 2960, 1240, 202 |
quiptin | quasiprismatotruncated penteract | 1.416813 | 960, 3360, 3760, 1560, 202 |
quithesc | quasitruncated-hexahedral scalene, quasitruncated-hexahedral-pyramid pyramid, line atop fully orthogonal quasitruncated hexahedron | 0.633157 | 26, 85, 110, 65, 16 |
quititip | quasitruncated-tesseract prism | 0.792893 | 128, 320, 304, 136, 26 |
quittin | quasitruncated penteract | 0.649286 | 160, 400, 400, 200, 42 |
rabird | retrobirhombidodecateron | 1.414214 | 90, 360, 360, 120, 18 |
raccoth | retrocellitriacontadiahexadecateron | 1.224745 | 80, 480, 960, 640, 88 |
racpix | retrocelliprismated hexateron | 1.632993 | 120, 420, 450, 195, 33 |
racyxh | rhombated cyclohexateric honeycomb, cyclorhombated hexateric honeycomb | ||
radah | retrodishexadecateron | 0.790569 | 16, 80, 220, 160, 32 |
..., ragaghi || tigaghi | (degenerate) ragaghi atop tigaghi | ∞ i.e. flat in euclidean space | 3600, 10800, 9120, 2640, 242 |
ragashia | rectified grand stellated hecatonicosachoron alterprism | 1.248606 | 1440, 10800, 11520, 3360, 242 |
raggixu | raggix-based ursateron | 1.175984 | 5040, 22320, 26640, 10800, 1442 |
..., rahi || tex | (degenerate) rahi atop tex | ∞ i.e. flat in euclidean space | 2640, 15120, 21120, 10080, 1442 |
rahia sidpixhi | (degenerate) rahi atop sidpixhi | ∞ i.e. flat in euclidean space | 3600, 18000, 28560, 16800, 2642 |
rahipe | rectified-hecatonicosachoron prism | 4.562051 | 2400, 8400, 9840, 4560, 722 |
rapaco (alt.: tetoct cotric) | rap atop co, 0.176208-luna of rat, (tet,oct,co)-trigonic | 1 | 22, 90, 128, 75, 17 |
rapadeca | rap atop deca, rap-first cap of sirhin | 1.620185 | 40, 120, 130, 60, 12 |
rapalprip, rap || inv prip | (degenerate) rap atop inverted prip | ∞ i.e. flat in euclidean space | 70, 240, 300, 160, 32 |
rapalsrip | rap atop inverted srip, rap-first cap of spix | 1.190238 | 40, 150, 200, 110, 22 |
rapaltip | (degenerate) rap atop inverted tip | ∞ i.e. flat in euclidean space | 30, 130, 180, 100, 22 |
rapaspid | rectified pentachoron atop small prismated decachoron, rap-first half of rat | 1 | 30, 150, 250, 160, 32 |
rapasrip | rectified pentachoron atop small rhombated pentachoron, rap-first cap of nit | 1.224745 | 40, 180, 230, 110, 22 |
rapatip | rap atop tip, rap-first cap of sarx | 0.774597 | 30, 90, 100, 50, 12 |
rapatut (alt.: tetoct tuttric) | rap atop tut, (tet,oct,tut)-trigonic | 1.190238 | 22, 72, 86, 45, 11 |
rapirx | retroprismatorhombated hexateron | 1.914854 | 180, 540, 540, 225, 38 |
rappip | rectified-pentachoron prism, vertex figure of rojak | 0.921954 | 20, 70, 90, 50, 12 |
rappy | rectified-pentachoric pyramid, vertex cap of hin | 0.790569 | 11, 40, 60, 40, 11 |
rapt | rectified-pentachoric (line-)tegum, rectified-pentachoric dipyramid | ... | 12, 50, 90, 70, 20 |
raptum | rap-first bistratic cap of thin, rap-based tutsatope, rap-based tutism | 1.903943 | 80, 220, 230, 110, 22 |
rapu | rectified-pentachoron-based ursateron, rap-based ursulate | 1.258489 | 50, 190, 230, 110, 22 |
rasishia | rasishi alterprism | 2.829949 | 2400, 14400, 18720, 5520, 362 |
... | rasishia + 2 2rasishi | 2.829949 | |
rat | rectified triacontiditeron, rectified pentacross, vertex figure of hinoh, lattice B5 contact polytope (span of its small roots), lattice D5 contact polytope (span of its roots), equatorial cross-section of tac-first rag, equatorial cross-section of hin-first mo | 1 | 40, 240, 400, 240, 42 |
ratchet | retrotriacontidicellihemitriacontaditeron | 1 | 40, 240, 600, 560, 88 |
rawcax (old: rawvdipdopdix) | retrosphenary cellihexateron, (retrosphenoverted disprismatoduoprismatodiakishexateron) | 1.290994 | 60, 240, 440, 285, 62 |
rawcbinant (old: recarnit) | retrosphenary cellibiprismatopenteractipenteractitriacontaditeron, retrocellirhombated penteractitriacontaditeron | 2.660531 | 960, 3840, 4240, 1600, 172 |
rawn (old: rawvanant) | retrosphenary penteract | 2.207107 | 320, 1280, 1280, 440, 52 |
rawx | retrosphenary hexateron | 1.290994 | 60, 240, 260, 105, 18 |
recaptid | retrocelliprismatotruncated dodecateron | 2.236068 | 360, 1080, 1050, 390, 48 |
recard | retrocellirhombated dodecaateron | 1.658312 | 180, 720, 780, 300, 44 |
... | rectification/ambification of icoap | 1.847759 | 336, 2304, 3744, 2064, 290 |
repenp (alt.: ampenp) | rectified/ambified penp | 1.264911 | 25, 100, 130, 70, 17 |
repirt | retroprismatorhombated triacontiditeron | 3 | 960, 2880, 2800, 1040, 132 |
rerin | rectified rectified-penteract | 2.645751 | 320, 1280, 1520, 680, 122 |
rescad | rectified scad | 1.732051 | 120, 720, 1170, 660, 92 |
resibrid | rectified sibrid | 2.645751 | 360, 1440, 1680, 720, 122 |
retratet (alt.: amtratet) | rectified/ambified tratet | 1.354006 | 30, 120, 144, 81, 19 |
rhohid | rectified hexadecahemidecateron | 1 | 40, 240, 400, 200, 31 |
ricasrit, rico || srit | rectified-icositetrachoron atop small-rhombated-tesseract | 1.847759 | 192, 960, 1256, 568, 82 |
ricatah | rico atop tah, rico-first cap of sibrant | 2.236068 | 192, 672, 744, 312, 50 |
..., rico || gyro srico | (degenerate) rico atop gyrated srico | ∞ i.e. flat in euclidean space | 384, 1440, 1824, 912, 146 |
..., rico || proh | (degenerate) rico atop proh | ∞ i.e. flat in euclidean space | 288, 960, 1088, 496, 82 |
ricoa (old: ricoalrico), rico || gyro rico | rectified icositetrachoron alterprism, rectified icositetrachoron atop gyrated rectified icositetrachoron | 1.778824 | 192, 864, 1056, 432, 50 |
ricoa ticotum | rico-based tutsatope, rico-based tutism, rico-first bistratic cap of pattit | 2.738613 | 384, 1152, 1168, 456, 58 |
ricoasadi | rico atop sadi | 1.738546 | 192, 1008, 1584, 912, 146 |
ricoaspic | rectified icositetrachoron atop small prismated icositetrachoron | 1.847759 | 240, 1440, 2352, 1392, 242 |
ricoatico | (degenerate) rico atop tico | ∞ i.e. flat in euclidean space | 288, 864, 864, 336, 50 |
ricope | rectified-icositetrachoron prism | 1.802776 | 192, 672, 768, 336, 50 |
..., rigfix || quipdohi | (degenerate) rigfix atop quipdohi | ∞ i.e. flat in euclidean space | 2160, 18000, 28080, 14880, 2162 |
..., rigfix || sirgaghi | (degenerate) rigfix atop sirgaghi | ∞ i.e. flat in euclidean space | 4320, 18000, 21600, 9840, 1442 |
righia | rectified great hecatonicosachoron alterprism | 1.917564 | 1440, 10800, 11520, 3360, 242 |
rin | rectified penteract, equatorial cross-section of nit-first brox | 1.414214 | 80, 320, 400, 200, 42 |
rinah | retropenteractihexadecateron | 0.790569 | 16, 80, 220, 200, 26 |
rinoh | rectified penteractic pentacomb | ||
rippix | retroprismated hexateron | 1.190238 | 60, 270, 300, 120, 18 |
..., rit || tat | (degenerate) rit atop tat | ∞ i.e. flat in euclidean space | 96, 288, 304, 136, 26 |
rita (old: ritag rit) | rit atop gyro rit, medial segment of hex-first siphin | 1.274755 | 64, 288, 464, 288, 50 |
rita sidpith, rit || sidpith | rectified-tesseract atop small-disprismated-tesseractihexadecachoron | 1.502958 | 96, 480, 776, 472, 82 |
ritag thex | rit atop gyrated thex, rit-first cap of sirhin | 1.620185 | 80, 312, 376, 168, 26 |
ritarico | rectified-tesseract atop rectified-icositetrachoron, rectified-tesseract-first segment of small-prismated-triacontiditeron | 1.870829 | 128, 480, 616, 312, 50 |
ritasrit, rit || srit | rectified-tesseract atop small-rhombated-tesseract | 2.632865 | 128, 576, 720, 328, 58 |
ritatah, rit || tah | (degenerate) rit atop tah | ∞ i.e. flat in euclidean space | 128, 384, 400, 168, 26 |
ritathex | (degenerate) rit atop thex | ∞ i.e. flat in euclidean space | 80, 408, 568, 288, 50 |
ritathexu | rit-based ursateron | 1.627127 | 112, 392, 456, 208, 34 |
rittip | rectified-tesseract prism | 1.322876 | 64, 224, 272, 136, 26 |
rix | rectified hexateron, vertex figure of hax, Gosset polytope 03,1, equatorial cross-section of hix-first jak | 0.816497 | 15, 60, 80, 45, 12 |
rocgrax | retrocelligreat rhombated hexateron | 2.327373 | 360, 1080, 1080, 420, 53 |
rocrax (old: sircrax) | (small) retrocellirhombated hexateron | 1.658312 | 180, 720, 840, 360, 53 |
..., rofix || sirsashi | (degenerate) rofix atop sirsashi | ∞ i.e. flat in euclidean space | 4320, 18000, 21600, 9840, 1442 |
roxahi, rox || hi | (degenerate) rox atop hi | ∞ i.e. flat in euclidean space | 1320, 8400, 15120, 9960, 1922 |
roxip | rectified-hexacosachoron prism | 3.118034 | 1440, 7920, 10800, 5040, 722 |
... | tetrahedral - n-prismantiprismoid | ... | 8n, 44n, 80n+8, 54n+12, 10n+6 |
... | tetrahedral - 2n-prismantiprismoid | ... | 16n, 64n, 100n+8, 64n+12, 12n+6 |
... | hyperbolic s3s4o3o4o3o pentacomb | 0.351578 i | |
... | tetrahedral - square-prismantiprismoid | ... | 32, 128, 208, 140, 30 |
... | s4x2x3o4s, trip-alternated osirco | 1.914214 | 96, 336, 448, 256, 50 |
... | triangular,tetrahedral duoantiprism | ... | 24, 132, 248, 174, 36 |
... | tetrahedral - hexagon-prismantiprismoid | ... | 48, 192, 308, 204, 42 |
sadiap | snub disicositetrachoric antiprism, triangle-alternation of truncated icositetrachoric prism | 2.692582 | 192, 1248, 2112, 1296, 242 |
sadinnert | small dispenteractirhombated triacontaditeron | 2.010695 | 1920, 4800, 3760, 1080, 92 |
sadip | snub-icositetrachoron prism, snub-disicositetrachoron prism, semistruncated-icositetrachoron prism | 1.693527 | 192, 960, 1392, 768, 146 |
sart | small rhombated triacontiditeron, cantellated pentacross, equatorial cross-section of nit-first ram | 1.732051 | 240, 1200, 1520, 640, 82 |
sarx | small rhombated hexateron, cantellated hexateron | 1.290994 | 60, 240, 290, 135, 27 |
scad (old: shad) | small cellated dodecateron, small hedrated dodecateron, stericated hexateron, expanded hexateron, vertex figure of cyxh, lattice A5 contact polytope (span of its roots), equatorial cross-section of hix-first staf, equatorial cross-section of rix-first rag, equatorial cross-section of vertex-first mo | 1 | 30, 120, 210, 180, 62 |
scant | small cellated penteractitriacontiditeron, stericated penteract, stericated pentacross | 1.567516 | 160, 640, 1040, 800, 242 |
setitdin | small tesseractitriacontidiadispenteract | 2.423081 | 640, 2240, 2160, 760, 92 |
shadow | small heptagrammic disphenoid, small heptagramm atop fully orthogonal small heptagramm | 0.674163 | 14, 63, 100, 63, 14 |
sibcotdin | small biprismatocellitriacontadiadispenteract | 3.534493 | 1920, 5760, 5440, 1840, 172 |
sibrant | small birhombated penteractitriacontiditeron, bicantellated penteract, bicantellated pentacross | 2.236068 | 480, 1920, 2160, 840, 122 |
sibrid (old: sadrid) | small birhombated dodecateron, bicantellated hexateron, equatorial cross-section of scad-first trim, equatorial cross-section of rix-first brox | 1.414214 | 90, 360, 420, 180, 32 |
... | isomorph of small birhombated dodecateron | 0.816497 | 90, 360, 420, 180, 32 |
sibtadin | small biprismatotriacontadiadispenteract | 3.047217 | 960, 2880, 2720, 1000, 132 |
sid pippadia | sid pippady alterprism | 2.527959 | 2880, 21600, 34560, 14880, 1082 |
... | sid pippadia + 240 2sissid | 2.527959 | |
..., sidpith || prit | (degenerate) sidpith atop prit | ∞ i.e. flat in euclidean space | 256, 864, 1056, 528, 82 |
..., sidpith || tat | (degenerate) sidpith atop tat | ∞ i.e. flat in euclidean space | 128, 512, 776, 472, 82 |
sidpithip | small-disprismatotesseractihexadecachoron prism, runcinated-tesseract prism, small-prismated-tesseract prism, central segment of scant | 1.567516 | 128, 448, 608, 368, 82 |
..., sidpixhi || srix | (degenerate) sidpixhi atop srix | ∞ i.e. flat in euclidean space | 6000, 25200, 34080, 17520, 2642 |
sidpixhip | small-disprismatohexacosihecatonicosachoron prism, runcinated-hecatonicosachoron prism, runcinated-hexacosachoron prism | 5.259887 | 4800, 16800, 22080, 12720, 2642 |
sidtaxhiap | small ditetrahedrary hexacontahecatonicosachoron antiprism | 2.321762 | 1200, 9600, 13440, 6960, 1322 |
sidtixhipy, pt || sidtixhi | (degenerate) sidtixhi pyramid | ∞ i.e. flat in euclidean space | 121, 1320, 3600, 3120, 721 |
sidtixhiu | sidtixhi-based ursateron | 1.008123 | 1440, 10920, 17040, 7800, 842 |
sinnont | small penteractipenteractitriacontiditeron | 1.567516 | 160, 640, 640, 280, 52 |
siphin | small prismated hemipenteract, runcinated demipenteract, steric penteract | 1.274755 | 80, 400, 720, 480, 82 |
sircaptint (old: srecaptint) | small retrocelliprismatotruncated penteractitriacontaditeron | 3.701317 | 1920, 5760, 5440, 1840, 172 |
sirco acope | small-rhombicuboctahedron atop cuboctahedron-prism | 1.502958 | 48, 204, 270, 141, 29 |
sircoa ticcup | small-rhombicuboctahedron atop truncated-cube-prism | 2.207107 | 72, 240, 282, 141, 29 |
sirdtaxadiap | small retroditetrahedronary hexacosidishecatonicosachoron atop alternate small retroditetrahedronary hexacosidishecatonicosachoron, small retroditetrahedronary hexacosidishecatonicosachoron alterprism | 2.321762 | 1200, 9600, 14880, 7920, 1442 |
sirgashia | small rhombated grand stellated hecatonicosachoron alterprism | 1.618034 | 7200, 36000, 43200, 17040, 1682 |
sirgaship | small-rhombated-grand-stellated-hecatonicosachoron prism | 1.666693 | 7200, 25200, 25200, 9120, 962 |
sirghia | small rhombated great hecatonicosachoron alterprism | 3.404434 | 7200, 36000, 43200, 17040, 1682 |
sirghipe | small-rhombated-great-hecatonicosachoron prism | 3.423760 | 7200, 25200, 25200, 9120, 962 |
sirhin | small rhombihemipenteract, cantellated demipenteract, runcic penteract | 1.620185 | 160, 720, 880, 360, 42 |
... | isomorph of small rhombihemipenteract | 0.790569 | |
sirn | small rhombated penteract, cantellated penteract | 2.207107 | 320, 1280, 1520, 680, 122 |
sirnoh | small rhombated penteractic honeycomb | ||
sirpin | small retroprismated penteract | 1.914214 | 320, 1440, 1440, 480, 52 |
..., sishi || fix | (degenerate) sishi atop fix, (degenerate) sishi antiprism, (degenerate) fix antiprism | ∞ i.e. flat in euclidean space | 240, 3360, 9120, 7680, 2162 |
sishia | small stellated hecatonicosachoron alterprism, narrower sishi atop sishi | 1.074481 | 240, 3840, 8640, 3840, 362 |
... | sishia + 2 2sishi | 1.074481 | |
sishipy, pt || sishi | (degenerate) sishi pyramid | ∞ i.e. flat in euclidean space | 121, 1320, 1920, 840, 121 |
sissidisc | small-stellated-dodecahedral scalene, small-stellated-dodecahedral-pyramid pyramid, line atop fully orthogonal small stellated dodecahedron | 0.636010 | 14, 55, 84, 55, 14 |
sistadow | (square,pentagram)-disphenoid, square atop fully orthogonal pentagram | 0.707107 | 9, 29, 42, 29, 9 |
sitpodadia | small (intersected) tripesic dodecahedronary dishecatonicosachoron alterprism | 1.074481 | 240, 8640, 13440, 6000, 362 |
skatbacadint | small skewtrigonary biprismatocellidispenteractitriacontiditeron | 1.5 | 640, 2880, 3920, 1920, 172 |
snan | snub penteract, alternation of great cellated penteractitriacontiditeron | ... | 1920, 13440, 21600, 12240, 2162 |
snippit (old: spitac, alt.: snahin) | snub prismatotriacontaditeron, snub demipenteract, alternation of great prismated triacontaditeron | ... | 960, 6720, 10880, 6240, 1122 |
snod (snix) | snub dodecateron (snub hexateron), alternation of great cellated hexateron | ... | 360, 2520, 4080, 2340, 422 |
sophip | small-prismatohecatonicosachoron prism | 3.118034 | 1440, 7920, 10080, 4920, 842 |
spacyxh | small prismated cyclohexateric honeycomb | ||
span | small prismated penteract, runcinated penteract | 1.914214 | 320, 1440, 2160, 1240, 202 |
spaquinoh | small prismated quarterpenteractic pentacomb | ||
spat | small prismated triacontiditeron, runcinated pentacross | 1.870829 | 320, 1440, 2160, 1200, 162 |
sphiddixa | small prismatohecatonicosadishexacosachoron alterprism | 6.893126 | 14400, 50400, 53280, 19920, 2042 |
..., spic || srico | (degenerate) spic atop srico | ∞ i.e. flat in euclidean space | 432, 2016, 2832, 1488, 242 |
spiccup | small-prismatotetracontoctachoron prism, runcinated-icositetrachoron prism | 1.914214 | 288, 1296, 1920, 1152, 242 |
spidadeca, spid || deca | (degenerate) spid atop deca | ∞ i.e. flat in euclidean space | 50, 240, 350, 190, 32 |
spidaprip | spid atop prip, spid-first monostratic cap of spat | 1.870829 | 80, 270, 340, 180, 32 |
spidasrip | spid atop srip, spid-first cap of spix | 1.190238 | 50, 210, 300, 170, 32 |
spidasripu | (spid,srip)-based ursateron | 1.331369 | 70, 260, 350, 195, 37 |
spidatip | small-prismate-pentachoron atop alternate truncated-pentachoron | 1.274755 | 40, 160, 250, 160, 32 |
spiddip | small-prismatodecachoron prism | 1.118034 | 40, 140, 200, 130, 32 |
spidpy | (degenerate) spid pyramid | ∞ i.e. flat in euclidean space | 21, 80, 130, 100, 31 |
... | vertex figure of spil | 0.924211 | 12, 39, 52, 33, 10 |
spix | small prismated hexateron, runcinated hexateron | 1.190238 | 60, 270, 420, 255, 47 |
squaco | square-cuboctahedron duoprism | 1.224745 | 48, 144, 164, 84, 18 |
squadinit | square-diminished nit | 1.224745 | 56, 240, 344, 200, 42 |
squadoe | square-dodecahedron duoprism | 1.569562 | 80, 200, 188, 82, 16 |
squagirco | square great-rhombicuboctahedron duoprism | 2.423081 | 192, 480, 440, 180, 30 |
squagrid | square - great-rhombicosidodecahedron duoprism | 3.867584 | 480, 1200, 1088, 432, 66 |
... | squap - square duoprism, {4}-wedge of tessap | 1.050501 | 20, 68, 89, 52, 13 |
squascop | squasc prism, square-scalene prism, square atop cube | 0.866025 | 12, 32, 39, 25, 8 |
squasirco | square - small-rhombicuboctahedron duoprism | 1.567516 | 96, 288, 320, 156, 30 |
squasnic | square - snub-cube duoprism | 1.518409 | 96, 336, 416, 216, 42 |
squasnid | square - snub-dodecahedron duoprism | 2.268840 | 240, 840, 1028, 522, 96 |
squasquasc | {4} atop squasc | 0.790569 | 10, 29, 38, 25, 8 |
squasquippy | square-squippy duoprism, squippyp prism | 1 | 20, 52, 57, 32, 9 |
squasrid | square - small-rhombicosidodecahedron duoprism | 2.342236 | 240, 720, 788, 372, 66 |
squatet | square-tetrahedron duoprism, square duofastegium, 2,4-duoprism cupoliprism, vertex figure of brox | 0.935414 | 16, 40, 44, 26, 8 |
squati | square - truncated-icosahedron duoprism | 2.576932 | 240, 600, 548, 222, 36 |
squatic | square - truncated-cube duoprism | 1.914214 | 96, 240, 224, 96, 18 |
squatid | square - truncated-dodecahedron duoprism | 3.052479 | 240, 600, 548, 222, 36 |
squatoe (old: squato) | square - truncated-octahedron duoprism | 1.732051 | 96, 240, 224, 96, 18 |
squatricu | square-tricu duoprism | 1.224745 | 36, 96, 101, 51, 12 |
squatut | square - truncated-tetrahedron duoprism | 1.369306 | 48, 120, 116, 54, 12 |
squete | square-pyramidal pyramid pyramid, square-tettene, triangular-square disphenoid, half of the triacontiditeron | 0.707107 | 7, 19, 26, 19, 7 |
squicuffip | squicuf prism, tes atop op | 1.567516 | 32, 88, 98, 53, 13 |
squid | square-icosidodecahedron duoprism | 1.765796 | 120, 360, 398, 192, 36 |
squiddaf | square duoantifastegium, digonal-square duoantiwedge, square prism atop bidual square prism | 0.895420 | 16, 56, 76, 46, 12 |
squike | square-icosahedron duoprism | 1.185120 | 48, 168, 212, 114, 24 |
squippyippy | square-pyramidal-prismatic pyramid, half of vertex pyramid of rectified triacontiditeron | 1 | 11, 31, 39, 25, 8 |
squoct | square-octahedron duoprism, vertex figure of brinoh | 1 | 24, 72, 86, 48, 12 |
..., srahi || xhi | (degenerate) srahi atop xhi | ∞ i.e. flat in euclidean space | 7200, 25200, 27840, 11760, 1922 |
srahip (old: srahipe) | small-rhombated-hecatonicosachoron prism | 6.753568 | 7200, 25200, 29040, 12960, 1922 |
..., srico || cont | (degenerate) srico atop cont | ∞ i.e. flat in euclidean space | 576, 2016, 2208, 912, 146 |
..., srico || prico | (degenerate) srico atop prico | ∞ i.e. flat in euclidean space | 864, 2880, 3264, 1488, 242 |
sricoa (old: sricoalsrico), srico || gyro srico | small-rhombated-icositetrachoron alterprism, small-rhombated-icositetrachoron atop gyrated small-rhombated-icositetrachoron | 2.632865 | 576, 2880, 3744, 1680, 242 |
sricope (old: sripe) | small-rhombated-icositetrachoron prism, cantellated-icositetrachoron prism | 2.660531 | 576, 2016, 2304, 1008, 146 |
sripa (alt: pabdinit, old: sripalsrip) | small rhombated pentachoron alterprism, small rhombated pentachoron atop inverted small rhombated pentachoron, parabidiminished nit, equatorial segment of nit | 1.224745 | 60, 300, 400, 190, 32 |
sripa gippidtum | srip-first bistratic cap of pithin, (srip,gippid)-based tutsateron, (srip,gippid)-based tutism | 2.371708 | 180, 510, 510, 210, 32 |
sripadeca | srip atop deca, srip-first half of sibrid | 1.414214 | 60, 210, 240, 110, 22 |
sripadecu | (srip,deca)-based ursateron | 1.514954 | 90, 300, 340, 155, 27 |
sripagrip | srip atop grip, srip-first cap of sibrant | 2.236068 | 90, 270, 280, 120, 22 |
sripal pripu | (srip,inv.prip)-based ursateron | 1.637956 | 120, 420, 480, 210, 32 |
sripalgrip, srip || inv grip | (degenerate) srip atop inverted grip | ∞ i.e. flat in euclidean space | 90, 330, 400, 190, 32 |
sripalprip | srip atop inverted prip, srip-first cap of sart | 1.732051 | 90, 360, 440, 200, 32 |
sripaltip | srip atop inverted tip | 1.274755 | 50, 190, 260, 150, 32 |
sripaprip | srip atop prip, srip-first cap of card | 1.658312 | 90, 300, 350, 170, 32 |
sripatip | srip atop tip, srip-first segment of sarx | 1.290994 | 50, 190, 230, 110, 22 |
srippip | small-rhombated-pentachoron prism | 1.284523 | 60, 210, 250, 120, 22 |
..., srit || proh | (degenerate) srit atop proh | ∞ i.e. flat in euclidean space | 288, 1152, 1384, 600, 82 |
sritaprohu | (srit,proh)-based ursateron | 2.706827 | 384, 1344, 1504, 624, 82 |
srittip | small-rhombated-tesseract prism | 1.914214 | 192, 672, 784, 360, 58 |
srixasrahi | (degenerate) srix atop srahi | ∞ i.e. flat in euclidean space | 7200, 36000, 46560, 20400, 2642 |
srixip | small-rhombated-hexacosachoron prism, cantellated-hexacosachoron prism | 6.094140 | 7200, 25200, 28080, 11520, 1442 |
srocgrin | small retrocelligreat rhombated penteract | 3.988340 | 1920, 5760, 5680, 2080, 212 |
sroptin | small retroprismatotruncated penteract | 3.239235 | 960, 3360, 3440, 1240, 132 |
stade | stellated dodecateron, compound of 2 hix | 0.645497 | |
stadow | pentagrammic disphenoid, pentagram atop fully orthogonal pentagram | 0.623054 | 10, 35, 52, 35, 10 |
starpedippy, pt || starpedip | (degenerate) starpedip pyramid | ∞ i.e. flat in euclidean space | 26, 75, 85, 45, 11 |
state | stellar tettene, pentagrammic tettene, pentagram-pyramidal pyramid pyramid, triangle atop fully orthogonal pentagram | 0.636010 | 8, 23, 32, 23, 8 |
stethip | small-tesseractitesseractihexadecachoron prism | 1.567516 | 128, 448, 464, 200, 34 |
stoct | pentagram - octahedron duoprism | 0.881132 | 30, 90, 106, 57, 13 |
stotet | octagram-tetrahedron duoprism, octagram duofastegium | 0.817247 | 32, 80, 84, 46, 12 |
stotoe | octagram truncated-octahedron duoprism, star-octagon truncated-octahedron duoprism | 1.671195 | 192, 480, 424, 156, 22 |
stowoct | octagram octahedron duoprism | 0.890446 | 48, 144, 166, 84, 16 |
stut phiddixa | small tritrigonal prismatohecatonicosidishexacosachoron alterprism | 3.855219 | 4800, 28800, 41280, 19920, 2042 |
sutia | small-tetrakisicositetrachoron alterprism | 1.677756 | 1152, 4032, 4224, 1440, 98 |
tac | triacontiditeron, pentacross (β5), aeropet(id), pentachoral antiprism, vertex figure of gee, Gosset polytopes 21,1, lattice C5 contact polytope (span of its small roots), equatorial cross-section of vertex-first gee | 0.707107 | 10, 40, 80, 80, 32 |
..., tah || grit | (degenerate) tah atop grit | ∞ i.e. flat in euclidean space | 288, 768, 752, 328, 58 |
taha (old: tahagtah), tah || gyro tah | tah alterprism, tah atop gyro tah | 2.150581 | 192, 576, 624, 288, 50 |
tahatico | tah atop tico, tah-first segment of pirt | 3 | 288, 768, 744, 312, 50 |
tahp | tesseractihexadecachoron prism, bitruncated-tesseract prism, bitruncated-hexadecachoron prism | 2.179449 | 192, 480, 432, 168, 26 |
tan | truncated penteract | 2.465447 | 160, 400, 400, 200, 42 |
tanoh | truncated penteractic pentacomb | ||
taope | triangle atop octahedral-prism | 0.866025 | 15, 51, 68, 41, 11 |
..., tat || grit | (degenerate) tat atop grit | ∞ i.e. flat in euclidean space | 256, 704, 720, 328, 58 |
..., tat || prit | (degenerate) tat atop prit | ∞ i.e. flat in euclidean space | 256, 992, 1224, 568, 82 |
tattip | truncated-tesseract prism | 2.207107 | 128, 320, 304, 136, 26 |
teddot | tetradiminished dodecateron, bidrap alterprism, bidrap atop gyroinverted bidrap | 0.866025 | 16, 54, 78, 54, 16 |
tedhin | tetradiminished hemipenteract, square || hex | 0.790569 | 12, 44, 73, 56, 17 |
tedrat | (cyclo-)tetra-diminished rat | 1 | 36, 192, 328, 212, 42 |
tedrix | tridiminished rectified hexateron, square triorthowedge, lace simplex of 3 mutually orthogonal squares | 0.816497 | 12, 36, 47, 30, 9 |
tepaco (alt.: tettet cotric) | tepe atop co, 0.217953-luna of scad, (tet,tet,co)-trigonic, partial Stott expansion of hix | 1 | 20, 64, 88, 59, 17 |
tepacube | tepe || cube, bidrap prism, bi-edge-dimin. rappip, wedge-faceted rappip | 0.921954 | 16, 44, 52, 31, 9 |
tepatut (alt.: tettet tuttric) | tepe atop tut, tepe-first wedge of siphin, (tet,tet,tut)-trigonic | 1.274755 | 20, 58, 70, 41, 11 |
tepeacope | tepe atop cope, tepe-first half of spiddip | 1.118034 | 32, 100, 126, 74, 18 |
tepeatuttip | tepe atop tuttip, tetatut-prism | 1.322876 | 32, 88, 96, 50, 12 |
tepepy | tetrahedral-prismatic pyramid, vertex pyramid of rectified hexateron | 0.816497 | 9, 24, 30, 20, 7 |
..., tes || sadi | tes atop sadi | ∞ i.e. flat in euclidean space | 112, 656, 1176, 808, 178 |
..., tes || srit | (degenerate) tes atop srit | ∞ i.e. flat in euclidean space | 112, 416, 560, 312, 58 |
tespy | (degenerate) tes pyramid | ∞ i.e. flat in euclidean space | 17, 48, 56, 32, 9 |
tessap | tesseract antiprism, hexadecachoron antiprism | 1.050501 | 24, 120, 248, 232, 82 |
tessarit | tesseract atop rectified tesseract | 1.227160 | 48, 192, 240, 120, 26 |
teta ope (alt.: octarap, tetoct octtric) | tetrahedron atop octahedron-prism, octahedron atop rectified-pentachoron, half of dodecateron (its tet-first rotunda), (tet,oct,oct)-trigonic | 0.866025 | 16, 60, 80, 45, 11 |
teta tuttip (alt.: tettut tuttric) | tet atop tuttip, tet-first cap of sirhin, (tet,tut,tut)-trigonic | 1.620185 | 28, 78, 86, 45, 11 |
tetacope | tet atop cope, tet-first segment of spix | 1.190238 | 28, 90, 116, 69, 17 |
tetaf (alt.: tetaltepe, tettet altettric) | tetrahedral antifastegium, tet atop inverted tepe, tet-first rotunda of hin, (tet,tet,dual tet)-trigonic | 0.790569 | 12, 46, 78, 59, 17 |
tetco tuttric | (tet,co,tut)-trigonic | 1.274755 | 28, 96, 128, 75, 17 |
tetcubedaw (alt.: daworsquip) | (tet,cube)-disphenoid, 1/6-lune of dodecateron, digonal antiprism atop axis-orthogonal square prism | 0.866025 | 12, 34, 42, 26, 8 |
..., tex || sidpixhi | (degenerate) tex atop sidpixhi | ∞ i.e. flat in euclidean space | 3840, 18720, 29040, 16800, 2642 |
texip | truncated-hexacosachoron prism | 4.749980 | 2880, 10080, 11520, 5040, 722 |
..., thex || prit | (degenerate) thex atop prit | ∞ i.e. flat in euclidean space | 240, 792, 944, 472, 82 |
thexa (old: thexag thex), thex || gyro thex | thex alterprism, thex atop gyro thex, equatorial segment of sirhin | 1.620185 | 96, 336, 384, 168, 26 |
thexagtah | thex atop gyrated tah | 2.371708 | 144, 408, 408, 168, 26 |
thexarico | thex atop rico, ico-first subsegment of sart | 1.732051 | 144, 600, 720, 312, 50 |
thexatah | (degenerate) thex atop tah | ∞ i.e. flat in euclidean space | 144, 504, 600, 288, 50 |
thexip | truncated-hexadecachoron prism | 1.658312 | 96, 288, 312, 144, 26 |
thin | truncated hemipenteract, cantic penteract | 1.903943 | 160, 560, 640, 280, 42 |
thinoh | truncated hemipenteractic pentacomb | ||
thipe | truncated-hecatonicosachoron prism | 8.233530 | 4800, 12000, 11040, 4560, 722 |
ticca gircope | truncated-cube atop great-rhombicuboctahedron-prism | 3.239235 | 120, 324, 330, 153, 29 |
ticca sircope | truncated-cube atop small-rhombicuboctahedron-prism | 1.914214 | 72, 252, 306, 153, 29 |
..., tico || gidpith | (degenerate) tico atop gidpith | ∞ i.e. flat in euclidean space | 576, 1536, 1472, 592, 82 |
..., tico || gyro prico | (degenerate) tico atop gyrated prico | ∞ i.e. flat in euclidean space | 768, 2400, 2784, 1392, 242 |
..., tico || prissi | tico atop prissi | 2.647378 | 480, 1968, 2640, 1392, 242 |
ticope | truncated-icositetrachoron prism | 2.692582 | 384, 960, 864, 336, 50 |
tin | triacontadipenteract | 1.414214 | 80, 320, 480, 320, 42 |
tipadeca | tip atop deca, 2nd segment of rin in pen-first orientation | 1.414214 | 50, 160, 190, 100, 22 |
tipagrip | tip atop grip | 2.150581 | 80, 220, 230, 110, 22 |
tipalprip | tip atop inverted prip | 1.632993 | 80, 250, 300, 160, 32 |
tipaprip, tip || prip | (degenerate) tip atop prip | ∞ i.e. flat in euclidean space | 80, 310, 390, 190, 32 |
tippip | truncated-pentachoron prism | 1.360147 | 40, 100, 100, 50, 12 |
tiscad | truncated small-cellated-dodecateron | sqrt[(3y2+12y+14)/3] | 240, 840, 1170, 660, 92 |
tisdipah | tisdip atop hexagon | 1 | 18, 54, 68, 41, 11 |
tisdippy | triangle-square-duoprism pyramid, vertex pyramid of nit | 1.224745 | 13, 36, 43, 26, 8 |
tisquippy | triangle-squippy douprism, half of troct, (triangle,trip,trip)-trigonic | 0.912871 | 15, 39, 44, 26, 8 |
titanoh | tritruncated penteractic pentacomb, Voronoi complex of body-centered penteractic lattice (lattice D5*) | ||
tix (alt.: pentum) | truncated hexateron, pen-based tutism | 1.322876 | 30, 75, 80, 45, 12 |
toa sircope | truncated-octahedron atop small-rhombicuboctahedron-prism | 1.583946 | 72, 252, 306, 153, 29 |
todin | triacontadiadispenteract, compound of 2 hin | 0.790569 | |
togdow | triangle-octagrammic disphenoid, triangle atop fully orthogonal octagram | 0.638475 | 11, 35, 50, 35, 11 |
topax | pteroprismated hexateron | 1.190238 | 60, 270, 330, 135, 21 |
tot | truncated triacontiditeron, truncated pentacross, equatorial cross-section of tac-first tag | 1.581139 | 80, 280, 400, 240, 42 |
traco (alt.: cocoe cotric) | triangle - cuboctahedron duoprism, (co,co,co)-trigonic | 1.154701 | 36, 108, 126, 69, 17 |
tracube | triangle - cube duoprism | 1.040833 | 24, 60, 62, 33, 9 |
tradoe | triangle - dodecahedron duoprism | 1.515539 | 60, 150, 146, 69, 15 |
traffip | traf prism, trip atop inverted tisdip | 0.921954 | 18, 57, 72, 42, 11 |
trafpy | triangular antifastegium pyramid, (triangular prism, gyro triangular pyramid)-disphenoid | 0.790569 | 10, 33, 48, 33, 10 |
tragirco | triangle - great-rhombicuboctahedron duoprism | 2.388442 | 144, 360, 342, 153, 29 |
tragocco | triangle - great-cubicuboctahedron duoprism | 0.936070 | 72, 216, 228, 111, 23 |
tragrid | triangle - great-rhombicosidodecahedron duoprism | 3.845977 | 360, 900, 846, 369, 65 |
trahip (old: thiddippip) | triangle hexagonal-prism duoprism, triangle-hexagon duoprismatic prism | 1.258306 | 36, 90, 90, 45, 11 |
traltisdip | triangle atop gyrated tisdip | 1 | 15, 51, 68, 41, 11 |
trapip (old: trapedippip) | triangle pentagonal-prism duoprism, triangle-pentagon duoprismatic prism | 1.143215 | 30, 75, 76, 39, 10 |
traquith | triangle quasitruncated-cube duoprism | 0.817997 | 72, 180, 174, 81, 17 |
trashiddip | triangle atop shiddip | 1.732051 | 27, 75, 83, 44, 11 |
trasirco | triangle small-rhombicuboctahedron duoprism | 1.513420 | 72, 216, 246, 129, 29 |
trasnic | triangle - snub-cube duoprism | 1.462497 | 72, 252, 318, 177, 41 |
trasnid | triangle - snub-dodecahedron duoprism | 2.231808 | 180, 630, 786, 429, 95 |
trasocco | triangle - small-cubicuboctahedron duoprism | 1.513420 | 72, 216, 228, 111, 23 |
trasrid | triangle - small-rhombicosidodecahedron duoprism | 2.306383 | 180, 540, 606, 309, 65 |
tratet (alt.: tettet tettric) | triangle - tetrahedron duoprism, triangle duofastegium, vertex figure of bril, (tet,tet,tet)-trigonic | 0.841625 | 12, 30, 34, 21, 7 |
trathiddip | triangle atop thiddip, triangle-first cap of sarx | 1.290994 | 21, 57, 64, 36, 10 |
trati | triangle - truncated-icosahedron duoprism | 2.544388 | 180, 450, 426, 189, 35 |
tratic | triangle truncated-cube duoprism | 1.870173 | 72, 180, 174, 81, 17 |
tratid | triangle - truncated-dodecahedron duoprism | 3.025056 | 180, 450, 426, 189, 35 |
tratoe (alt.: totoe totric) | triangle truncated-octahedron duoprism, (toe,toe,toe)-trigonic | 1.683251 | 72, 180, 174, 81, 17 |
tratrip (old: triddippip) | triangle triangular-prism duoprism, triangle-triangle duoprismatic prism, vertex figure of ram | 0.957427 | 18, 45, 48, 27, 8 |
tratut (alt.: tuttut tuttric) | triangle truncated-tetrahedron duoprism, (tut,tut,tut)-trigonic | 1.307032 | 36, 90, 90, 45, 11 |
trawp (alt.: opea hip) | traw prism, ope atop hip, 1/6-lune of icope | 1.118034 | 24, 72, 84, 45, 11 |
trial tricupe | triangle atop gyrated tricupe, (triangle,gyro trip,hip)-trigonic | 1.224745 | 21, 66, 80, 44, 11 |
trial triddip | {3} atop gyrated triddip, {3}-first cap of rix | 0.816497 | 12, 39, 52, 33, 10 |
tricufip | tricuf prism | 1.118034 | 24, 66, 75, 42, 11 |
trid | triangle - icosidodecahedron duoprism | 1.717954 | 90, 270, 306, 159, 35 |
tridafup (alt.: pabdidot) | triangular duoantifastegiaprism, triangular duoantiwedge, triddip atop bidual triddip, central segment of vertex first dot, parabidiminished dot | 0.866025 | 18, 72, 102, 60, 14 |
triddaf | triangular duoantifastegium, digonal-triangular duoantiwedge, trip atop bidual trip | 0.790569 | 12, 42, 58, 36, 10 |
triddip althiddip | triddip atop gyrated thiddip | 1.190238 | 27, 90, 114, 63, 14 |
triddipa hip | triddip atop hip, (triangle,trip,hip)-trigonic | 1.190238 | 21, 60, 71, 41, 11 |
triddippa hiddip | triddip atop hiddip, triddip-first cap of card | 1.658312 | 45, 126, 135, 66, 14 |
triddippy | trigonal-duoprismatic pyramid, vertex pyramid of the dodecateron | 0.866025 | 10, 27, 33, 21, 7 |
trike | triangle - icosahedron duoprism | 1.112583 | 36, 126, 162, 93, 23 |
tripa thiddip | trip atop thiddip, (hexagon,trip,hip)-trigonic | 1.190238 | 24, 69, 80, 44, 11 |
tripgytricudaw | (trip, gyro tricu)-disphenoid | 1 | 15, 48, 61, 36, 10 |
triphipdaw (alt.: tripalhip) | (trip,hip)-disphenoid, trip atop lacing-orthogonal hip | 1.274755 | 18, 51, 61, 36, 10 |
trippasc | triangular-prismatic scalene, triangular-prismatic-pyramid pyramid, line atop fully orthogonal triangular-prism | 0.790569 | 8, 22, 29, 20, 7 |
trippyp | trigonal-prismatic pyramid prism, lacing edge cap of the rectified-pentachoron prism | 0.921954 | 14, 37, 43, 26, 8 |
tripufip (alt.: tripa shiddip) | tripuf prism, trip-first cap of srippip | 1.284523 | 30, 81, 87, 45, 11 |
tritricu | triangle-tricu duoprism, half of traco | 1.154701 | 27, 72, 78, 42, 11 |
troct (alt.: octoct octtric) | triangle-octahedron duoprism, vertex figure of brag, (oct,oct,oct)-trigonic | 0.912871 | 18, 54, 66, 39, 11 |
... | truncation of icoap | 2.816377 | 672, 2640, 3744, 2064, 290 |
tutaf (old: tutaltuttip) | tut alterfastegium, tut atop inverted tuttip | 1.274755 | 36, 114, 138, 75, 17 |
tutatope | tut atop tope, tut-first cap of pattix | 1.848423 | 60, 162, 168, 81, 17 |
tutcupa toe (alt.: tutaltut toetric) | tuta atop toe, (tut,inv tut,toe)-trigonic | 1.620185 | 48, 144, 162, 81, 17 |
tutcupip | tuttip atop inverted tuttip, tuta-prism, medial segment of rittip | 1.322876 | 48, 144, 164, 84, 18 |
tuttipa toe (alt.: tuttut totric) | tuttip atop toe, (tut,tut,toe)-trigonic | 1.632993 | 48, 132, 144, 75, 17 |
tuttipa tope | tuttip atop tope, tutatoe-prism, tuttip-first cap of prippip | 1.688194 | 72, 192, 194, 90, 18 |
twacube | dodecagon - cube duoprism | 2.117085 | 96, 240, 224, 96, 18 |
wacbinant | sphenary cellibiprismatopenteractipenteractitriacontaditeron | 1.192297 | 960, 3840, 4240, 1600, 172 |
wavhiddixa | sphenoverted hecatonicosadishexacosachoron alterprism | 5.345177 | 7200, 28800, 30240, 10560, 1322 |
wavinant | sphenoverted penteractipenteractitriacontaditeron | 0.792893 | 320, 1280, 1280, 440, 52 |
... | hyperbolic (order 3) triacontiditeric pentacomb, hyperbolic Gosset pentacomb 21,1,1 | 0 i | |
... | hyperbolic x3x4o3o3o4o pentacomb | 1.414214 i | |
... | hyperbolic x3x4o3o4o3o pentacomb | 0.447214 i | |
..., xhi || thi | (degenerate) xhi atop thi | ∞ i.e. flat in euclidean space | 6000, 19200, 21840, 10560, 1922 |
xhip | hexacosihecatonicosachoron prism, bitruncated-hecatonicosachoron prism, bitruncated-hexacosachoron prism | 7.596108 | 7200, 18000, 15840, 5760, 722 |
... | xo3oo3oo3ox&#q, longer variant of pentachoral antiprism, vertex figure of staf | 0.866025 | 10, 40, 80, 80, 32 |
zucypit | schmoozed cyclopentachoric tetracomb, schmoozed pentachoric-dispentachoric tetracomb |
Count of actually available polytopes: 744
---- 6D ----
Acronym | Name | Circumradius | Face vector |
..., 03,1,1,1 | hyperbolic Gosset hexacomb 03,1,1,1 | 1.414214 i | |
..., 11,1,1,1,1 | hyperbolic Gosset hexacomb 11,1,1,1,1 | 0.25 | |
..., 13,1,1 | hyperbolic Gosset hexacomb 13,1,1 | 0.707107 i | |
... | 2firl (?) | 0.845154 | |
... | 2kaje (?) | 0.816497 | |
... | 2thox (?) | 0.707107 | |
..., 31,1,1 | hyperbolic (order 3) hexacontitetrapetic hexacomb, hyperbolic Gosset hexacomb 31,1,1 | 0.5 | |
4,n,m-tip | square - n-gon - m-gon - triprism | sqrt[1/2+1/(4 sin2(π/n))+1/(4 sin2(π/m))] | 4nm, 12nm, 13nm+4n+4m, 6nm+8n+8m, nm+5n+5m+4, n+m+4 |
4,n,n-tip | square - n-gon - n-gon - triprism | sqrt[1/2+1/(2 sin2(π/n))] | 4n2, 12n2, 13n2+8n, 6n2+16n, n2+10n+4, 2n+4 |
ax (old: hexe) | hexeract, dodecapeton, 6D measure-polytope (γ6), geoex(id) | 1.224745 | 64, 192, 240, 160, 60, 12 |
axh | hexeractic hexacomb, 6D hypercubical honeycomb (δ6) | ||
bapril | biprismatorhombated heptapeton, biruncitruncated heptapeton | 2.203893 | 630, 2520, 3570, 2310, 714, 84 |
barm (old: scram, bram, remak, kram) | birectified pentacontitetrapeton, (small centrorhombated pentacontitetrapeton) | 2.449490 | 2160, 12960, 19440, 10800, 2286, 126 |
... | isomorph of birectified pentacontitetrapeton | 0.816497 | 2160, 12960, 19440, 10800, 2286, 126 |
batal | bitruncated heptapeton | 1.647509 | 105, 315, 385, 245, 84, 14 |
bicotoe | bi - (cuboctahedron, truncated octahedron)-duoprism | 1.870829 | 576, 2592, 4464, 3696, 1472, 224 |
bife | bitetradecapeton, tetradecapeton dual, 14-3-5 step prism | 0.774597 | 14, 84, 280, 490, 420, 140 |
big dispox | bi-hexacontatetra (= g)-diminished small-prismated-hexeract | 2.263033 | 1152, 6336, 12000, 9792, 3404, 428 |
bitem (old: gacram, botam, kobtam) | bitruncated pentacontitetrapeton, (great centrorhombated pentacontitetrapeton, heptacontidia-bitruncated pentacontitetrapeton) | 4.123106 | 6480, 19440, 21600, 10800, 2286, 126 |
bitettut (alt.: pabex gee) | bi - (tetrahedron, truncated tetrahedron)-duoprism, partially bi-expanded hexacontitetrapeton | 1.322876 | 96, 432, 808, 780, 388, 80 |
bittita sibrant | bitruncated triacontadipeton atop small birhombated penteractitriacontiditeron, sart-first subsegment of small birhombated hexacontitetrapeton | 2.236068 | 720, 3600, 5280, 3280, 1004, 124 |
bittixa (old: bittixalbittix) | bitruncated-hexateron alterprism, bitruncated-hexateron atop inverted bitruncated-hexateron, equatorial segment of rectified hexeract | 1.581139 | 120, 480, 730, 540, 204, 34 |
boprag | biprismatorhombated hexacontitetrapeton, biruncitruncated hexeract | 3.674235 | 5760, 23040, 32160, 19680, 5276, 476 |
boprax | biprismatorhombated hexeract, biruncitruncated hexacross | 3.464102 | 5760, 23040, 31680, 19200, 5276, 476 |
botag | bitruncated hexacontitetrapeton, bitruncated hexacross | 2.121320 | 480, 1920, 3040, 2160, 636, 76 |
botajik | bitruncated icosiheptaheptacontidipeton | 2.943920 | 2160, 8640, 11520, 6480, 1566, 126 |
botox | bitruncated hexeract | 2.915476 | 960, 2880, 3440, 2080, 636, 76 |
brag (old: dric) | birectified hexacontitetrapeton, Voronoi cell of lattice D6*, equatorial cross-section of rag-first barz | 1.224745 | 160, 1440, 2880, 2160, 636, 76 |
braxh | birectified hexeractic honeycomb | ||
bril (old: driss, alt.: rixadot) | birectified heptapeton, rectified hexateron atop dodecateron, vertex figure of lin, Gosset polytope 03,2 | 0.925820 | 35, 210, 350, 245, 84, 14 |
brox (old: drax) | birectified hexeract, Gosset polytope 03,1,1, equatorial cross-section of brag-first sez | 1.414214 | 240, 1920, 3200, 2080, 636, 76 |
cagorg (old: gacorg) | celligreatorhombihexacontitetrapeton, (old: great cellirhombated hexacontatetrapeton), stericantitruncated hexacontatetrapeton | 3.937004 | 11520, 46080, 63360, 36480, 8216, 536 |
cagral (old: gacral) | celligreatorhombated heptapeton, stericantitruncated heptapeton | 2.618615 | 1260, 5040, 7140, 4410, 1155, 105 |
cakix | celliskewed hexeract | 1.581139 | 1920, 11520, 23040, 21120, 8048, 548 |
cappixa (old: cappixalcappix) | cappix alterprism, cappix atop alternate cappix | 1.658312 | 240, 1200, 2220, 1770, 574, 64 |
caprohax | small celliprismatorhombated hemihexeract, steriruncicantellated demihexeract, pentisteriruncic hexeract | 3.278719 | 3840, 15360, 21760, 13440, 3496, 296 |
captal | celliprismatotruncated heptapeton, steriruncitruncated heptapeton | 2.591194 | 1260, 4410, 5670, 3360, 945, 105 |
capthix | small celliprismatotruncated hemihexeract, steriruncitruncated demihexeract, pentistericantic hexeract | 3.278719 | 5760, 23040, 31200, 17760, 4136, 296 |
captog | celliprismatotruncated hexacontitetrapeton, steriruncitruncated hexacross | 4.123106 | 11520, 40320, 50880, 28320, 6446, 536 |
cardip | cellirhombated-dodecateron prism | 1.732051 | 360, 1620, 2520, 1740, 544, 64 |
catal | cellitruncated heptapeton, steritruncated heptapeton | 1.851640 | 420, 2100, 3780, 2940, 945, 105 |
catax | cellitruncated hexeract | 3.456841 | 3840, 19200, 34080, 25440, 7388, 668 |
cathix | cellitruncated hemihexeract, steritruncated demihexeract, penticantic hexeract | 2.598076 | 1920, 9600, 16800, 12480, 3656, 296 |
catjak (old: detidjik) | cellitruncated icosiheptapeton (disteridisicosiheptaheptacontidipeton) | 2.581989 | 2160, 11880, 23760, 19440, 5958, 558 |
catog | cellitruncated hexacontitetrapeton, steritruncated hexacross | 2.828427 | 3840, 19200, 33600, 24480, 6776, 536 |
cocube | cuboctahedron-cube duoprism | 1.322876 | 96, 336, 482, 332, 120, 20 |
codibrox | tetracontaocta-diminished birectified hexeract | 1.414214 | 192, 1152, 2336, 2080, 828, 124 |
codip | cuboctahedron-cuboctahedron duoprism | 1.414214 | 144, 576, 912, 696, 244, 28 |
codoe | cuboctahedron-dodecahedron duoprism | 1.721489 | 240, 840, 1144, 740, 222, 26 |
cograxa (old: cograxalcograx) | cograx alterprism, cograx atop alternate cograx | 2.345208 | 720, 2880, 4080, 2520, 664, 64 |
coid | cuboctahedron-icosidodecahedron duoprism | 1.902113 | 360, 1440, 2244, 1650, 532, 46 |
coike | cuboctahedron-icosahedron duoprism | 1.380039 | 144, 648, 1128, 924, 334, 34 |
copal | celliprismated heptapeton, steriruncinated heptapeton | 1.963961 | 420, 1680, 2660, 1995, 700, 105 |
cophix | small celliprismated hemihexeract, steriruncinated demihexeract, pentisteric hexeract | 2.179449 | 960, 5280, 10720, 9120, 3016, 296 |
copog | celliprismated hexacontitetrapeton, steriruncinated hexacross | 3.316625 | 3840, 15360, 24000, 17280, 5336, 536 |
copox | celliprismated hexeract, steriruncinated hexeract | 3.087966 | 3840, 15360, 23360, 16320, 5148, 668 |
coprag | celliprismatorhombated hexacontitetrapeton, steriruncicantellated hexacross | 4.415880 | 11520, 40320, 52800, 31200, 7736, 536 |
copril | celliprismatorhombated heptapeton, steriruncicantellated heptapeton | 2.725541 | 1260, 4410, 5880, 3675, 1050, 105 |
coprix | (small) celliprismatorhombated hexeract, steriruncicantellated hexeract | 4.400450 | 11520, 40320, 52800, 31680, 8348, 668 |
cotoe | cuboctahedron - truncated-octahedron duoprism | 1.870829 | 288, 1008, 1368, 876, 256, 28 |
crag (old: scrag) | cellirhombated hexacontitetrapeton, stericantellated hexacross | 3.082207 | 5760, 28800, 45120, 29280, 7736, 536 |
cral (old: scral) | cellirhombated heptapeton, stericantellated heptapeton | 1.927248 | 630, 3150, 5040, 3465, 1050, 105 |
crax (old: scrax) | (small) cellirhombated hexeract, stericantellated hexeract | 3.277597 | 5760, 28800, 45600, 30240, 8348, 668 |
crohax (old: scrohax) | (small) cellirhombated hemihexeract, pentiruncinated demihexeract, pentiruncic hexeract | 2.397916 | 1920, 10560, 16960, 11040, 3016, 296 |
cubedoe | cube-dodecahedron duoprism | 1.647278 | 160, 480, 576, 352, 114, 18 |
cubesirco | cube-small-rhombicuboctahedron duoprism | 1.645329 | 192, 672, 928, 632, 216, 32 |
cubid | cube-icosidodecahedron duoprism | 1.835220 | 240, 840, 1156, 782, 264, 38 |
cubike | cube-icosahedron duoprism | 1.286277 | 96, 384, 592, 440, 162, 26 |
cyloh | cycloheptapetic hexacomb, Delone complex of lattice A6 | ||
cytloh | cyclotruncated heptapetic honeycomb | ||
daj (old: dije) | disicosiheptapeton, vertex figure of nal | 0.816497 | 27, 216, 720, 1080, 783, 54 |
dedjak | decadiminished icosiheptaheptacontidipeton | 0.816497 | 17, 86, 205, 255, 158, 39 |
dihinpy | diminished-demipenteractic pyramid, (rap, dual pen, point)-trigonic | 0.816497 | 16, 85, 200, 225, 117, 23 |
dijak (alt.: taccahin) | (mono-)diminished icosiheptaheptacontidipeton, tac atop hin, vertex figure of jaka | 0.816497 | 26, 200, 640, 920, 538, 84 |
dodoe | dodecahedron-dodecahedron duoprism (or simply: dodecahedral duoprism) | 1.981679 | 400, 1200, 1380, 760, 204, 24 |
dotet | (line,)dodecateron-tegum, dodecateron dipyramid | 22, 130, 300, 300, 132, 24 | |
dotip | dodecateron prism | 1 | 40, 200, 330, 240, 84, 14 |
dotpy | dodecateron pyramid, vertex pyramid of mo | 1 | 21, 110, 210, 180, 72, 13 |
dottascad | dodecateron atop small cellated dodecateron | 1 | 50, 390, 1050, 1140, 494, 64 |
dottasibrid | dot atop sibrid, dot-first cap of ram | 1.732051 | 110, 630, 990, 660, 224, 34 |
dottaspix | dodecateron atop small prismated hexateron, dot-first cap of birectified hexacontitetrapeton | 1.224745 | 80, 540, 1080, 885, 314, 49 |
dotu | dot-based ursapeton | 1.432173 | 130, 650, 990, 660, 224, 34 |
dotum | dot-first bistratic cap of tim, dot-based tutsatope, dot-based tutism | 2.645751 | 220, 740, 990, 660, 224, 34 |
endjak | ennea-diminished jak | 0.816497 | 18, 90, 192, 213, 126, 33 |
fe | tetradecapeton, tritruncated heptapeton, equatorial cross-section of (vertex first) q-hept | 1.732051 | 140, 420, 490, 280, 84, 14 |
firl | facetorectified heptapeton | 0.845154 | 21, 105, 245, 315, 217, 63 |
fohaf | tetradecahemitetradecapeton | 1 | 42, 210, 315, 245, 105, 21 |
forx | facetorectified hexeract | 1.581139 | 192, 960, 1920, 1920, 960, 192 |
gaborg | great birhombihexacontitetrapeton, bicantitruncated hexacross | 3.391165 | 2880, 10080, 13440, 8400, 2396, 236 |
gaborx | great birhombated hexeract, bicantitruncated hexeract | 4 | 3840, 11520, 13760, 8320, 2556, 316 |
gabril | great birhombated heptapeton, bicantitruncated heptapeton | 2.390457 | 420, 1260, 1540, 960, 329, 49 |
gabrim (old: prarm, older: girmak, oldest: gokorm) | great birhombated pentacontitetrapeton (prismatorhombated rectified pentacontitetrapeton), bicantitruncated pentacontitetrapeton | 5.385165 | 25920, 77760, 86400, 43200, 9198, 558 |
gacal | great cellated heptapeton, steriruncicantitruncated heptapeton | 3.380617 | 2520, 7560, 8610, 4620, 1155, 105 |
gacnetip | great-cellated-penteractitriacontiditeron prism | 4.855004 | 7680, 23040, 25920, 13440, 3124, 244 |
gaje (old: gaj, older: gij) | great icosiheptaheptacontidipeton | 0.816497 | 27, 216, 990, 990, 216, 27 |
gapil | great prismated heptapeton, runcicantitruncated heptapeton | 2.803060 | 840, 2520, 3010, 1820, 560, 70 |
gaqrox | great quasirhombihexeract | 1.906840 | 1920, 5760, 7280, 4960, 1788, 268 |
gaquitxog | great quasiterated hexeractihexacontatetrapeton | 4.288753 | 46080, 138240, 151680, 72960, 14168, 728 |
gedak | hexacontitetradishexeract, compound of 2 hax | 0.866025 | |
gee (old: xic) | hexacontitetrapeton, hexacross (β6), aeroex(id), hexateral antiprism, triacontaditeric bipyramid, octahedral duotegum, square triotegum, vertex figure of zee, Gosset polytope 31,1, lattice C6 contact polytope (span of its small roots), equatorial cross-section of vertex-first zee | 0.707107 | 12, 60, 160, 240, 192, 64 |
gibpof | great biprismated tetradecapeton, biruncicantitruncated heptapeton | 3 | 1260, 3780, 4410, 2520, 714, 84 |
ginnontip | ginnont prism | 1.137055 | 320, 1440, 1920, 1200, 384, 54 |
gippitip | great-prismated-triacontiditeron prism | 3.905125 | 3840, 11520, 13120, 7040, 1764, 164 |
girhax | great rhombated hemihexeract, cantitruncated demihexeract, runcicantic hexeract | 3.278719 | 1920, 5760, 6560, 3520, 876, 76 |
girjak | great rhombated icosiheptaheptacontidipeton | 3.605551 | 4320, 17280, 24480, 15120, 3942, 342 |
gisdiddit | (gisdid,gisdid)-duotegum, gisdid duotegum, tegum product of 2 great snub dodekicosidodecahedra | 0.707107 | 120, 3960, 21808, 44880, 37440, 10816 |
gocadip | great-cellated-hexateron prism | 3 | 1440, 4320, 4920, 2640, 664, 64 |
gocog | great cellated hexacontitetrapeton, steriruncicantitruncated hemihexeract, omnitruncated hemihexeract | 5.244044 | 23040, 69120, 76800, 38400, 8216, 536 |
gopam (old: gakpam) | great prismated pentacontitetrapeton, (great heptaheptacontidiprismated pentacontitetrapeton), omnitruncated pentacontitetrapeton, omnitruncated icosiheptaheptacontidipeton | 6.244998 | 51840, 155520, 172800, 86400, 18558, 1278 |
gophax | great prismated demihexeract, steriruncicantic hexeract | 4.092676 | 5760, 17280, 19680, 10560, 2636, 236 |
gopog | great prismated hexacontitetrapeton, runcicantitruncated hexacross | 3.872983 | 5760, 20160, 26400, 15600, 3896, 296 |
gotaf | great terated tetradecapeton, omnitruncated heptapeton, Voronoi cell of lattice A6*, permutopeton of 7 elements | 3.741657 | 5040, 15120, 16800, 8400, 1806, 126 |
gotaxog | great terated hexeractihexacontatetrapeton | 6.293378 | 46080, 138240, 151680, 72960, 14168, 728 |
goxaxog | great hexeractihexeractihexacontitetrapeton | 1.137055 | 384, 1920, 2480, 1600, 564, 88 |
gram (old: gakbram) | great rhombated pentacontitetrapeton, (old: great heptacontiduo-birhombated pentacontitetrapeton), cantitruncated pentacontitetrapeton | 5 | 12960, 38880, 45360, 25920, 7326, 846 |
gril | great rhombated heptapeton, cantitruncated heptapeton | 2.104417 | 210, 630, 805, 560, 210, 35 |
grog | great rhombihexacontitetrapeton, cantitruncated hexacross | 2.645751 | 960, 3840, 6400, 5040, 1656, 136 |
grox | great rhombihexeract, cantitruncated hexeract | 4.045239 | 1920, 5760, 7280, 4960, 1788, 268 |
hagippid | hexagon - great-prismated-decachoron duoprism | 2.449490 | 720, 2160, 2460, 1320, 336, 36 |
haprojak | demiprismatorhombated icosiheptapeton | 3.559026 | 6480, 25920, 34560, 19440, 4662, 342 |
harjak (old: trojak) | demirectified icosiheptaheptacontidipeton (trirectified icosiheptaheptacontidipeton) | 2.160247 | 1080, 6480, 10080, 6120, 1566, 126 |
hatico | hexagon - truncated-icositetrachoron duoprism | 2.828427 | 1152, 3456, 3936, 2112, 534, 54 |
hatope | hexagon - truncated-octahedron duoprismatic prism | 1.936492 | 288, 864, 1008, 576, 166, 22 |
hax | hemihexeract, vertex figure of laq, Gosset polytope 13,1, equatorial cross-section of gee-first naq | 0.866025 | 32, 240, 640, 640, 252, 44 |
haxh | hemihexeractic pentacomb, Delone complex of lattice D6 | ||
hedjak | heptadiminished jak, square || hin | 0.816497 | 20, 116, 289, 328, 166, 31 |
hejak | demified icosiheptaheptacontidipeton | 1.632993 | 432, 3240, 7920, 7200, 2430, 342 |
hexaf, hex || gyro hexip | hexadecachoral alterfastegium, hex atop gyrated hexip, hex-first rotunda of hax | 0.866025 | 24, 144, 344, 352, 155, 27 |
hexarat | hex atop rat, hex-first half of tedrag | 1 | 48, 328, 696, 656, 283, 43 |
hexasc | hexadecachoric scalene, hexadecachoron-pyramid pyramid, line atop fully orthogonal hexadecachoron, 1/4-lune of hexacontatetrapeton | 0.707107 | 10, 41, 88, 104, 65, 18 |
hexcopedaw (alt.: hexorcope) | (hex,cope)-disphenoid, tetrahedral antiprism atop axis-orthogonal cuboctahedron prism | 1.224745 | 32, 132, 228, 196, 86, 18 |
hexipaco | hexip atop co | 1 | 28, 128, 246, 229, 102, 19 |
hexipaico | hexip atop ico, diminished 1/4-lune of rag | 1 | 40, 248, 472, 400, 163, 27 |
hexippy | hexip pyramid, vertex pyramid of rag | 1 | 17, 72, 144, 152, 82, 19 |
hidbrag | hexadeca-diminished brag, tegum sum of 2 antialigned octcoes | 1.224745 | 144, 1152, 2592, 2280, 788, 92 |
hinaco | hemipenteract atop cuboctahedron | 1 | 28, 152, 342, 345, 154, 27 |
hinanit | hin atop nit, hin-first cap of rojak | 1.290994 | 96, 720, 1360, 1040, 348, 44 |
hinarin | demipenteract atop rectified penteract, demipenteract-first cap of demified icosiheptaheptacontidipeton | 1.632993 | 96, 480, 880, 720, 268, 44 |
hinasiphin | hin atop siphin, hin-first cap of sochax | 1.322876 | 96, 560, 1280, 1320, 588, 84 |
hinnip | hemipenteractic prism, vertex figure of ranq | 0.935414 | 32, 176, 400, 400, 172, 28 |
hinpy | demipenteractic pyramid, vertex pyramid of jak | 0.816497 | 17, 96, 240, 280, 146, 27 |
hinro (alt.: hinarat) | demipenteractic rotunda, hin-first half of mo, hin atop rat | 1 | 56, 480, 1280, 1240, 428, 44 |
hint | demipenteractic (line-)tegum, demipenteractic dipyramid | ... | 18, 112, 320, 440, 266, 52 |
hinu | hin-based ursapeton | 1.287166 | 112, 736, 1360, 1040, 348, 44 |
hittip | hexagon-hexagon-hexagon-triprism | 1.732051 | 216, 648, 756, 432, 126, 18 |
hixacube | hix atop edge-parallel cube | 0.866025 | 14, 51, 86, 78, 39, 10 |
hixadot | hexateron atop dodecateron, hix-first half of hax | 0.866025 | 26, 165, 380, 365, 153, 29 |
hixalrix | hexateron atop inverted rectified hexateron, hix-first rotunda of jak | 0.816497 | 21, 135, 370, 480, 273, 49 |
hixaltriddip | hix atop alternate triddip, ({3}, perp. {3}, alt. triddip)-trigonic, 1/6-lune of jak | 0.816497 | 15, 69, 143, 147, 73, 15 |
hixascad | hexateron atop small cellated decateron, hix-first rotunda of small terated tetradecapeton | 1 | 36, 165, 350, 405, 248, 64 |
hixip | hexateron prism, vertex figure of roc | 0.816497 | 12, 36, 55, 50, 27, 8 |
hixit | hexateral (line-)tegum, hexateral dipyramid | 8, 27, 50, 55, 36, 12 | |
hixu | hexateral-based ursapeton ofx3xoo3ooo3ooo3ooo&#xt, hix-based ursulate | 1.048383 | 27, 111, 175, 140, 63, 14 |
hop (old: hep) | heptapeton, 6D simplex (α6), pyroex(id), hexateral pyramid, vertex figure of oca, Gosset polytope 05 | 0.654654 | 7, 21, 35, 35, 21, 7 |
hopitjak (old: hoptijak) | demiprismatotruncated icosiheptaheptacontidipeton | 3.109126 | 4320, 21600, 32400, 19440, 4662, 342 |
hotjak | demitruncated icosiheptapeton | 2.828427 | 2160, 9720, 14400, 9360, 2862, 342 |
icaf (alt.: icalicope) | icositetrachoron antifastegium, icositetrachoron atop inverted icositetrachoral-prism | 1.123033 | 72, 600, 1680, 2088, 1179, 243 |
icoahin | ico atop hin, 1/6-lune of mo | 1 | 40, 272, 592, 528, 195, 27 |
iddoe | icosidodecahedron-dodecahedron duoprism | 2.140458 | 600, 2100, 2800, 1730, 474, 44 |
idodip | icosidodecahedron-icosidodecahedron duoprism | 2.288246 | 900, 3600, 5520, 3900, 1144, 64 |
ikedip | icosahedron-icosahedron duoprism | 1.344997 | 144, 720, 1380, 1224, 460, 40 |
ikedoe | icosahedron-dodecahedron duoprism | 1.693527 | 240, 960, 1444, 992, 300, 32 |
ikid | icosahedron-icosidodecahedron duoprism | 1.876844 | 360, 1620, 2784, 2202, 730, 52 |
jak (old: yaz) | icosiheptaheptacontidipeton, argyropeton, sideropeton, Gosset polypeton 22,1, vertex figure of naq, Delone cell of lattice E6 | 0.816497 | 27, 216, 720, 1080, 648, 99 |
jakoh | icosiheptaheptacontidipetic hexacomb, Gosset hexacomb 22,2, Delone complex of lattice E6 | ||
kaje | heptacontidiaicosiheptapeton, vertex figure of quil | 0.816497 | 27, 216, 720, 1080, 567, 99 |
ladbril | heptadiminished birectified heptapeton | 0.925820 | 28, 126, 245, 238, 112, 21 |
madek | pentacontatetradisheptacontadipeton, compound of 2 jak | 0.816497 | |
medrojak (alt.: tritith) | pentacontitetra-diminished rojak, tri - (triangle,triangle,hexagon)-trioprism | 1.290994 | 162, 1134, 2754, 3078, 1638, 342 |
mo | pentacontitetrapeton, chrysopeton, Gosset polypeton 12,2, vertex figure of jakoh, lattice E6 contact polytope (span of its roots), equatorial cross-section of jak-first laq | 1 | 72, 720, 2160, 2160, 702, 54 |
n,co-dippip | n-gon - cuboctahedron duoprismatic prism | 24n, 84n, 112n+24, 68n+60, 17n+52, n+16 | |
n,doe-dippip | n-gon - dodecahedron duoprismatic prism | 40n, 120n, 134n+40, 68n+80, 15n+54, n+14 | |
n,ex-dip | n-gon - hexacosachoron duoprism | 120n, 740n, 1920n+120, 1800n+720, 601n+1200, n+600 | |
n,hex-dip | n-gon - hexadecachoron duoprism | sqrt[2+1/sin2(π/n)] | 8n, 32n, 56n+8, 48n+24, 17n+32, n+16 |
n,hi-dip | n-gon - hecatonicosachoron duoprism | 600n, 1800n, 1920n+600, 840n+1200, 121n+720, n+120 | |
n,ico-dip | n-gon - icositetrachoron duoprism | 24n, 120n, 192n+24, 120n+96, 25n+96, n+24 | |
n,id-dippip | n-gon - icosidodecahedron duoprismatic prism | 60n, 210n, 274n+60, 158n+150, 35n+124, n+34 | |
n,ike-dippip | n-gon - icosahedron duoprismatic prism | 24n, 96n, 142n+24, 92n+72, 23n+70, n+22 | |
n,m,k-tip | n-gon - m-gon - k-gon - triprism | sqrt[1/(4 sin2(π/n))+1/(4 sin2(π/m))+1/(4 sin2(π/k))] | nmk, 3nmk, 3nmk+nm+nk+mk, nmk+2nm+2nk+2mk, nm+nk+mk+n+m+k,n+m+k |
n,n,k-tip | n-gon - n-gon - k-gon - triprism | sqrt[1/(2 sin2(π/n))+1/(4 sin2(π/k))] | n2k, 3n2k, 3n2k+n2+2nk, n2k+2n2+4nk, n2+2nk+2n+k, 2n+k |
n,n,n-tip | n-gon - n-gon - n-gon - triprism | sqrt[3/(4 sin2(π/n))] | n3, 3n3, 3n3+3n2, n3+6n2, 3n2+3n, 3n |
n,oct-dippip | n-gon - octahedron duoprismatic prism | 12n, 42n, 58n+12, 38n+30, 11n+28, n+10 | |
N,pen-dip | N-gon - pentachoron duoprism | sqrt[1/(4 sin2(π/N))+2/5] | 5n, 15n, 20n+5, 15n+10, 6n+10, n+5 |
n,rahi-dip | n-gon - rectified-hecatonicosachoron duoprism | 1200n, 4800n, 6720n+1200, 3840n+3600, 721n+3120, n+720 | |
n,rap-dip | n-gon - rectified-pentachoron duoprism | 10n, 40n, 60n+10, 40n+30, 11n+30, n+10 | |
n,rico-dip | n-gon - rectified-icositetrachoron duoprism | 96n, 384n, 576n+96, 264n+288, 49n+216, n+48 | |
n,rit-dip | n-gon - rectified-tesseract duoprism | 32n, 128n, 184n+32, 112n+96, 25n+88, n+24 | |
n,rox-dip | n-gon - rectified-hexacosachoron duoprism | 720n, 4320n, 7200n+720, 4320n+3600, 721n+3600, n+720 | |
n,tes-dip | n-gon - tesseract duoprism | 16n, 48n, 56n+16, 32n+32, 9n+24, n+8 | |
n,tet-dippip | n-gon - tetrahedron duoprismatic prism | 8n, 24n, 30n+8, 20n+16, 7n+14, n+6 | |
... | (N-g, dual N-g, para N-p, gyro N-p) lace simplex | ... | 6n, 26n, 44n+6, 36n+13, 14n+13, 2n+6 |
..., N,M-dip || N,M-dafup | (N,M)-duoprism atop (N,M)-duoantifastegiaprism, ((N,M)-dip, (N,dual M)-dip, (dual N,M)-dip)-trigonic | ... | 3nm, 14nm, 23nm+3n+3m, 16nm+8n+8m, 4nm+7n+7m+3, 2n+2m+3 |
nitarin | nit atop rin, nit-first rotunda of brox | 1.414214 | 160, 1120, 1840, 1200, 364, 44 |
nitasiphin | nit atop siphin, hin-first medial segment of rojak | 1.290994 | 160, 1360, 3040, 2600, 844, 84 |
nitasirhin | nit atop sirhin, nit-first cap of ram | 1.732051 | 240, 1680, 2720, 1680, 444, 44 |
nitip | penteractitriacontiditeron prism | 1.322876 | 160, 1040, 1760, 1200, 364, 44 |
... | hyperbolic Gosset pentacomb 01,1,1,1,1,1 | 0.707107 i | |
... | bidodecateric heptacontadipeton, pentacontitetrapeton dual, convex hull of madek | 0.816497 | 54, 702, 2160, 2160, 720, 72 |
octa tratet | oct atop tratet, oct-first cap of ril | 0.845154 | 18, 78, 132, 112, 52, 12 |
octco | octahedron-cuboctahedron duoprism | 1.224745 | 72, 288, 468, 378, 148, 22 |
octcube | octahedron-cube duoprism | 1.118034 | 48, 168, 244, 182, 72, 14 |
octdip | octahedron-octahedron duoprism, dual of Delone cell of lattice D6*, vertex figure of traxh | 1 | 36, 144, 240, 204, 88, 16 |
octdoe | octahedron-dodecahedron duoprism | 1.569562 | 120, 420, 592, 410, 138, 20 |
octete | octahedral tettene, octahedral-pyramid pyramid pyramid, triangle atop fully orthogonal octahedron | 0.707107 | 9, 33, 63, 67, 39, 11 |
octid | octahedron-icosidodecahedron duoprism | 1.765796 | 180, 720, 1152, 900, 328, 40 |
octike | octahedron-icosahedron duoprism | 1.185120 | 72, 324, 576, 498, 202, 28 |
oddimo (alt.: bittip) | octadeca-diminished mo, bitriangular trioprism, triangular trioalterprism | 1 | 54, 378, 864, 864, 396, 72 |
odhax | octadiminished hemihexeract | 0.866025 | 24, 132, 310, 336, 162, 28 |
ogquithdow | (octagram,quith)-disphenoid, octagram atop fully orthogonal quasitruncated hexahedron | 0.639069 | 32, 236, 495, 425, 156, 22 |
open | octagon-pentachoron duoprism | 1.451588 | 40, 120, 165, 130, 58, 13 |
otcyloh | omnitruncated cycloheptapetic hexacomb, Voronoi complex of lattice A6* | ||
... | (mono) tetal tratet augmented tetdip | 0.866025 | 20, 90, 180, 183, 97, 24 |
pabdimo, dot||scad||dot | parabidiminished mo, dodecateron atop pseudo small cellated dodecateron atop dodecateron | 1 | 70, 680, 1980, 1980, 666, 56 |
pabex hax | partially biexpanded hemihexeract, truncated tetrahedral duoalterprism | 1.658312 | 288, 1440, 2688, 2208, 756, 84 |
patal | prismatotruncated heptapeton, runcitruncated heptapeton | 2 | 420, 1890, 2800, 1820, 560, 70 |
patom (old: kaprom) | prismatotruncated pentacontitetrapeton, runcitruncated pentacontitetrapeton, (heptacontidiprismatorhombated pentacontitetrapeton) | 3.872983 | 12960, 58320, 86400, 54000, 14238, 1278 |
pedril (alt.: squatratet) | pentadiminished rectified heptapeton, square atop tratet | 0.845154 | 16, 58, 95, 83, 40, 10 |
penaf (old: penalpenp) | pentachoron antifastegium, pentachoron atop inverted pentachoral-prism, pen-first cap of jak | 0.816497 | 15, 75, 180, 225, 138, 33 |
penarappip | pen-first cap of birectified heptapeton | 0.925820 | 25, 120, 200, 155, 63, 13 |
penppy | penp pyramid, vertex-pyramid of ril | 0.845154 | 11, 35, 55, 50, 27, 8 |
pentanit | pent atop nit | 1.228783 | 112, 880, 2000, 1840, 732, 124 |
pentarin | tesseract atop rectified tesseract | 1.418705 | 112, 560, 880, 640, 252, 44 |
pettip | pentagon-pentagon-pentagon-triprism | 1.473370 | 125, 375, 450, 275, 90, 15 |
pexhax | partially expanded hemihexeract | 1.322876 | 96, 576, 1312, 1256, 488, 64 |
pithax | prismatotruncated hemihexeract, runcitruncated demihexeract, stericantic hexeract | 2.958040 | 2880, 12960, 18240, 10560, 2636, 236 |
potag | prismatotruncated hexacontitetrapeton, runcitruncated hexacross | 2.738613 | 2880, 15840, 24960, 15600, 3896, 296 |
potax | prismatotruncated hexeract, runcitruncated hexeract | 3.762560 | 3840, 17280, 25280, 16000, 4668, 508 |
pril | prismatorhombated heptapeton, runcicantellated heptapeton | 2.104417 | 420, 1470, 1960, 1295, 455, 70 |
prog | prismatorhombated hexacontitetrapeton, runcicantellated hexacross | 3 | 2880, 11520, 16800, 11280, 3416, 296 |
prohax | prismatorhombated hemihexeract, runcicantellated demihexeract, steriruncic hexeract | 2.783882 | 1920, 7680, 10720, 6720, 1996, 236 |
prom (old: kaptom) | prismatorhombated pentacontitetrapeton, (heptacontidiprismatotruncated pentacontitetrapeton) | 4.582576 | 25960, 103680, 140400, 79920, 18558, 1278 |
prox | prismatorhombated hexeract, runcicantellated hexeract | 3.598576 | 3840, 13440, 17600, 11200, 3708, 508 |
qrax | quasirhombated hexeract | 0.819496 | 960, 4800, 7280, 4960, 1788, 268 |
quacox | quasicellihexeract | 1.042011 | 960, 5760, 12320, 12000, 5148, 668 |
quactix | quasicellitruncated hexeract | 1.431870 | 3840, 19200, 34080, 25440, 7388, 668 |
quapox | quasiprismated hexeract | 0.937379 | 1280, 7680, 14400, 11200, 3708, 508 |
quitoxog | quasiterated hexeractihexacontatetrapeton | 1.137055 | 384, 1920, 4160, 4800, 2904, 728 |
quoptax | quasiprismatotruncated hexeract | 1.686163 | 3840, 17280, 25280, 16000, 4668, 508 |
quotacog | quasitericellated hexacontatetrapeton | 1.121320 | 1920, 8640, 16320, 15360, 6488, 728 |
quotox | quasitruncated hexeract | 0.681517 | 384, 1152, 1520, 1120, 444, 76 |
rackix | retrocelliskewed hexeract | 1.581139 | 1920, 11520, 23040, 21120, 8048, 548 |
raddirag | rhombidodecahedraly-diminished rectified hexacontatetrapeton | 1 | 48, 312, 758, 906, 532, 120 |
rag (old: ric) | rectified hexacontitetrapeton, lattice B6 contact polytope (span of its small roots), lattice D6 contact polytope (span of its roots), equatorial cross-section of gee-first rez, equatorial cross-section of vertex-first laq | 1 | 60, 480, 1120, 1200, 576, 76 |
ram | rectified pentacontitetrapeton, Gosset polypeton 02,2,1, Voronoi cell of lattice E6*, equatorial cross-section of rojak-first rolaq | 1.732051 | 720, 6480, 10800, 6480, 1566, 126 |
ramoh | rectified-pentacontitetrapetic hexacomb, Gosset hexacomb 02,2,2, Voronoi complex of lattice E6* | ||
rapa penp | rap atop penp, rap-first cap of ril | 0.845154 | 20, 95, 160, 130, 58, 13 |
rapalpenp | rap atop inverted penp, pen-first medial subsegment of jak | 0.816497 | 20, 115, 270, 280, 128, 23 |
rapesc | rectified-pentachoric scalene, rectified-pentachoron-pyramid pyramid, line atop fully orthogonal rectified pentachoron | 0.816497 | 12, 51, 100, 100, 51, 12 |
rappaf (alt.: rapalrappip) | rectified-pentachoral antifastegium, rectified pentachoron atop inverted rectified-pentachoral prism | 0.925820 | 30, 160, 270, 200, 73, 13 |
ratanit | rectified triacontaditeron atop penteractitriacontiditeron, rat-first rotunda of brag | 1.224745 | 120, 960, 1760, 1240, 364, 44 |
ratasiphin | rat atop siphin, rat-first cap of rojak | 1.290994 | 120, 960, 2240, 2000, 684, 84 |
ratip | rectified-triacontiditeron prism | 1.118034 | 80, 520, 1040, 880, 324, 44 |
rax | rectified hexeract, rectified dodecapeton, equatorial cross-section of brox-first bersa | 1.581139 | 192, 960, 1520, 1120, 444, 76 |
raxh | rectified hexeractic pentacomb | ||
redscox (alt.: trisoo) | hecatonenenecontadia-diminished small cellihexeract, partially triexpanded xedrag, tri - (4,8,8)-trioprism | 1.978437 | 768, 3840, 7616, 7296, 3288, 536 |
rerax | rectified rectified-hexeract, variation of small rhombated hexeract | 2.645751 | 960, 4800, 7280, 4960, 1788, 268 |
restaf | rectified staf | 1.732051 | 210, 1680, 3850, 3990, 1778, 168 |
rettidjak | rectification of tridiminished icosiheptaheptacontidipeton | 1.632993 | 168, 1440, 2880, 2256, 723, 75 |
ril (old: riss) | rectified heptapeton, vertex figure of hesa, Gosset polytope 04,1 | 0.845154 | 21, 105, 175, 140, 63, 14 |
rinathin | rectified penteract atop truncated demipenteract, rectified demipenteract-first cap of demirectified icosiheptaheptacontidipeton | 2.160247 | 240, 1200, 1840, 1200, 364, 44 |
rinnip | rectified-penteract prism | 1.5 | 160, 720, 1120, 800, 284, 44 |
ritas | rit altersquarism, cyclotetra-diminished sochax, medial segment of siphina, partial Stott expansion of hax | 1.322876 | 128, 832, 1984, 1984, 804, 100 |
ritgyt | rectified-tesseractic gyrotrigonism | 1.290994 | 96, 576, 1224, 1080, 387, 51 |
rixa (alt.: pabdihax, old: rixalrix) | rectified hexateron alterprism, parabidiminished demihexeract, rectified hexateron atop inverted rectified hexateron | 0.866025 | 30, 210, 520, 510, 204, 34 |
rixalspix | rectified hexateron atop small prismated hexateron, rix-first cap of scal | 1.195229 | 75, 390, 770, 720, 314, 49 |
rixasarx | rectified hexateron atop small rhombated hexateron, rix-first cap of brox | 1.414214 | 75, 420, 670, 470, 174, 29 |
rixascad | rectified hexateron atop small cellated dodecateron, half of rectified hexacontitetrapeton (its rix-first rotunda) | 1 | 45, 300, 710, 795, 404, 64 |
rixaspix | rectified hexateron atop small prismated hexateron, rix-first cap of rojak | 1.290994 | 75, 510, 1130, 1020, 374, 49 |
rixip | rectified-hexateron prism, vertex figure of rolaq | 0.957427 | 30, 135, 220, 170, 69, 14 |
rixpy | rectified-hexateronal pyramid, vertex pyramid of demihexeract | 0.866025 | 16, 75, 140, 125, 57, 13 |
rojak | rectified icosiheptaheptacontidipeton | 1.290994 | 216, 2160, 5040, 4320, 1350, 126 |
rojkoh | rectified icosiheptaheptacontidipetic hexacomb | ||
... | hyperbolic s3s4o3o3o4o pentacomb | 1.111786 i | |
saberjakh | small birhombated icosiheptaheptacontidipetic hexacomb | ||
saborx | small birhombated hexeract, bicantellated hexeract | 2.645751 | 1920, 9600, 13760, 8320, 2556, 316 |
sabril | small birhombated heptapeton, bicantellated heptapeton | 1.558387 | 210, 1050, 1540, 980, 329, 49 |
sabrim (old: pirm, sirmak, skorm) | small birhombated pentacontitetrapeton, (prismatorectified pentacontitetrapeton, small rhombated pentacontitetraheptacontidipeton, small heptacontidirhombated pentacontitetrapeton) | 3 | 6480, 38880, 62640, 38880, 9198, 558 |
sartabittit | small rhombated triacontadipeton atop bitruncated triacontadipeton, sart-first cap of small birhombated hexacontitetrapeton | 2.236068 | 480, 2400, 3680, 2440, 764, 84 |
sarxa gippixtum | sarx-first bistratic cap of shorjak, sarx-based tutsatope, sarx-based tutism | 3.265986 | 480, 1620, 2080, 1280, 389, 49 |
sarxasibrid | small rhombated hexateron atop small birhombated dodecateron, rix-first subsegment of brox | 1.414214 | 150, 960, 1610, 1125, 374, 49 |
sarxip | small-rhombated-hexateron prism | 1.384437 | 120, 540, 820, 560, 189, 29 |
scadaspix | small cellated dodecateron atop small prismated hexateron, scad-first cap of scal | 1.195229 | 90, 510, 1050, 1005, 439, 64 |
scadip | small-cellated-dodecateric prism | 1.118034 | 60, 270, 540, 570, 304, 64 |
scag | small cellihexacontitetrapeton, stericated hexacross | 2 | 960, 5760, 12480, 12480, 5336, 536 |
scajakh | small celliicosiheptaheptacontidipetic hexacomb | ||
scal | small cellated heptapeton, stericated heptapeton | 1.195229 | 105, 630, 1400, 1470, 700, 105 |
scox | small cellihexeract, stericated hexeract | 1.978437 | 960, 5760, 12320, 12000, 5148, 668 |
shihtip | square-hexagon-hexagon triprism | 1.581139 | 144, 432, 516, 312, 100, 16 |
shopjak | small demiprismated icosiheptaheptacontidipeton | 1.914854 | 1080, 8640, 19440, 16200, 4662, 342 |
shorjak | small demirhombated icosiheptaheptacontidipeton | 3.265986 | 4320, 19440, 27360, 15840, 3942, 342 |
sibcaxh | small bicellated hexeractic pentacomb | ||
siborg | small birhombated hexacontitetrapeton, bicantellated hexacross, rectified birectified-hexacontitetrapeton | 2.236068 | 1440, 8640, 13440, 8400, 2396, 236 |
sibpof | small biprismated tetradecapeton, biruncinated heptapeton | 1.414214 | 210, 1260, 2520, 2100, 716, 84 |
sibridacard | sibrid atop card, first subsegment of dot-first ram | 1.732051 | 270, 1800, 3120, 2160, 634, 64 |
sinnontip | sinnont prism | 1.645329 | 320, 1440, 1920, 1200, 384, 54 |
siphina | siphin alterprism, medial segment of sochax | 1.322876 | 160, 1120, 2880, 3120, 1364, 164 |
siphinnip | small-prismated-hemipenteractic prism | 1.369306 | 160, 880, 1840, 1680, 644, 84 |
sircotic | small-rhombicuboctahedron - truncated-cube duoprism | 2.263033 | 576, 2016, 2688, 1656, 448, 40 |
sirhax | small rhombated hemihexeract, cantellated demihexeract, runcic hexeract | 1.936492 | 640, 3840, 5920, 3520, 876, 76 |
sirhina | sirhin alterprism, medial segment of sophax | 1.658312 | 320, 1920, 3680, 2880, 924, 124 |
sirhinasart | sirhin atop sart, nit-first subsegment of ram | 1.732051 | 400, 2880, 4800, 3080, 844, 84 |
sirjak | small rhombated icosiheptaheptacontidipeton | 2.380476 | 2160, 15120, 24480, 15120, 3942, 342 |
sobpoxog | small biprismated hexeractihexacontatetrapeton, biruncinated hexeract, biruncinated hexacross | 2.345208 | 1920, 11520, 22560, 17760, 5276, 476 |
sochax | small cellated hemihexeract, stericated demihexeract, pentic hexaract, equatorial cross-section of hax-first lin | 1.322876 | 192, 1440, 4000, 4800, 2344, 296 |
sophax | small prismated hemihexeract, runcinated demihexeract, steric hexeract | 1.658312 | 480, 3360, 7360, 6240, 1996, 236 |
soxaxog | small hexeractihexeractihexacontitetrapeton | 1.645329 | 384, 1920, 2480, 1600, 564, 88 |
spam (old: skopam) | small prismated pentacontitetrapeton, (small hebdomecontadiaprismated pentacontitetrapeton) | 2.236068 | 2160, 15120, 36720, 36720, 14238, 1278 |
spida rappip | spid || rappip, (rap,rap,spid)-trigonic | 1 | 40, 250, 520, 470, 193, 33 |
spidapenp | spid atop penp, wedge of staf | 1 | 30, 125, 240, 250, 138, 33 |
spil | small prismated heptapeton, runcinated heptapeton | 1.309307 | 140, 840, 1610, 1295, 455, 70 |
spixa (old: spixalspix) | small prismated hexateron alterprism, small prismated hexateron atop inverted small prismated hexateron, medial segment of dot-first birectified hexacontitetrapeton | 1.224745 | 120, 900, 1920, 1620, 544, 64 |
spixalsarx | spix atop inverted sarx | 1.290994 | 120, 870, 1790, 1530, 554, 64 |
spixip | small-prismated-hexateron prism | 1.290994 | 120, 600, 1110, 930, 349, 49 |
spog | small prismatohexacontitetrapeton, runcinated hexacross | 1.870829 | 960, 7200, 14400, 11280, 3416, 296 |
spojak | small prismated icosiheptapeton | 2.768875 | 4320, 25920, 47520, 34560, 9702, 1062 |
spox | small prismated hexeract, runcinated hexeract | 2.263033 | 1280, 7680, 14400, 11200, 3708, 508 |
squagippid | square - great-prismated-pentachoron duoprism | 2.345208 | 480, 1440, 1680, 960, 274, 34 |
squahex | square-hexadecachoron duoprism, vertex figure of braxh | 1 | 32, 128, 232, 216, 100, 20 |
squahi | square-hecatonicosachoron duoprism | 3.769377 | 2400, 7200, 8280, 4560, 1204, 124 |
squapen | square-pentachoron duoprism, vertex figure of bersa | 0.948683 | 20, 60, 85, 70, 34, 9 |
squarahi | square - rectified-hecatonicosachoron duoprism | 4.589369 | 4800, 19200, 28080, 18960, 6004, 724 |
squarap | square - rectified-pentachoron duoprism | 1.048809 | 40, 160, 250, 190, 74, 14 |
squarico | square - rectified-icositetrachoron duoprism | 1.870829 | 384, 1536, 2208, 1440, 436, 52 |
squarit | square - rectified-tesseract duoprism | 1.414214 | 128, 512, 768, 544, 188, 28 |
squarox | square - rectified-hexacosachoron duoprism | 3.157869 | 2880, 17280, 29520, 20880, 6484, 724 |
squepe | square pennene | 0.707107 | 8, 26, 45, 45, 26, 8 |
squex | square-hexacosachoron duoprism | 1.765796 | 480, 3360, 7800, 7920, 3604, 604 |
squico | square-icositetrachoron duoprism | 1.224745 | 96, 480, 792, 576, 196, 28 |
sram (old: skobram, skabram) | small rhombated pentacontitetrapeton, (small hebdomecontadiabirhombated pentacontitetrapeton) | 3.316625 | 6480, 32400, 45360, 25920, 7326, 846 |
sril | small rhombated heptapeton, cantellated heptapeton | 1.362770 | 105, 525, 805, 560, 210, 35 |
srog | small rhombihexacontitetrapeton, cantellated hexacross | 1.732051 | 480, 3360, 6400, 5040, 1656, 136 |
srox | small rhombated hexeract, cantellated hexeract | 2.515637 | 960, 4800, 7280, 4960, 1788, 268 |
staf (interim: stef) | small terated tetradecapeton, pentellated heptapeton, expanded heptapeton, lattice A6 contact polytope (span of its roots), equatorial cross-section of hop-first suph, equatorial cross-section of ril-first rez, equatorial cross-section of hop-first laq | 1 | 42, 210, 490, 630, 434, 126 |
starpglassdit | pentagrammic-retroprismatic-hourglass duotegum | 0.707107 | 20, 120, 229, 190, 75, 14 |
stasissiddow | (pentagramm,sissid)-disphenoid, pentagram atop fully orthogonal small stellated doedcahedron | 0.639240 | 17, 95, 223, 223, 95, 17 |
stef | stellated tetradecapeton, compound of 2 hop | 0.654654 | |
stopen | octagram-pentachoron duoprism | 1.092197 | 40, 120, 165, 130, 58, 13 |
stoxog | small terated hexeractihexacontatetrapeton, pentellated hexeract, pentellated hexacross | 1.645329 | 384, 1920, 4160, 4800, 2904, 728 |
taccarat | triacontaditeron atop rectified triacontaditeron, tac-first rotunda of rectified hexacontitetrapeton, rectified triacontaditeron-pyramid | 1 | 50, 360, 760, 720, 314, 44 |
taccup | triacontiditeron prism, vertex figure of rez | 0.866025 | 20, 90, 200, 240, 144, 34 |
tacog | tericellated hexacontitetrapeton, pentitruncated hexeract | 3.121320 | 1920, 8640, 16320, 15360, 6488, 728 |
tacogral (old: gatocral) | tericelligreatorhombated heptapeton, pentistericantitruncated heptapeton | 2.976095 | 2520, 8820, 11340, 6510, 1596, 126 |
tacox | tericellated hexeract, pentitruncated hexacross | 2.474130 | 1920, 8640, 15680, 13920, 5688, 728 |
tacpy | triacontaditeric pyramid, vertex-first rotunda of gee | 0.707107 | 11, 50, 120, 160, 112, 33 |
tactaf | tericellitruncated tetradecapeton, pentisteritruncated heptapeton | 2.236068 | 840, 3360, 5250, 3780, 1176, 126 |
tacu | tac-based ursapeton | 1.144123 | 60, 370, 760, 720, 314, 44 |
tag | truncated hexacontitetrapeton, equatorial cross-section of gee-first taz | 1.581139 | 120, 540, 1120, 1200, 576, 76 |
tagopal (old: gatopal) | terigreatoprismated heptapeton, pentiruncicantitruncated heptapeton | 3.116775 | 2520, 8820, 11550, 6825, 1701, 126 |
tahgyt | tesseractihexadecachoric gyrotrigonism | 2.160247 | 288, 1152, 1704, 1176, 387, 51 |
taporf (old: staporf) | teriprismatorhombitetradecapeton, pentiruncicantellated heptapeton | 2.449490 | 1260, 5040, 7560, 5250, 1596, 126 |
tapox (old: stapox) | teriprismated hexeract, penticantellated hexacross | 2.707107 | 3840, 21120, 38720, 30240, 9528, 728 |
tatraffip | triangle atop traffip | 0.925820 | 21, 84, 139, 117, 53, 12 |
tedjak (alt.: hexgyt, hexalhin) | tridiminished icosiheptaheptacontidipeton, tridiminished 22,1, hexadecachoral gyrotrigonism | 0.816497 | 24, 168, 480, 600, 315, 51 |
tedrag | (cyclo-)tetra-diminished rag | 1 | 56, 416, 992, 1072, 516, 76 |
tepasc | tetrahedral-prismatic scalene, tetrahedron-prism-pyramid pyramid, line atop fully orthogonal tetrahedron prism | 0.866025 | 10, 33, 54, 50, 27, 8 |
tepepyp | tetrahedral-prismatic pyramid prism, prism of tepepy | 0.957427 | 18, 57, 84, 70, 34, 9 |
terjakh | tetrarectified icosiheptaheptacontidipetic hexacomb | ||
teta troct | tetrahedron atop triangle-octahedron duoprism | 0.925820 | 22, 96, 160, 130, 56, 12 |
tetaco altepetric | (tetaco,tepe)-disphenoid, (tet,co,inv tepe)-trigonic | 1 | 24, 106, 200, 186, 86, 18 |
tetafip | prism of tetrahedral antifastegium, tetaf prism, tepe atop inverted squatet, half of hinnip | 0.935414 | 24, 104, 202, 196, 93, 19 |
tetal tratet | tetrahedron atop alternate triangle,tetrahedron-duoprism | 0.866025 | 16, 72, 146, 148, 76, 18 |
tetco | tetrahedron-cuboctahedron duoprism | 1.172604 | 48, 168, 248, 196, 86, 18 |
tetcube | tetrahedron - cube duoprism | 1.060660 | 32, 96, 128, 96, 42, 10 |
tetdip | tetrahedron-tetrahedron duoprism, vertex figure of he | 0.866025 | 16, 48, 68, 56, 28, 8 |
tetdoe | tetrahedron-dodecahedron duoprism | 1.529224 | 80, 240, 308, 216, 84, 16 |
tetgocco | (tet,gocco)-duoprism | 0.958067 | 96, 336, 464, 340, 134, 24 |
tetid | tetrahedron-icosidodecahedron duoprism | 1.730039 | 120, 420, 608, 466, 194, 36 |
tetike | tetrahedron-icosahedron duoprism | 1.131154 | 48, 192, 308, 256, 116, 24 |
tetoct | tetrahedron-octahedron duoprism, vertex figure of sez | 0.935414 | 24, 84, 128, 106, 50, 12 |
tetsocco | (tet,socco)-duoprism | 1.527124 | 96, 336, 464, 340, 134, 24 |
tettidjak | truncation of tridiminished icosiheptaheptacontidipeton | 2.449490 | 336, 1608, 2880, 2256, 723, 75 |
tettut | (tetrahedron,truncated-tetrahedron)-duoprism | 1.322876 | 48, 144, 188, 136, 56, 12 |
thax | truncated hemihexeract, cantic hexeract | 2.179449 | 480, 2160, 3200, 2080, 636, 76 |
thexgyt (alt.: pex tedjak) | truncated-hexadecachoral gyrotrigonism, partially expanded tridiminished icosiheptaheptacontidipeton, partially expanded tridiminished 21,2 | 1.632993 | 144, 648, 1056, 816, 315, 51 |
thox (old: thod) | triacontidiahemihexeract, triacontidihemidodecapenton, cytohemiectid, vertex figure of guhsa | 0.707107 | 12, 60, 160, 240, 192, 38 |
tidril | tridiminished rectified heptapeton, (pen,pen,bidrap)-trigonic | 0.845154 | 18, 75, 127, 107, 48, 11 |
til | truncated heptapeton | 1.362771 | 42, 126, 175, 140, 63, 14 |
tim | truncated pentacontitetrapeton | 2.645751 | 1440, 7200, 10800, 6480, 1566, 126 |
tiquithdow | (triangle,quith)-disphenoid, triangle atop fully orthogonal quasitruncated hexahedron | 0.645976 | 27, 111, 195, 175, 81, 17 |
tisdip altratet | tisdip atop gyrated tratet | 0.925820 | 24, 102, 173, 144, 62, 13 |
titajak (old: totajik, oldest: hibtajak) | tritruncated icosiheptaheptacontidipeton, (demibitruncated icosiheptaheptacontidipeton) | 3.829708 | 4320, 12960, 14400, 7200, 1566, 126 |
titam (old: cacram, totam, tomak, katom) | tritruncated pentacontitetrapeton, (centrocellirhombated pentacontitetrapeton, trunkated pentacontitetraheptacontidipeton, heptacontiditruncated pentacontitetrapeton) | 3.741657 | 8640, 34560, 47520, 28080, 7038, 558 |
tithtip | triangle-triangle-hexagon triprism | 1.290994 | 54, 162, 207, 144, 57, 12 |
titraf | triangle-traf duoprism | 0.966092 | 27, 99, 153, 123, 54, 12 |
titstip | triangle-triangle-square triprism | 1.080123 | 36, 108, 141, 102, 43, 10 |
tixip | truncated-hexateron prism | 1.414214 | 60, 180, 235, 170, 69, 14 |
tocal | teracellated heptapeton, pentitruncated heptapeton | 1.647509 | 210, 945, 1820, 1785, 826, 126 |
tocral (old: stocral) | tericellirhombated heptapeton, pentiruncitruncated heptapeton | 2.329929 | 1260, 5670, 8610, 5565, 1491, 126 |
tocrax (old: stocrax) | (small) tericellirhombated hexeract, pentiruncitruncated hexacontitetrapeton | 3.734936 | 11520, 51840, 77760, 48480, 11768, 728 |
toedip | truncated-octahedron - truncated-octahedron duoprism | 2.236068 | 576, 1728, 1968, 1056, 268, 28 |
togral (old: gotral) | terigreatorhombated heptapeton, penticantitruncated heptapeton | 2.390457 | 840, 3360, 5390, 4096, 1351, 126 |
togrig (old: gotrig) | terigreatorhombihexacontitetrapeton, (old: great terirhombated hexacontatetrapeton), penticantitruncated hexacontitetrapeton | 3.569684 | 7680, 30720, 47360, 33600, 10008, 728 |
tojak | truncated icosiheptaheptacontidipeton | 2 | 432, 2376, 5040, 4320, 1350, 126 |
topag (old: stopag) | teriprismated hexacontitetrapeton, penticantellated hexeract | 2.921564 | 3840, 21120, 39360, 31680, 10328, 728 |
topal (old: stopal) | teriprismated heptapeton, penticantellated heptapeton | 1.690309 | 420, 2310, 4340, 3570, 1246, 126 |
tox | truncated hexeract | 2.745093 | 384, 1152, 1520, 1120, 444, 76 |
tracope | triangle-cuboctahedron duoprismatic prism | 1.258306 | 72, 252, 360, 264, 103, 19 |
tradope | triangle-dodecahedron duoprismatic prism | 1.595888 | 120, 360, 442, 284, 99, 17 |
tragittith | (triangle,gittith)-duoprism | 1.061238 | 192, 768, 1048, 696, 235, 35 |
tragrip | triangle - great-rhombated-pentachoron duoprism | 1.932184 | 180, 540, 660, 420, 143, 23 |
trahex | triangle - hexadecachoron duoprism, vertex figure of barz | 0.912871 | 24, 96, 176, 168, 83, 19 |
trahi | triangle - hecatonicosachoron duoprism | 3.747204 | 1800, 5400, 6360, 3720, 1083, 123 |
trapen | triangle - pentachoron duoprism, vertex figure of broc | 0.856349 | 15, 45, 65, 55, 28, 8 |
trarahi | triangle - rectified-hecatonicosachoron duoprism | 4.571175 | 3600, 14400, 21360, 15120, 5283, 723 |
trarap | triangle - rectified-pentachoron duoprism, vertex figure of branq | 0.966092 | 30, 120, 190, 150, 63, 13 |
trarico | triangle - rectified-icositetrachoron duoprism | 1.825742 | 288, 1152, 1680, 1152, 387, 51 |
trarit | triangle - rectified-tesseract duoprism | 1.354006 | 96, 384, 584, 432, 163, 27 |
trarox | triangle - rectified-hexacosachoron duoprism | 3.131369 | 2160, 12960, 22320, 16560, 5763, 723 |
traspid | triangle - small-prismated-pentachoron duoprism | 1.154701 | 60, 240, 410, 360, 163, 33 |
trasrip | (triangle,small rhombated pentachoron)-duoprism | 1.316561 | 90, 360, 540, 390, 143, 23 |
trasteth | (triangle,steth)-duoprism | 1.593876 | 192, 768, 1048, 696, 235, 35 |
tratah | triangle - tesseractihexadecachoron duoprism | 2.198484 | 288, 864, 1032, 624, 195, 27 |
tratepe | triangle-tetrahedron-duoprism prism, vertex figure of lanq | 0.978945 | 24, 72, 98, 76, 35, 9 |
tratess | triangle - tesseract duoprism | 1.154701 | 48, 144, 184, 128, 51, 11 |
tratet altroct | triangle-tetrahedron duoprism atop gyrated triangle-octahedron duoprism, vertex-first medial segment of birectified heptapeton | 0.925820 | 30, 156, 280, 228, 90, 16 |
tratetdafup | triangular-tetrahedral duoantifastegiaprism, tratet atop bidual tratet | 0.866025 | 24, 132, 284, 282, 128, 22 |
tratetpy | (triangle,tetrahedron)-duoprism pyramid, vertex-pyramid of bril | 0.925820 | 13, 42, 64, 55, 28, 8 |
tratriddipdit | (triangle,triangular duoprism)-duotegum, tegum product of triangle and triangular duoprism | 12, 48, 96, 105, 63, 18 | |
traxh | tri-rectified hexeractic pentacomb, Voronoi complex of body-centered hexeractic lattice (lattice D6*) | ||
trex | triangle - hexacosachoron duoprism | 1.717954 | 360, 2520, 5880, 6120, 3003, 603 |
trial tratet | triangle atop dual tratet, triangle-first cap of ril | 0.845154 | 15, 57, 95, 85, 43, 11 |
trico | triangle - icositetrachoron duoprism | 1.154701 | 72, 360, 600, 456, 171, 27 |
tridafupip | tridafup prism | 1 | 36, 162, 276, 222, 88, 16 |
triddipabl tratrip | triddip atop bidual tratrip | 1 | 27, 135, 243, 201, 81, 15 |
triddipasc | triangle-duoprismatic scalene, triangle-duoprism-pyramid pyramid, line atop fully orthogonal triangle duoprism | 1 | 11, 37, 60, 54, 28, 8 |
triddippa tridafup | triddip atop tridafup, ((3,3)-dip, (3,dual 3)-dip, (dual 3,3)-dip)-trigonic | 0.925820 | 27, 126, 225, 192, 81, 15 |
tridep | triangle-icosidodecahedron duoprismatic prism | 1.789237 | 180, 630, 882, 624, 229, 37 |
trikep | triangle-icosahedron duoprismatic prism | 1.219771 | 72, 288, 450, 348, 139, 25 |
trim (old: cacam, tram, mak) | trirectified pentacontitetrapeton, (centrocellated pentacontitetrapeton, pentacontitetraheptacontidipeton) | 1.414214 | 270, 2160, 6480, 8640, 4608, 558 |
tripal triddip | trip atop gyro-perp triddip | 0.816497 | 15, 63, 110, 97, 46, 11 |
trippete | trip tettene, {3}-first cap of jak | 0.816497 | 9, 30, 51, 49, 27, 8 |
tritra ope | (triangle, dual triangle, trip, gyro trip) lace simplex | 0.866025 | 18, 78, 138, 121, 55, 12 |
trittip | triangle-triangle-triangle-triprism, vertex figure of ramoh | 1 | 27, 81, 108, 81, 36, 9 |
troctpy | troct pyramid, vertex pyramid of brag | 1.224745 | 19, 72, 120, 105, 50, 12 |
trojkoh | trirectified icosiheptaheptacontidipetic hexacomb | ||
trope (old: troctip) | triangle-octahedron duoprismatic prism | 1.040833 | 36, 126, 186, 144, 61, 13 |
tutdip | truncated-tetrahedron duoprism | 1.658312 | 144, 432, 516, 312, 100, 16 |
xedrag | hexeractidiminished rectified hexacontatetrapeton, square cuboctahedroltriate, scaliform dodecadiminished rectified hexacontatetrapeton | 1 | 48, 288, 688, 768, 396, 76 |
xog | hexeractihexacontatetrapeton, tritruncated hexeract, tritruncated hexacross | 2.549510 | 960, 3360, 4160, 2320, 636, 76 |
Count of actually available polytopes: 439
---- 7D ----
Acronym | Name | Circumradius | Face vector |
(N,M)-dafupap | (N,M)-duoantifastegiaprismatic alterprism, (N,M)-duoantifastegiaprism atop lacing-ortho (N,M)-duoantifastegiaprism | ... | 4nm, 24nm, 52nm+4n+4m, 52nm+14n+14m, 24nm+18n+18m+4, 4nm+10n+10m+6, 2n+2m+4 |
..., 03,2,2 | hyperbolic Gosset heptacomb 03,2,2 | 2.449490 i | |
... | 2guhsa (?) | 0.707107 | |
..., 23,2 | hyperbolic Gosset heptacomb 23,2 | 0.577350 i | |
..., 32,2 | hyperbolic hecatonicosihexapentacosiheptacontihexaexic heptacomb, hyperbolic Gosset heptacomb 32,2 | 0 i | |
barz (old: drhio) | birectified hecatonicosoctaexon, equatorial cross-section of rez-first bark | 1.224745 | 280, 3360, 8960, 10640, 6048, 1428, 142 |
berlin (old: shabrilq) | birectified pentacontihexahecatonicosihexaexon (small demibirhombated pentacontihexapentacosiheptacontihexaexon) | 3.570714 | 40320, 302400, 544320, 403200, 142632, 22428, 758 |
bersa (old: dars) | birectified hepteract, Gosset polytope 04,1,1 | 1.581139 | 672, 6720, 13440, 11760, 5656, 1428, 142 |
betsa | bitruncated hepteract | 3.240370 | 2688, 9408, 14112, 11760, 5656, 1428, 142 |
bittoc | bitruncated octaexon | 1.713914 | 168, 588, 896, 770, 392, 112, 16 |
botaz | bitruncated hecatonicosoctaexon, bitruncated heptacross | 2.121320 | 840, 4200, 9240, 10640, 6048, 1428, 142 |
botlaq | bitruncated pentacontihexapentacosiheptacontihexaexon | 4.123106 | 30240, 151200, 252000, 191520, 72072, 12348, 758 |
botnaq | truncated hecatonicosihexapentacosiheptacontihexaexon | 3.278719 | 12096, 72576, 165312, 161280, 68040, 12348, 758 |
bragabrox | brag atop brox, brag-first rotunda of sez | 1.414214 | 400, 4320, 9440, 8400, 3592, 788, 78 |
bragasochax | brag atop sochax, 2nd subsegment of lin in hax-first orientation | 1.322876 | 352, 4800, 17440, 23920, 14020, 3388, 298 |
branq (old: dranq) | birectified hecatonicosihexapentacosiheptacontihexaexon | 1.936492 | 4032, 60480, 161280, 161280, 68040, 12345, 758 |
brilalspil | bril atop inverted spil | 1.322876 | 175, 1190 2800, 3150, 1834, 539, 72 |
brilastaf | bril atop staf, hop-first subsegment of laq | 1 | 77, 840, 3150, 5215, 4088, 1386, 128 |
brillip | birectified - heptapeton prism | 1.052209 | 70, 455, 910, 840, 413, 112, 16 |
brilpy | birectified-heptapetonal pyramid, vertex pyramid of pentacontihexahecatonicosihexaexon | 1.322876 | 36, 245, 560, 595, 329, 98, 15 |
broc (old: droc) | birectified octaexon, duorectified octaexon, vertex figure of bif, Gosset polytope 04,2 | 0.968246 | 56, 420, 840, 770, 392, 112, 15 |
broxa sophax | brox atop sophax, hax-first subsegment of rolaq | 1.732051 | 720, 8160, 23520, 26560, 13192, 2948, 238 |
copen | cuboctahedron - pentachoron duoprism | 1.183216 | 60, 240, 430, 445, 282, 104, 19 |
corap | cuboctahedron - rectified-pentachoron duoprism | 1.264911 | 120, 600, 1220, 1270, 702, 194, 24 |
corit | cuboctahedron - rectified-tesseract duoprism | 1.581139 | 384, 1920, 3808, 3776, 1916, 448, 38 |
cubhex | cube-hexadecachoron duoprism | 1.118034 | 64, 288, 592, 664, 416, 140, 22 |
cubpen | cube-pentachoron duoprism | 1.072381 | 40, 140, 230, 225, 138, 52, 11 |
cyooh | cyclo-octaexic heptacomb, Delone complex of lattice A7 | ||
dijakpy | diminished-icosiheptaheptacontidipetic pyramid, (hin, tac, point)-trigonic | 0.866025 | 27, 226, 840, 1560, 1458, 622, 85 |
... | point || pseudo hax || gee, Dutour polyexon type A | 45, 524, 2480, 5520, 5884, 2692, 329 | |
frasa | facetorectified hepteract | 1.732051 | 448, 2688, 6720, 8960, 6720, 2688, 448 |
froc | facetorectified octaexon | 0.866025 | 28, 168, 490, 840, 868, 504, 127 |
gabach | great bicellihexadecaexon | 3.872983 | 10080, 35280, 49560, 35700, 13832, 2688, 198 |
gahax | gee atop hax, gee-first segment of naq | 0.866025 | 44, 492, 2240, 4880, 5244, 2452, 298 |
garag | gee atop rag, gee-first rotunda of rez | 1 | 72, 660, 1820, 2560, 1968, 716, 78 |
geep | hexacontitetrapeton prism, hexacross prism, vertex figure of rek | 0.866025 | 24, 132, 380, 640, 624, 320, 66 |
geepy | hexacontitetrapeton pyramid, vertex-first rotunda of gee | 0.707107 | 13, 72, 220, 400, 432, 256, 64 |
goccopen | (gocco,pen)-duoprism | 0.971027 | 120, 480, 820, 805, 474, 158, 25 |
gopamp | great-prismated-pentacontitetrapeton prism | 6.264982 | 103680, 362880, 501120, 345600, 123516, 21114, 1280 |
gososaz | great hepteractihepteractihecatonicosoctaexon | 1.242133 | 896, 5376, 8512, 7280, 3808, 1148, 156 |
gotafip | great-terated-tetradecapeton prism | 3.774917 | 10080, 35280, 48720, 33600, 12012, 2058, 128 |
gotanq (old: gotalq) | great terated hecatonicosihexapentacosiheptacontihexaexon, omnitruncated Gosset polyexon 32,1, great terated pentacontihexapentacosiheptacontihexaexon, omnitruncated Gosset polyexon 21,3, great terated pentacontihexahecatonicosihexaexon, omnitruncated Gosset polyexon 12,3 | 9.987492 | 2903040, 10160640, 13789440, 9072000, 2938320, 415800, 17642 |
gotaz | great terated hecatonicosoctaexon, great terated heptacross | 6.745369 | 322560, 1128960, 1532160, 1008000, 326032, 45528, 1738 |
goxaxogip | goxaxog prism | 1.242133 | 768, 4224, 6880, 5680, 2728, 740, 90 |
guhsa (old: xhaf) | hexacontitetrahemihepteract, hexacontitetrahemitetradecaexon | 0.707107 | 14, 84, 280, 560, 672, 448, 71 |
guph | great petated hexadecaexon, hexipentisteriruncicantitruncated octaexon, omnitruncated octaexon, permutoexon of 8 elements | 4.582576 | 40320, 141120, 191520, 126000, 40824, 5796, 254 |
hagippiddip | hexagon - great-prismated-pentachoron duoprism prism | 2.5 | 1440, 5040, 7080, 5100, 1992, 408, 38 |
hagippit | hexagon - great-prismated-triacontiditeron duoprism | 4 | 11520, 40320, 55680, 38400, 13772, 2418, 168 |
hagocad | hexagon - great-cellated-dodecateron duoprism | 3.122499 | 4320, 15120, 20880, 14400, 5172, 918, 68 |
haxabrag | hax-first monostratic cap of lin, hax atop brag | 1.322876 | 192, 2320, 7360, 8720, 4408, 996, 78 |
haxabrox | hax atop brox, hax-first cap of rolaq | 1.732051 | 272, 2640, 6000, 5920, 2968, 756, 78 |
haxarag | hemihexeract atop rectified hexacontitetrapeton, vertex-first subsegment of pentacontihexapentacosiheptacontihexaexon | 1 | 96, 1200, 5120, 9200, 7068, 2116, 238 |
haxip | hemihexeractic prism, vertex figure of rinquoh | 1.060660 | 64, 512, 1520, 1920, 1144, 340, 46 |
haxpy | hemihexeractic pyramid, vertex pyramid of laq | 1 | 33, 272, 880, 1280, 892, 296, 45 |
haxt | demihexeractic (line-)tegum, demihexeractic bipyramid | ... | 34, 304, 1120, 1920, 1532, 548, 88 |
he (old: ache) | hexadecaexon, trirectified octaexon, equatorial cross-section of (vertex first) 1/q-octo, Gosset polytope 03,3 | 1 | 70, 560, 1120, 980, 448, 112, 16 |
hehah | hexadecahemihexadecaexon | 1 | 56, 336, 616, 630, 392, 140, 24 |
hejaka | hejak alterprism, hejak atop alternate hejak | 1.658312 | 864, 8640, 30960, 51120, 41580, 14922, 1280 |
hept | hepteract, tetradecaexon, 7D measure-polytope (γ7), geozett(id) | 1.322876 | 128, 448, 672, 560, 280, 84, 14 |
hepth | hepteractic heptacomb, 7D hypercubical honeycomb (δ7) | ||
hesa (old: hiss) | hemihepteract, vertex figure of bay, Gosset polytope 14,1 | 0.935414 | 64, 672, 2240, 2800, 1624, 532, 78 |
hexal trahex | hex atop gyrated trahex, hex-first cap of hesa | 0.935414 | 32, 216, 592, 768, 516, 182, 28 |
hexalhax | hex atop alternate hax | 0.866025 | 40, 392, 1504, 2640, 2237, 848, 101 |
hexete | hexadecachoric tettene, hexadecachoron-pyramid pyramid-pyramid, triangle atop fully orthogonal hexadecachoron | 0.707107 | 11, 51, 129, 192, 169, 83, 19 |
hidlin | hexadeca-diminished pentacontihexahecatonicosihexaexon | 1.322876 | 560, 9520, 36960, 46480, 22456, 4172, 198 |
hinaf, hin || alt. hinnip | hemipenteractic alterfastegium, hin atop alternate hinnip, hin-first rotunda of hesa | 0.935414 | 48, 416, 1280, 1640, 998, 313, 45 |
hinsc | demipenteractic scalene, demipenteractic-pyramid pyramid, line atop fully orthogonal demipenteract | 0.866025 | 18, 113, 336, 520, 426, 173, 28 |
hirlaq | demirectified pentacontihexapentacosiheptacontihexaexon | 2.958040 | 12096, 90720, 171360, 141120, 59976, 12348, 758 |
hixaf | hexateron antifastegium, hix atop inverted hixip, hix-first cap of naq | 0.866025 | 18, 111, 345, 605, 603, 313, 65 |
hixippy | hexateron prism pyramid, vertex-pyramid of roc | 0.866025 | 13, 48, 91, 105, 77, 35, 9 |
hopabril | heptapeton atop birectified heptapeton, hop-first monostratic cap of hesa | 0.935414 | 42, 336, 910, 1085, 665, 231, 37 |
hopalbril | hop atop inverted bril, hop-first cap of laq | 1 | 42, 371, 1225, 1890, 1400, 476, 72 |
hopalril | hop atop inverted ril, hop-first cap of naq | 0.866025 | 28, 231, 840, 1575, 1554, 721, 107 |
hopastaf | hop atop staf, half of suph (its hop-first rotunda), partial Stott expansion of oca | 1 | 49, 273, 735, 1155, 1085, 567, 128 |
hopip | heptapeton prism, vertex figure of rene | 0.823754 | 14, 49, 91, 105, 77, 35, 9 |
idinaq (alt.: trahixdap) | icosa-diminished naq, triangular-hexateric duoalterprism | 0.866025 | 36, 306, 1122, 2130, 2136, 1008, 152 |
ihdlaq | icositetra-hexa-diminished pentacontihexapentacosiheptacontihexaexon, hexadecachoral gyro-cuboctahedronism | 1 | 96, 1152, 4632, 7488, 5244, 1416, 86 |
jaka (alt.: pabdinaq, old: jakaljak) | jak alterprism, jak atop inverted jak, vertex-first medial segment of naq, parabidiminished naq | 0.866025 | 54, 702, 3600, 8640, 9936, 4806, 560 |
jakamo | jak atop mo, jak-first half of parabidiminished laq | 1 | 99, 1368, 6120, 11160, 8550, 2583, 344 |
jakatrim | jak atop trim, jak-first cap of stanq | 1.658312 | 297, 2646, 9360, 16200, 13896, 5265, 560 |
jakip | icosihepta-heptacontidi-peton prism, vertex figure of riffy | 0.957427 | 54, 459, 1656, 2880, 2376, 846, 101 |
jakpy | icosihepta-heptacontidi-peton pyramid, vertex-first cap of naq | 0.866025 | 28, 243, 936, 1800, 1728, 747, 100 |
jakte | icosihepta-heptacontidi-peton tegum | ... | 29, 270, 1152, 2520, 2808, 1395, 198 |
jaku | jak-based ursaexon | 1.335149 | 270, 2835, 8136, 10440, 6318, 1575, 128 |
lanq (inbetween: rolin) | pentacontihexa-hecatonicosihexa-pentacosiheptacontihexa-exon, rectified pentacontihexahecatonicosihexaexon, Gosset polytope 03,2,1 | 2.449490 | 10080, 120960, 241920, 191520, 72072, 12348, 758 |
lanquoh (old: rolinoh) | pentacontihexa-hecatonicosihexa-pentacosiheptacontihexa-exic heptacomb, rectified pentacontihexahecatonicosihexaexic heptacomb, Gosset heptacomb 03,3,1 | ||
laq | pentacontihexapentacosiheptacontihexaexon, argyroexon, Gosset polyexon 21,3, vertex figure of naquoh, lattice E7 contact polytope (span of its roots), equatorial cross-section of vertex-first fy | 1 | 126, 2016, 10080, 20160, 16128, 4788, 632 |
lin | pentacontihexahecatonicosihexaexon, chrysoexon, Gosset polyexon 12,3, Voronoi cell of lattice E7* | 1.322876 | 576, 10080, 40320, 50400, 23688, 4284, 182 |
linoh | pentacontihexahecatonicosihexaexic heptacomb, Gosset heptacomb 13,3, Voronoi complex of lattice E7* | ||
moarojak | mo-first monostratic cap of lin, mo atop rojak | 1.322876 | 288, 3960, 13680, 16560, 8172, 1746, 128 |
mou | mo-based ursaexon | 1.738546 | 864, 8712, 20160, 19440, 8748, 1746, 128 |
n,hix-dip | n-gon - hexateron duoprism | sqrt[5/12 + 1/(2 sin(π/n))2] | 6n, 21n, 35n+6, 35n+15, 21n+20, 7n+15, n+6 |
n,m,k-tippip | n-gon - m-gon - m-gon - triprismatic prism | sqrt[1/4+1/(4 sin2(π/n))+1/(4 sin2(π/m))+1/(4 sin2(π/m))] | 2nmk, 7nmk, 9nmk+2nm+2nk+2mk, 5nmk+5nm+5nk+5mk, nmk+4nm+4nk+4mk+2n+2m+2k, nm+nk+mk+3n+3m+3k, n+m+k+2 |
n,n,n-tippip | n-gon - n-gon - n-gon - triprismatic prism | sqrt[1/4+3/(4 sin2(π/n))] | 2n3, 7n3, 9n3+6n2, 5n3+15n2, n3+12n2+6n, 3n2+9n, 3n+2 |
nal | hecatonicosihexa-pentacontihexa-exon, vertex figure of fib | 0.866025 | 56, 756, 4032, 10080, 12096, 6804, 182 |
naq (alt: rocalroc) | hecatonicosihexapentacosiheptacontihexaexon, sideroexon, Gosset polyexon 32,1, alterelongated jak tegum, vertex figure of fy, (one of the) Delone cell(s) of lattice E7, tegum sum of 2 mutually inverted rectified octaexa, biambohexadecaexon, lattice E7* contact polytope (span of its roots) | 0.866025 | 56, 756, 4032, 10080, 12096, 6048, 702 |
naquoh | hecatonicosihexapentacosiheptacontihexaexic heptacomb, Gosset heptacomb 33,1, Delone complex of lattice E7 | ||
oca (old: oc) | octaexon, 7D simplex (α7), pyrozett(id), heptapetal pyramid, vertex figure of ene, (one of the) Delone cell(s) of lattice E7, Gosset polytope 06 | 0.661438 | 8, 28, 56, 70, 56, 28, 8 |
..., oct || perp oct | (degenerate) oct atop fully orthogonal oct, octahedron disphenoid | ∞ i.e. flat in euclidean space | 12, 60, 160, 242, 204, 88, 16 |
octatetdip | oct atop tetdip, oct-first half of roc | 0.866025 | 22, 108, 220, 245, 164, 64, 13 |
octepe | octahedral pennene | 0.707107 | 10, 42, 96, 130, 106, 50, 12 |
octhex | octahedron - hexadecachoron duoprism, vertex figure of troch | 1 | 48, 240, 544, 680, 478, 172, 24 |
octico | octahedron - icositetrachoron duoprism | 1.224745 | 144, 864, 1920, 2088, 1158, 300, 32 |
octpen | octahedron - pentachoron duoprism, vertex figure of tro | 0.948683 | 30, 120, 220, 235, 156, 62, 13 |
octrap | octahedron - rectified-pentachoron duoprism | 1.048809 | 60, 300, 620, 670, 396, 122, 18 |
odinaq (alt.: hexgyo) | octa-diminished naq, hexadecachoral gyro-octahedronism | 0.866025 | 48, 552, 2496, 5280, 5478, 2508, 320 |
ohix | octagon - hexateron duoprism | 1.457317 | 48, 168, 286, 295, 188, 71, 14 |
... | oxo3ooo3ooo3xoo3ooo3oxx&#xt | 1 | 84, 903, 3395, 5740, 4739, 1806, 233 |
penpasc | pentachoron-prismatic scalene, pentachoron-prism-pyramid pyramid, line atop fully orthogonal pentachoron prism | 0.935414 | 12, 46, 90, 105, 77, 35, 9 |
puph | petaprismated hexadecaexon | 1.732051 | 1120, 8400, 21560, 25760, 15288, 4060, 254 |
quersa | quasirhombated hepteract | 0.845261 | 2688, 16128, 29792, 27440, 15064, 4564, 590 |
quil | pentacosiheptacontihexa-pentacontihexa-exon, vertex figure of yab | 0.866025 | 56, 756, 4032, 10080, 12096, 4788, 632 |
quiposaz | quasipetated hepteractihecatonicosoctaexon | 1.242133 | 896, 5376, 14560, 22400, 20328, 10192, 2186 |
quitasa | quasitruncated hepteract | 0.712292 | 896, 3136, 5152, 5040, 2968, 980, 142 |
quithdow | (bi-)quithic disphenoid, quith atop fully orthogonal quith | 0.646447 | 48, 648, 1756, 1970, 1056, 268, 28 |
ragabrag | rag atop brag, rag-first rotunda of barz | 1.224745 | 220, 2400, 5920, 6400, 3372, 788, 78 |
ragip | rectified-hexacontitetrapeton prism | 1.118034 | 120, 1020, 2720, 3520, 2352, 728, 78 |
ranq | rectified hecatonicosihexapentacosiheptacontihexaexon, equatorial cross-section of laq-first bay | 1.414214 | 756, 12096, 44352, 70560, 48384, 11592, 758 |
rapaltrarap | rectified-pentachoron atop alternate (triangle, rectified pentachoron)-duoprism | 0.968246 | 40, 240, 490, 490, 274, 86, 14 |
rapatrapen | rectified pentachoron atop triangle-pentachoron duoprism, rap-first cap of roc | 0.866025 | 25, 135, 275, 295, 189, 71, 14 |
rapete | rap tettene | 0.866025 | 13, 63, 151, 200, 151, 63, 13 |
rasa (old: ras) | rectified hepteract, equatorial cross-section of roc-first bro | 1.732051 | 448, 2688, 5152, 5040, 2968, 980, 142 |
ratkus | retroteriskewed hepteract | 1.658312 | 5376, 40320, 106400, 143360, 101752, 32032, 1752 |
rez (old: rhio) | rectified hecatonicosoctaexon, lattice B7 contact polytope (span of its small roots), lattice D7 contact polytope (span of its roots), equatorial cross-section of zee-first fy, equatorial cross-section of zee-first rek | 1 | 84, 840, 2520, 3920, 3360, 1344, 142 |
rila (old: rilalril) | rectified heptapeton alterprism, rectified heptapeton atop inverted rectified heptapeton, hop-first medial segment of naq | 0.866025 | 42, 420, 1610, 2800, 2226, 742, 86 |
rilalbril | rectified heptapeton atop inverted birectified heptapeton, equatorial monostratic segment of demihepteract | 0.935414 | 56, 525, 1575, 1925, 1127, 357, 51 |
rilastaf | ril atop staf, ril-first rotunda of rez | 1 | 63, 525, 1610, 2590, 2282, 966, 128 |
rillip | rectified-heptapeton prism, vertex figure of robay | 0.981981 | 42, 231, 455, 455, 266, 91, 16 |
rilpy | rectified-heptapetonal pyramid, vertex pyramid of demihepteract | 0.935414 | 22, 126, 280, 315, 203, 77, 15 |
rinquoh | rectified hecatonicosihexapentacosiheptacontihexaexic honeycomb | ||
ritgyco | rectified-tesseractic gyro-cuboctahedronism | 1.414214 | 384, 3840, 12864, 18528, 12396, 3624, 350 |
ritgyo | rectified-tesseract gyro-octahedronism, 384-diminished pentacontihexahecatonicosihexaexon | 1.322876 | 192, 1824, 5904, 7920, 4758, 1188, 80 |
rixahixip | rectified hexateron atop hexateron prism, rix-first cap of roc | 0.866025 | 27, 156, 315, 330, 209, 78, 15 |
rixasc | rectified-hexateronal scalene, rectified-hexateronal-pyramid pyramid, line atop fully orthogonal rectified-hexateron | 1 | 17, 91, 215, 265, 182, 70, 14 |
roc | rectified octaexon, vertex figure of hocto, Gosset polytope 05,1 | 0.866025 | 28, 168, 336, 350, 224, 84, 16 |
rojaka (alt.: pabdilin, old: rojakalrojak) | rojak alterprism, parabidiminished lin, rojak atop alternate rojak | 1.322876 | 432, 6480, 23040, 28080, 13500, 2538, 128 |
rojaka hejak | rojak atop hejak, rojak-first cap of rolaq | 1.732051 | 648, 7560, 22680, 25920, 13140, 3330, 344 |
rolaq | rectified pentacontihexapentacosiheptacontihexaexon | 1.732051 | 2016, 30240, 90720, 100800, 47880, 10332, 758 |
sabach | small bicellated hexadecaexon, bistericated octaexon | 1.414214 | 420, 3360, 9520, 12600, 7952, 2128, 198 |
sabro | small birhombated octaexon, bicantellated octaexon | 1.658312 | 420, 2520, 4480, 3850, 1960, 560, 72 |
sadlaq | hepteract-diminished pentacontihexapentacosiheptacontihexaexon | 1 | 112, 1568, 6720, 11200, 7924, 2184, 198 |
saro | small rhombated octaexon, cantellated octaexon | 1.414214 | 168, 1008, 1876, 1750, 980, 308, 44 |
sarz | small rhombated hecatonicosoctaexon, cantellated heptacross | 1.732051 | 840, 7560, 19320, 24080, 15456, 4200, 226 |
scala (old: scalal scal) | small cellated heptapeton alterprism, small cellated heptapeton atop inverted small cellated heptapeton, medial segment of barz | 1.224745 | 210, 210, 6160, 8190, 5180, 1406, 148 |
scala spil | scal atop spil | 1.322876 | 245, 1890, 4690, 5425, 3150, 875, 107 |
scalq | small cellated pentacontihexapentacosiheptacontihexaexon | 2.236068 | 7560, 90720, 322560, 493920, 328608, 80892, 6806 |
sco | small cellated octaexon, stericated octaexon | 1.322876 | 280, 2240, 5880, 7280, 4508, 1316, 170 |
sersa | small rhombated hepteract, cantellated hepteract | 2.790257 | 2688, 16128, 29792, 27440, 15064, 4564, 590 |
sethalq | small terademified pentacontihexapentacosiheptacontihexaexon | 2.828427 | 24192, 241920, 826560, 1249920, 896112, 272664, 17642 |
seto | small terated octaexon, pentellated octaexon | 1.198958 | 168, 1260, 3640, 5460, 4452, 1764, 226 |
sez (old: shio) | hepteractihecatonicosoctaexon, equatorial cross-section of barz-first tark | 1.414214 | 560, 6720, 15680, 14560, 6328, 1428, 142 |
shanq | small demified hecatonicosihexapentacosiheptacontihexaexon | 2 | 4032, 52416, 201600, 302400, 192528, 48888, 5546 |
shilq | small demified pentacontihexapentacosiheptacontihexaexon | 2.179449 | 4032, 42336, 131040, 151200, 78120, 22428, 2774 |
sibpo | small biprismated octaexon, biruncinated octaexon | 1.561250 | 560, 4200, 10080, 10640, 5460, 1400, 142 |
sirhesa | small rhombated hemihepteract, cantellated demihepteract | 2.207940 | 2240, 16800, 31360, 25200, 10360, 2100, 142 |
sirlaq | small rhombated pentacontihexapentacosiheptacontihexaexon | 3.316625 | 30240, 272160, 534240, 443520, 186984, 38556, 2774 |
sissiddow | sissidic disphenoid, sissid atop fully orthogonal sissid | 0.831254 | 24, 204, 744, 1190, 744, 204, 24 |
soccopen | (socco,pen)-duoprism | 1.535287 | 120, 480, 820, 805, 474, 158, 25 |
sososaz | small hepteractihepteractihecatonicosoctaexon | 1.719624 | 896, 5376, 8512, 7280, 3808, 1148, 156 |
soxaxogip | soxaxog prism | 1.719624 | 768, 4224, 6880, 5680, 2728, 740, 90 |
spaz | small prismated hecatonicosoctaexon, runcinated heptacross | 1.870829 | 2240, 23520, 62720, 71120, 38696, 9520, 506 |
spila (old: spilal spil) | small prismated heptapeton atop inverted small prismated heptapeton | 1.322876 | 280, 2940, 8260, 10150, 6160, 1736, 128 |
spo | small prismated octaexon, runcinated octaexon | 1.391941 | 280, 2100, 4760, 4830, 2548, 756, 100 |
squahix | square - hexateron duoprism, hixip prism, vertex figure of bro | 0.957427 | 24, 84, 146, 155, 104, 43, 10 |
squarat | square rectified-triacontiditeron duoprism | 1.224745 | 160, 1120, 2600, 2800, 1528, 412, 46 |
squix | square hixene, square atop fully orthogonal pentachoron | 0.707107 | 9, 34, 71, 90, 71, 34, 9 |
sranq | small rhombated hecatonicosihexapentacosiheptacontihexaexon | 2.645751 | 12096, 133056, 346752, 372960, 178416, 32760, 1514 |
srillip | small-rhombated-heptapeton prism | 1.451600 | 210, 1155, 2135, 1925, 980, 280, 37 |
stafip | small terated tetradecapeton prism | 1.118034 | 84, 462, 1190, 1750, 1498, 686, 128 |
stanq | small terated hecatonicosihexapentacosiheptacontihexaexon | 1.658312 | 1512, 19656, 90720, 191520, 191520, 80136, 7562 |
stiroh | small trirhombihexadecaexon, tricantellated octaexon | 1.732051 | 560, 3360, 5880, 4900, 2408, 672, 86 |
stohix | octagram - hexateron duoprism | 0.842354 | 48, 168, 286, 295, 188, 71, 14 |
suph | small petated hexadecaexon, hexicated octaexon, expanded octaexon, lattice A7 contact polytope (span of its roots), equatorial cross-section of oca-first soxeb, equatorial cross-section of roc-first rek | 1 | 56, 336, 980, 1680, 1736, 1008, 254 |
suposaz | small petated hepteractihecatonicosoctaexon, hexicated hepteract | 1.719624 | 896, 5376, 14560, 22400, 20328, 10192, 2186 |
suthesa | small terated demihepteract, hexic hepteract | 1.369306 | 448, 4704, 17920, 31360, 27272, 10640, 1066 |
taccasc | triacontiditeron scalene, half of hexacontitetrapeton pyramid, quarter of hecatonicosoctaexon | 0.707107 | 12, 61, 170, 280, 272, 145, 34 |
taccuppy | triancontaditeron-prism pyramid, vertex pyramid of rectified hecatonicosoctaexon | 1 | 21, 110, 290, 440, 384, 178, 35 |
tacpyp | triacontaditeric-pyramid prism, edge-first rotunda of geep | 0.866025 | 22, 111, 290, 440, 384, 178, 35 |
takus | teriskewed hepteract | 1.658312 | 5376, 40320, 106400, 143360, 101752, 32032, 1752 |
talq | truncated pentacontihexapentacosiheptacontihexaexon | 2.645751 | 4032, 32256, 90720, 100800, 47880, 10332, 758 |
tanq | truncated hecatonicosihexapentacosiheptacontihexaexon | 2.179449 | 1512, 12852, 44352, 70560, 48384, 11592, 758 |
tasa | truncated hepteract | 2.998773 | 896, 3136, 5152, 5040, 2968, 980, 142 |
tatsa | tritruncated hepteract | 2.915476 | 3360, 13440, 20160, 15120, 6328, 1428142 |
tattoc | tritruncated octaexon | 1.854050 | 280, 980, 1400, 1050, 448, 112, 16 |
taz | truncated hecatonicosoctaexon, truncated heptacross, equatorial cross-section of zee-first tek | 1.581139 | 168, 924, 2520, 3920, 3360, 1344, 142 |
tedroc | tetradiminished rectified octaexon, (hix,hix,tedrix)-trigonic | 0.866025 | 24, 120, 246, 264, 164, 60, 12 |
tetal tetdip | tet atop dual tetdip | 0.935414 | 20, 102, 240, 305, 224, 94, 19 |
tetdippa octdip | tetrahedral-duoprism atop octahedral-duoprism, vertex-first subsegment of the hexadecaexon | 1 | 52, 336, 740, 776, 428, 124, 18 |
tetdippy | tetdip pyramid, vertex pyramid of he | 1 | 17, 64, 116, 124, 84, 36, 9 |
tetgittith | (tet,gittith)-duoprism | 1.080691 | 256, 1152, 2016, 1776, 932, 270, 36 |
tethex | tetrahedron - hexadecachoron duoprism, vertex figure of tark | 0.935414 | 32, 144, 304, 360, 252, 102, 20 |
tetocta | tetrahedron-octahedron-duoprismatic alterprism, tet-first medial segment of broc | 0.968246 | 48, 312, 688, 728, 412, 124, 18 |
tetpen | tetrahedron-pentachoron duoprism, vertex figure of trene | 0.880341 | 20, 70, 120, 125, 84, 36, 9 |
tetrap | tetrahedron - rectified-pentachoron duoprism, vertex figure of torfy | 0.987421 | 40, 180, 340, 350, 214, 76, 14 |
tetrit | tetrahedron - rectified-tesseract duoprism | 1.369306 | 128, 576, 1056, 1040, 596, 190, 28 |
tetsrip | tetrahedron - small-rhombated-pentachoron duoprism | 0.987421 | 120, 540, 980, 950, 534, 166, 24 |
tetsteth | (tet,steth)-duoprism | 1.606894 | 256, 1152, 1952, 1776, 932, 270, 36 |
tettepe | tetrahedron-tetrahedron duoprismatic prism, vertex figure of 03,3,1 | 1 | 32, 112, 184, 180, 112, 44, 10 |
tettes | tetrahedron-tesseract duoprism | 1.172604 | 64, 224, 352, 320, 180, 62, 12 |
thesa | truncated demihepteract, cantic hepteract | 2.423840 | 1344, 7392, 13440, 11760, 5656, 1428, 142 |
thid | triaconta-hexa-diminished pentacontihexapentacosiheptacontihexaexon | 1 | 90, 990, 3570, 5520, 3972, 1224, 104 |
titridafup | triangle-tridafup duoprism | 1.040833 | 54, 270, 540, 558, 324, 105, 17 |
toc | truncated octaexon | 1.391941 | 56, 196, 336, 350, 224, 84, 16 |
toegippid | truncated-octahedron - great-prismated-decachoron duoprism | 2.738613 | 2880, 10080, 13920, 9600, 3444, 606, 44 |
tolin | truncated pentacontihexahecatonicosihexaexon | 3.708099 | 20160, 131040, 241920, 191520, 72072, 12348, 758 |
totaz | tritruncated hecatonicosoctaexon, Voronoi cell of lattice D7* | 2.549510 | 2240, 10080, 17920, 15120, 6328, 1428, 142 |
traginnont | (triangle,ginnont)-duoprism | 1.173127 | 480, 2400, 4000, 3400, 1636, 439, 55 |
trahex aico | trahex atop ico | 1 | 48, 336, 776, 888, 564, 190, 28 |
trahex dafup | triangular-hexadecachoral duoantifastegiaprism, trahex atop dual-gyrated trahex | 0.935414 | 48, 384, 1120, 1472, 934, 276, 32 |
trahexpy | trahex pyramid, vertex pyramid of barz | 1.224745 | 25, 120, 272, 344, 251, 102, 20 |
trahin | triangle - hemipenteract duoprism, vertex figure of borfy | 0.978945 | 48, 288, 736, 920, 598, 201, 29 |
trahix | triangle - hexateron duoprism, vertex figure of brene | 0.866025 | 18, 63, 111, 120, 83, 36, 9 |
trapendafup | triangular-pentachoron duoantifastegiaprism, trapen atop bidual trapen | 0.866025 | 30, 210, 610, 910, 716, 272, 38 |
trapent | triangle-penteract duoprism | 1.258306 | 96, 336, 512, 440, 230, 73, 13 |
trarapdafup | (triangle, rectified-pentachoron)-duoantifastegiaprism, pentachoron-first parabidiminished hexadecaexon | 1 | 60, 420, 920, 930, 486, 132, 18 |
trarix | triangle-rix duoprism | 1 | 45, 225, 435, 435, 251, 84, 15 |
trarixdit | (triangle,rix)-duotegum, tegum product of triangle and rectified hexateron | 18, 108, 305, 465, 387, 171, 36 | |
trasarx | triangle-rsarxix duoprism | 1.414214 | 180, 900, 1650, 1515, 776, 219, 30 |
trasinnont | (triangle,sinnont)-duoprism | 1.670461 | 480, 2400, 4000, 3400, 1636, 439, 55 |
tratac | triangle - triacontiditeron duoprism, vertex figure of bark | 1.154701 | 30, 150, 370, 520, 416, 179, 35 |
tratratet | triangle-triangle-tetrahedron-triprism, vertex figure of Gosset polytope 03,2,2 | 1.020621 | 36, 126, 204, 195, 118, 45, 10 |
tratratrip | triangle - triangle - triangle - triprismatic prism | 1.118034 | 54, 189, 297, 270, 153, 54, 11 |
trial trahex | triangle atop inverted trahex | 1 | 27, 147, 369, 512, 395, 153, 23 |
trial trapen | triangle atop inverted triangle-pentachoron duoprism, triangle-first cap of roc | 0.866025 | 18, 78, 156, 180, 128, 54, 12 |
tridafupap | trigonal-duoantifastegiaprismatic alterprism, trigonal-duoantifastegiaprism atop lacing-ortho trigonal-duoantifastegiaprism | 0.935414 | 36, 216, 492, 552, 328, 102, 16 |
trippen | triangle - pentachoron duoprism-prism, vertex figure of buffy | 0.991632 | 30, 105, 175, 175, 111, 44, 10 |
trippepe | trip pennene | 0.866025 | 10, 39, 81, 100, 76, 35, 9 |
zee (old: hio) | hecatonicosoctaexon, heptacross (β7), aerozett(id), heptapetal antiprism, vertex figure of ek, Gosset polytope 41,1, lattice C7 contact polytope (span of its small roots), equatorial cross-section of vertex-first ek | 0.707107 | 14, 84, 280, 560, 672, 448, 128 |
Count of actually available polytopes: 228
---- 8D ----
Acronym | Name | Circumradius | Face vector |
..., 14,3 | hyperbolic Gosset octacomb 14,3 | 1.5 i | |
..., 24,2 | hyperbolic Gosset octacomb 24,2 | 0.288675 i | |
..., 34,1 | hyperbolic Gosset octacomb 34,1 | 0.5 i | |
..., 42,2 | hyperbolic dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zettic octacomb, hyperbolic Gosset octacomb 42,2 | 0.5 | |
..., 43,1 | hyperbolic Gosset octacomb 43,1 | 0 i | |
bark | birectified diacosipentacontahexazetton, equatorial cross-section of rek-first brav | 1.224745 | 448, 6720, 22400, 36960, 34048, 16128, 3184, 272 |
batene | bitruncated enneazetton | 1.795055 | 252, 1008, 1848, 2016, 1386, 588, 144, 18 |
bato | bitruncated octeract | 3.535534 | 7168, 28672, 51968, 55552, 36960, 14784, 3184, 272 |
bay | diacositetraconta-myriaheptachiliadiacosioctaconta-zetton, argyrozetton, Gosset polyzetton 24,1 | 1.414214 | 2160, 69120, 483840, 1209600, 1209600, 544320, 144960, 17520 |
bayoh | diacositetracont-myriaheptachiliadiacosioctaconta-zettic octacomb, Gosset octacomb 25,1 | ||
be | octadecazetton, enneaenneazetton, bi-enneazetton, quadritruncated enneazetton, equatorial cross-section of (vertex first) q-enne | 2 | 630, 2520, 4200, 3780, 2016, 672, 144, 18 |
bif | diacositetracont-dischiliahectohexaconta-zetton, chrysozetton, Gosset polyzetton 14,2 | 2 | 17280, 483840, 2419200, 3628800, 2298240, 725760, 106080, 2400 |
bifoh | diacositetracont-dischiliahectohexaconta-zettic octacomb, Gosset octacomb 15,2 | ||
borfy | birectified dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton, t2(41,2) | 2.449490 | 60480, 1451520, 5806080, 9918720, 7741440, 2600640, 382560, 19680 |
brene | birectified enneazetton, Gosset polytope 05,2 | 1 | 84, 756, 1764, 2016, 1386, 588, 144, 18 |
bro | birectified octeract, birectified hexadecazetton, Gosset polytopes 05,1,1 | 1.732051 | 1792, 21504, 50176, 55552, 36960, 14784, 3184, 272 |
broca (old: brocalbroc) | broc alterprism, broc atop inverted broc, central segment of hocto | 1 | 112, 1400, 5040, 7420, 5684, 2632, 704, 88 |
buffy | diacositetracont-dischiliahectohexacont-myriaheptachiliadiacosioctaconta-zetton, rectified bif: t1(12,4), birectified bay: t2(21,4), tetrarectified fy: t4(41,2), Gosset polytope 04,2,1 | 3.872983 | 483840, 7257600, 16934400, 16934400, 9072000, 2661120, 382560, 19680 |
codify (alt.: hexgyi, trihexdip) | tetracontaocta-diminished dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton, hexadacachoron gyro-icositetrachoronism, tegum sum of 3 pairwise bigyrated hexadecachoron duoprisms, tri-hexadecachoron-duoprism | 1 | 192, 4224, 29184, 86784, 124464, 84672, 23808, 1968 |
... | point || pseudo hesa || zee, Dutour polyzetton type A | 79, 1268, 7896, 23520, 36456, 29876, 11364, 1131 | |
ek | diacosipentacontahexazetton, octacross (β8), aeroyott(id), octaexal antiprism, vertex figure of vee, (one of the) Delone cell(s) of lattice E8, Gosset polytope 51,1, lattice C8 contact polytope (span of its small roots), equatorial cross-section of vertex-first vee | 0.707107 | 16, 112, 448, 1120, 1792, 1792, 1024, 256 |
ene | enneazetton, 8D simplex (α8), pyroyott(id), octaexal pyramid, vertex figure of day, (one of the) Delone cell(s) of lattice E8, Gosset polytope 07 | 0.666667 | 9, 36, 84, 126, 126, 84, 36, 9 |
fib | dischiliahectohexaconta-diacositetraconta-zetton | 1 | 240, 6720, 60480, 241920, 483840, 483840, 222480, 2400 |
fro | facetorectified octeract | 1.870829 | 1024, 7168, 21504, 35840, 35840, 21504, 7168, 1024 |
fy | dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton, siderozetton, Gosset polyzetton 41,2, Witting polytope, vertex figure of goh, lattice E8 contact polytope (span of its roots) | 1 | 240, 6720, 60480, 241920, 483840, 483840, 207360, 19440 |
geeasc | hexacontitetrapeton scalene, half of hecatonicosoctaexon pyramid, quarter of diacosipentacontahexazetton | 0.707107 | 14, 85, 292, 620, 832, 688, 321, 66 |
goh | Gosset octacomb 52,1, Delone complex of lattice E8 | ||
gook | great octeractiocteractidiacosipentacontahexazetton | 1.338990 | 2048, 14336, 26880, 28672, 19936, 8960, 2384, 288 |
goxeb | great exi-octadecazetton, permutozetton of 9 elements | 5.477226 | 362880, 1451520, 2328480, 1905120, 834120, 186480, 18150, 510 |
gupofy | great petated dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton | 17.606817 | 696729600, 2786918400, 4470681600, 3657830400, 1601268480, 357557760, 34508640, 881760 |
hauhocto | hexadeca-augmented hemiocteract | ... | 144, 2816, 17920, 46592, 53088, 30016, 9648, 1376 |
haxesc | (degenerate) demihexaractic scalene, line atop fully orthogonal demihexaract | ∞ i.e. flat in euclidean space | 34, 305, 1152, 2160, 2172, 1188, 341, 46 |
hesapy | hemihepteractic pyramid, vertex pyramid of bay | 1.414214 | 65, 736, 2912, 5040, 4424, 2156, 610, 79 |
hexal hesa | hex atop alternated hesa, hex-first cap of codify | 1 | 72, 952, 4576, 10112, 11481, 6748, 1834, 151 |
hexdip | hexadecachoron duoprism | 1 | 64, 384, 1088, 1792, 1808, 1072, 320, 32 |
hextes | hexadecachoron-tesseract duoprism | 1.224745 | 128, 640, 1472, 1920, 1496, 696, 184, 24 |
hocto (alt.: gecdify) | hemiocteract, 64(=g)+48(=c)-diminished fy, Gosset polytope 15,1 | 1 | 128, 1792, 7168, 10752, 8288, 4032, 1136, 144 |
icodip | icositetrachoron duoprism | 1.414214 | 576, 4608, 13824, 19584, 13872, 4800, 768, 48 |
idirek | icositetra-diminished rectified diacosipentacontahexazetton | 1 | 88, 864, 3296, 6992, 8840, 6424, 2336, 280 |
jakaf (old: jakaljakip) | icosiheptaheptacontidipeton alterfastegium, icosiheptaheptacontidipeton atop inverted icosiheptaheptacontidipeton-prism | 1 | 81, 1215, 6966, 19080, 26784, 18801, 5826, 561 |
jakap | jaka prism, jakip alterprism | 1 | 108, 1458, 7902, 20880, 28512, 19548, 5926, 562 |
jakapy (alt.: pabdinaqpy) | icosiheptaheptacontidipetic-alterprism pyramid, parabidimished-hecatonicosihexapentacosiheptacontihexaexon pyramid, (jak, alt. jak, point)-trigonic | 1 | 55, 756, 4302, 12240, 18576, 14742, 5366, 561 |
jakoha | icosiheptaheptacontidipetic hexacomb alterprism | ∞ i.e. flat in euclidean space | 2N, 99N, 912N, 3060N, 4464N, 2814N, 670N, 75N+2 |
kadify (or: brena) | heptacontadia-diminished dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton, tegum sum of two mutually inverted birectified enneazetta, bidiambooctadecazetton | 1 | 168, 3192, 18648, 46872, 57960, 38052, 13320, 1980 |
laqalin | pentacontihexapentacosiheptacontihexaexon atop pentacontihexahecatonicosihexaexon, 21,3 atop 12,3 , laq-first cap of bay, 21,3 -first cap of 21,4 | 1.414214 | 702, 16128, 92736, 201600, 191016, 87192, 23242, 2776 |
laqpe | pentacontihexapentacosiheptacontihexaexon prism | 1.118034 | 252, 4158, 22176, 50400, 52416, 25704, 6052, 634 |
linaranq | pentacontihexahecatonicosihexaexon atop rectified pentacontihexapentacosiheptacontihexaexon, laq-first subsegment of bay | 1.414214 | 1332, 34272, 205632, 463680, 445032, 194796, 45544, 4792 |
n,m,p,q-quip | n-gon - m-gon - p-gon - q-gon - tetraprism (or: -quadprism) | sqrt[1/(4 sin2(π/n))+1/(4 sin2(π/m))+1/(4 sin2(π/p))+1/(4 sin2(π/q))] | nmpq, 4nmpq, 6nmpq+nmp+nmq+npq+mpq, 4nmpq+3nmp+3nmq+3npq+3mpq, nmpq+3nmp+3nmq+3npq+3mpq+nm+np+nq+mp+mq+pq, nmp+nmq+npq+mpq+2nm+2np+2nq+2mp+2mq+2pq, nm+np+nq+mp+mq+pq+n+m+p+q, n+m+p+q |
n,n,n,n-quip | n-gon - n-gon - n-gon - n-gon - tetraprism (or: -quadprism) | sqrt[1/sin2(π/n)] | n4, 4n4, 6n4+4n3, 4n4+12n3, n4+12n3+6n2, 4n3+12n2, 6n2+4n, 4n |
naqalaq | naq atop laq, second stratos of vertex-first fy, E7 1/2 polytope | 1 | 182, 4284, 33768, 120960, 219744, 202356, 81470, 7564 |
naqpe | naq prism, prism of Gosset polyexon 32,1 , vertex figure of rigoh | 1 | 112, 1568, 8820, 24192, 34272, 24192, 7452, 704 |
naqpy | hecatonicosihexapentacosiheptacontihexaexon pyramid, vertex-first cap of fy | 1 | 57, 812, 4788, 14112, 22176, 18144, 6750, 703 |
ocalroc | oca atop inverted roc, oca-first cap of fy | 1 | 36, 364, 1652, 4060, 5740, 4564, 1788, 228 |
ocpe | octaexon prism, vertex figure of reday | 0.829156 | 16, 64, 140, 196, 182, 112, 44, 10 |
octa tethex | oct atop tethex | 1 | 38, 252, 744, 1241, 1220, 682, 198, 25 |
octo | octeract, hexadecazetton, 8D measure-polytope (γ8), geoyott(id) | 1.414214 | 256, 1024, 1792, 1792, 1120, 448, 112, 16 |
pendip | pentachoron duoprism, vertex figure of icoy | 0.894427 | 25, 100, 200, 250, 210, 120, 45, 10 |
penrap | (pentachoron, rectified pentachoron)-duoprism, vertex figure of tergoh | 1 | 50, 250, 550, 700, 565, 290, 90, 15 |
penrapdit | (pen,rap)-duotegum, tegum product of pentachoron and rectified pentachoron | 15, 90, 290, 565, 700, 550, 250, 50 | |
puko | petiskewed octeract | 1.732051 | 14336, 129024, 422912, 752640, 784896, 459648, 123712, 5552 |
qro | quasirhombated octeract | 0.870264 | 7168, 50176, 109312, 127232, 94304, 43456, 11376, 1296 |
quaxoke | quasi-exiocteracti-diacosipentacontahexazetton | 1.338990 | 2048, 14336, 46592, 89600, 108416, 81536, 34976, 6560 |
queto | quasitruncated octeract | 0.741790 | 2048, 8192, 16128, 19712, 15456, 7616, 2160, 272 |
rapdip | rectified-pentachoron duoprism | 1.095445 | 100, 600, 1500, 2000, 1520, 660, 160, 20 |
rapepe | rap peppene | 1 | 14, 76, 214, 351, 351, 214, 76, 14 |
recto | rectified octeract, rectified hexadecazetton, equatorial cross-section of rene-first barn | 1.870829 | 1024, 7168, 16128, 19712, 15456, 7616, 2160, 272 |
rek | rectified diacosipentacontahexazetton, lattice B8 contact polytope (span of its small roots), lattice D8 contact polytope (span of its roots), equatorial cross-section of ek-first riv | 1 | 112, 1344, 4928, 10080, 12544, 8960, 3072, 272 |
rene | rectified enneazetton, vertex figure of henne, Gosset polytope 06,1 | 0.881917 | 36, 252, 588, 756, 630, 336, 108, 18 |
repuko | retropetiskewed octeract | 1.732051 | 14336, 129024, 422912, 752640, 784896, 459648, 123712, 5552 |
ribfoh | rectified diacositetracont-dischiliahectohexaconta-zettic octacomb, Gosset heptacomb 05,2,1 | ||
riffy | rectified dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton, t1(41,2) | 1.732051 | 6720, 181440, 1028160, 2661120, 3386880, 1935360, 375840, 19680 |
rigoh | rectified Gosset octacomb 52,1 | ||
ritdip | rectified-tesseractic duoprism | 1.732051 | 1024, 6144, 14848, 18432, 12416, 4416, 752, 48 |
robay | rectified diacositetracont-myriaheptachiliadiacosioctaconta-zetton, t1(21,4) | 2.645751 | 69120, 1451520, 5322240, 7257600, 4717440, 1693440, 313440, 19680 |
robyah | rectified diacositetracont-myriaheptachiliadiacosioctaconta-zettic octacomb, heptacomb t1(25,1) | ||
roca | (degenerate) rectified octaexon alterprism | ∞ i.e. flat in euclidean space | 56, 1176, 4032, 10220, 13048, 8120, 2160, 200 |
rocalbroc | roc atop inverted broc, oca-first subsegment of fy | 1 | 84, 1148, 5376, 11200, 11256, 5656, 1432, 144 |
rocasuph | roc atop suph | 1 | 84, 840, 3164, 6650, 8400, 6132, 2230, 256 |
rocip | rectified-octaexon prism, vertex figure of robyah | 1 | 56, 364, 840, 1036, 798, 392, 116, 18 |
rocpy | rectified-octaexonal pyramid, vertex pyramid of demiocteract | 1 | 29, 196, 504, 686, 574, 308, 100, 17 |
satpeb | small triprismated bi-enneazetton, triruncinated enneazetton | 1.732051 | 1680, 15120, 42840, 55440, 38052, 14784, 3042, 270 |
saxoke | small exiocteracti-diacosipentacontahexazetton, heptellated octeract | 1.790840 | 2048, 14336, 46592, 89600, 108416, 81536, 34976, 6560 |
sobteb | small biterated bi-enneazetton, bipentellated enneazetton | 1.414214 | 756, 7560, 27720, 50400, 49056, 24696, 5562, 438 |
soro | small rhombated octeract, cantellated octeract | 3.040171 | 7168, 50176, 109312, 127232, 94304, 43456, 11376, 1296 |
sotho | small terated hemiocteract, hexic octeract | 1.732051 | 3584, 48384, 222208, 474880, 513856, 269248, 56496, 3632 |
soxeb | small exiated bi-enneazetton, heptellated enneazetton, expanded enneazetton, lattice A8 contact polytope (span of its roots), equatorial cross-section of rene-first riv | 1 | 72, 504, 1764, 3780, 5208, 4536, 2286, 510 |
spene | small prismated enneazetton, runcinated enneazetton | 1.452966 | 504, 4536, 11844, 14616, 10374, 4620, 1188, 138 |
spiffy | small petated dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton | 2.236068 | 30240, 665280, 4475520, 13305600, 19837440, 15180480, 5206080, 397920 |
spuho | small petated hemiocteract | 1.414214 | 1024, 14336, 69888, 161280, 203392, 140672, 45728, 3744 |
squahop | square - heptapenton duoprism, vertex figure of barn | 0.963624 | 28, 112, 231, 301, 259, 147, 53, 11 |
srek | small rhombated diacosipentacontahexazetton, cantellated octacross | 1.732051 | 1344, 14784, 47488, 81760, 82432, 44800, 10464, 384 |
srene | small rhombated enneazetton, cantellated enneazetton | 1.452966 | 252, 1764, 3864, 4536, 3402, 1596, 432, 54 |
tabif | truncated diacositetracont-dischiliahectohexaconta-zetton | 5.830952 | 967680, 7741440, 16934400, 16934400, 9072000, 2661120, 382560, 19680 |
tark | trirectified diacosipentacontahexazetton | 1.414214 | 1120, 17920, 53760, 71680, 48384, 16576, 3184, 272 |
tek | truncated diacosipentacontahexazetton, truncated octacross, equatorial cross-section of ek-first tiv | 1.581139 | 224, 1456, 4928, 10080, 12544, 8960, 3072, 272 |
tene | truncated enneazetton | 1.414214 | 72, 288, 588, 756, 630, 336, 108, 18 |
tethex aico | tethex atop ico | 1 | 56, 432, 1168, 1680, 1453, 754, 218, 29 |
tethin | tetrahedron - hemipenteract duoprism, vertex figure of trigoh | 1 | 64, 416, 1184, 1776, 1544, 800, 230, 30 |
tethix | tetrahedron-hexateron duoprism, vertex figure of treday | 0.889757 | 24, 96, 194, 246, 209, 120, 45, 10 |
tetrappal octrap | (tetrahedron, rectified pentachoron)-duoprism atop alternate (octahedron, rectified pentachoron)-duoprism | 1.054093 | 100, 840, 2220, 2820, 1960, 770, 170, 20 |
tettac | tetrahedron-triacontiditeron duoprism, vertex figure of tarv | 0.935414 | 40, 220, 600, 970, 968, 596, 214, 36 |
thocto | truncated hemiocteract, cantic octeract | 2.645751 | 3584, 23296, 50176, 55552, 36960, 14784, 3184, 272 |
thrathibbit | trihexagonal-rhombitrihexagonal duoprismatic tetracomb | ||
tiffy | truncated dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton | 2.645751 | 13440, 188160, 1028160, 2661120, 3386880, 1935360, 375840, 19680 |
tijakdap | triangle-jak duoalterprism | 1 | 162, 3078, 20250, 59022, 83808, 56322, 15738, 1536 |
toby (old: tobay) | truncated diacositetracont-myriaheptachiliadiacosioctaconta-zetton | 4 | 138240, 1520640, 5322240, 7257600, 4717440, 1693440, 313440, 19680 |
tocto | truncated octeract | 3.232607 | 2048, 8192, 16128, 19712, 15456, 7616, 2160, 272 |
torfy | trirectified dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton, t3(41,2) | 3.162278 | 241920, 4838400, 14515200, 16934400, 9313920, 2661120, 382560, 19680 |
trajak | triangle - icosiheptaheptacontidipeton duoprism, vertex figure of bargoh | 1 | 81, 729, 2835, 5616, 5904, 3321, 948, 102 |
trajakdit | (triangle,jak)-duotegum, tegum product of triangle and icosiheptaheptacontidipeton | 30, 300, 1449, 3888, 6048, 5283, 2241, 297 | |
trene | trirectified enneazetton, Gosset polytope 04,3 | 1.054093 | 126, 1260, 2940, 3150, 1890, 672, 144, 18 |
trigee | triangle - hexacontitetrapeton duoprism, vertex figure of brav | 0.912871 | 36, 216, 672, 1260, 1456, 1008, 387, 67 |
trihop | triangle - heptapenton duoprism, vertex figure of breday | 0.872872 | 21, 84, 175, 231, 203, 119, 45, 10 |
triphix | triangle - hexateron duoprismatic prism, vertex figure of ribfoh | 1 | 36, 144, 285, 351, 286, 155, 54, 11 |
triquip | triangle-triangle-triangle-triangle-tetraprism (or: -quadprism) | 1.154701 | 81, 324, 594, 648, 459, 216, 66, 12 |
tro | trirectified octeract, trirectified hexadecazetton | 1.581139 | 1792, 26880, 71680, 80640, 47712, 16576, 3184, 272 |
xorene | exirhombated enneazetton | 1.732051 | 1512, 12852, 40824, 68670, 66192, 35028, 8532, 510 |
yab | myriaheptachiliadiacosioctaconta-diacositetraconta-zetton | 1 | 240, 6720, 60480, 241920, 483840, 483840, 153360, 17520 |
zahesa | zee || hesa | 1 | 78, 1204, 7224, 21280, 33656, 28252, 10846, 1068 |
zarez | zee atop rez, rectified diacosipentacontahexazetton half | 1 | 98, 1092, 3724, 7000, 7952, 5152, 1614, 144 |
zeep | hecatonicosoctaexon prism, vertex figure of riv | 0.866025 | 28, 182, 644, 1400, 1904, 1568, 704, 130 |
zeepy | zee pyramid, heptacross pyramid, vertex pyramid of ek | 0.707107 | 15, 98, 364, 840, 1232, 1120, 576, 129 |
Count of actually available polytopes: 122
---- 9D ----
Acronym | Name | Circumradius | Face vector |
..., 15,3 | hyperbolic Gosset enneacomb 15,3 | 1.118034 i | |
..., 16,2 | hyperbolic Gosset enneacomb 16,2 | 2.236068 i | |
..., 26,1 | hyperbolic Gosset enneacomb 26,1 | 1.414214 i | |
..., 35,1 | hyperbolic Gosset enneacomb 35,1 | 0 i | |
..., 53,1 | hyperbolic Gosset enneacomb 53,1 | 0.5 | |
..., 62,1 | hyperbolic Gosset enneacomb 62,1 | 0 i | |
barn | birectified enneract, birectified octadecayotton, Gosset polytope 06,1,1 | 1.870829 | 4608, 64512, 172032, 231168, 197568, 109536, 37536, 7056, 530 |
brav | birectified pentacosidodecayotton, equatorial cross-section of riv-first brake | 1.224745 | 672, 12096, 48384, 102816, 133056, 102144, 41472, 7056, 530 |
breday | birectified decayotton, Gosset polytope 06,2, vertex figure of hyperbolic 16,2 | 1.024695 | 120, 1260, 3360, 4620, 4032, 2310, 840, 180, 20 |
brena | (degenerate) birectified enneazetton alterprism | ∞ i.e. flat in euclidean space | 168, 3192, 18648, 46872, 58212, 39228, 15072, 3078, 272 |
day | decayotton, 9D simplex (α9), pyroxenn(id), enneazettal pyramid, vertex figure of ux, Gosset polytope 08 | 0.670820 | 10, 45, 120, 210, 252, 210, 120, 45, 10 |
ekip | diacosipentacontahexazetton prism, vertex figure of rake | 0.866025 | 32, 240, 1008, 2688, 4704, 5376, 3840, 1536, 258 |
enep | enneazetton prism, vertex figure of ru | 0.833333 | 18, 81, 204, 336, 378, 294, 156, 54, 11 |
enne | enneract, octadecayotton, 9D measure-polytope (γ9), geoxenn(id) | 1.5 | 512, 2304, 4608, 5376, 4032, 2016, 672, 144, 18 |
henne | demi-enneract, Gosset polytope 16,1 | 1.060660 | 256, 4608, 21504, 37632, 36288, 23520, 9888, 2448, 274 |
icoy | icosayotton, quadrirectified decayotton, equatorial cross-section of (vertex first) 1/q-deker, Gosset polytope 04,4 | 1.118034 | 252, 3150, 8400, 10500, 7560, 3360, 960, 180, 20 |
penhix | pentachoron - hexateron duoprism, vertex figure of teru | 0.903696 | 30, 135, 310, 455, 461, 330, 165, 55, 11 |
quiten | quasitruncated enneract | 0.770160 | 4608, 20736, 47616, 69888, 68544, 45024, 19104, 4752, 530 |
rapdafup | rectified-pentachoron duoantifastegium | 1.118034 | 200, 2100, 6600, 10000, 8440, 4180, 1240, 220, 22 |
reday | rectified decayotton, vertex figure of hede, Gosset polytope 07,1 | 0.894427 | 45, 360, 960, 1470, 1512, 1050, 480, 135, 20 |
ren | rectified enneract, rectified octadecayotton, equatorial cross-section of reday-first brade | 2 | 2304, 18432, 47616, 69888, 68544, 45024, 19104, 4752, 530 |
renepy | rectified-enneazettonal pyramid, vertex pyramid of demienneract | 1.060660 | 37, 288, 840, 1344, 1386, 966, 444, 126, 19 |
riv | rectified pentacosidodecayotton, lattice B9 contact polytope (span of its small roots), lattice D9 contact polytope (span of its roots), equatorial cross-section of vee-first rake | 1 | 144, 2016, 8736, 22176, 36288, 37632, 23040, 6912, 530 |
squoc | square - octaexon duoprism, vertex figure of brade | 0.968246 | 32, 144, 344, 532, 560, 406, 200, 64, 12 |
tarv | trirectified pentacosidodecayotton | 1.414214 | 2016, 40320, 147840, 262080, 262080, 145152, 42144, 7056, 530 |
teday | truncated decayotton | 1.431782 | 90, 405, 960, 1470, 1512, 1050, 480, 135, 20 |
ten | truncated enneract | 3.450631 | 4608, 20736, 47616, 69888, 68544, 45024, 19104, 4752, 530 |
tethop | tetrahedron-heptapeton duoprism, vertex figure of tru | 0.896421 | 28, 126, 294, 441, 455, 329, 165, 55, 11 |
thenne | truncated hemienneract, cantic enneract | 2.850439 | 9216, 69120, 172032, 231168, 197568, 109536, 37536, 7056, 530 |
tiv | truncated pentacosidodecayotton, truncated enneacross, equatorial cross-section of vee-first take | 1.581139 | 288, 2160, 8736, 22176, 36288, 37632, 23040, 6912, 530 |
treday | trirectified decayotton, Gosset polytope 05,3 | 1.095445 | 210, 2520, 6720, 8610, 6552, 3150, 960, 180, 20 |
trioc | triangle - octaexon duoprism, vertex figure of bru | 0.877971 | 24, 108, 260, 406, 434, 322, 164, 55, 11 |
trizee | triangle - hecatonicosoctaexon duoprism, vertex figure of brake | 0.912871 | 42, 294, 1106, 2604, 3976, 3920, 2400, 835, 131 |
vee | pentacosidodecayotton, enneacross (β9), aeroxenn(id), enneazettal antiprism, vertex figure of ka, Gosset polytope 61,1, lattice C9 contact polytope (span of its small roots), equatorial cross-section of vertex-first ka | 0.707107 | 18, 144, 672, 2016, 4032, 5376, 4608, 2304, 512 |
Count of actually available polytopes: 34
----- 10D -----
Acronym | Name | Circumradius | Face vector |
brade | birectified dekeract, birectified icosaxennon, Gosset polytope 07,1,1 | 2 | 11520, 184320, 552960, 875520, 916608, 653184, 310560, 93120, 15540, 1044 |
brake | birectified chilliaicositetraxennon | 1.224745 | 960, 20160, 94080, 245280, 411264, 443520, 291840, 103680, 15540, 1044 |
bru | birectified hendecaxennon, Gosset polytope 07,2 | 1.044466 | 165, 1980, 5940, 9570, 10164, 7392, 3630, 1155, 220, 22 |
deker | dekeract, icosaxennon, 10D measure-polytope (γ10), geodak(id) | 1.581139 | 1024, 5120, 11520, 15360, 13440, 8064, 3360, 960, 180, 20 |
hede | demi-dekeract, Gosset polytope 17,1 | 1.118034 | 512, 11520, 61440, 122880, 142464, 115584, 64800, 2400, 5300, 532 |
ka | chilliaicositetraxennon, decacross (β10), aerodak(id), decayottal antiprism, Gosset polytope 71,1, lattice C10 contact polytope (span of its small roots) | 0.707107 | 20, 180, 960, 3360, 8064, 13440, 15360, 11520, 5120, 1024 |
rade | rectified dekeract, rectified icosaxennon | 2.121320 | 5120, 46080, 134400, 230400, 271488, 223104, 126240, 47040, 10420, 1044 |
rake | rectified chilliaicositetraxennon, lattice B10 contact polytope (span of its small roots), lattice D10 contact polytope (span of its roots) | 1 | 180, 2880, 14400, 43680, 88704, 120960, 107520, 57600, 15360, 1044 |
ru | rectified hendecaxennon, rectified undecaxennon, Gosset polytope 08,1 | 0.904534 | 55, 495, 1485, 2640, 3234, 2772, 1650, 660, 165, 22 |
take | truncated chilliaicositetraxennon, truncated decacross | 1.581139 | 360, 3060, 14400, 43680, 88704, 120960, 107520, 57600, 15360, 1044 |
teru | tetrarectified hendecaxennon, quadrirectified hendecaxennon, Gosset polytope 05,4 | 1.167748 | 462, 6930, 20790, 30030, 25872, 14322, 5280, 1320, 220, 22 |
tru | trirectified hendecaxennon, Gosset polytope 06,3 | 1.128152 | 330, 4620, 13860, 20790, 19404, 12012, 4950, 1320, 220, 22 |
tu | truncated hendecaxennon, truncated undecaxennon | 1.445998 | 110, 550, 1485, 2640, 3234, 2772, 1650, 660, 165, 22 |
ux | hendecaxennon, undecaxennon, 10D simplex (α10), pyrodak(id), decayottal pyramid, Gosset polytope 09 | 0.674200 | 11, 55, 165, 330, 462, 462, 330, 165, 55, 11 |
Count of actually available polytopes: 14
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