Site Map Polytopes Dynkin Diagrams Vertex Figures Incidence Matrices Index

Index of Polytopes, sorted by Dimension

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
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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
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
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: 171


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----
 3D
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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) 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
datha ditetratihemiapeiratic honeycomb
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
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
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
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
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
... 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
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
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 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 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 (?) ... 12, 36, 20
... hyperbolic o3β4β3o5*a tesselation
... o3β4x (?) ... 24, 60, 32
... o3β5o (?) ... 30, 120, 62
... o3β5x (?) ... 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 (?) ... 30, 120, 54
... o5/2β5x (?) ... 60, 150, 54
... 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) 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
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, 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 (?) ... 24, 60, 32
... β3o5β (?) ... 60, 180, 92
... hyperbolic s3s4o4o tesselation ...
... hyperbolic s3s4o4x tesselation ...
... β3x4β (?) ... 48, 96, 44
... β3x5β (?) ... 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
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+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
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
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
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
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
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 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
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 (?) ... 24, 48, 20
... x3β5o (?) ... 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 (?) ...
... 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: 1039


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----
 4D
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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
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 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
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, 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
... 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
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
... 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
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
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
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
girfaddic great retrofrustic distetracontoctachoron 1.414214 288, 1152, 816, 96
girfix great rhombated faceted hexacosachoron 7.404918 7200, 14400, 7680, 960
girfixthi great retrofrustic hexacositrishecatonicosachoron 2.236068 3600, 14400, 10080, 960
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
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) 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 duoprismatic tetracomb, hexagonal biprismated tetracomb, 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
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
... 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) 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
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
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
oh octahemihexadecachoron 1 24, 96, 80, 16
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 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
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
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
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
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
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 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
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 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
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
... 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 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
... 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
... 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
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
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
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
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
sirfixthi small retrofrustic hexacositrishecatonicosachoron 2.236068 3600, 14400, 11280, 960
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
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) 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
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, 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 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
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
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 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
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
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 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)
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
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
... 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
... 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: 1797


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----
 5D
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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
..., 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 0.866025 20, 90, 120, 60, 12
... 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
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
gyepcuro, J47 gyroelongated pentagonal cupolarotunda 35, 80, 47
gyetac gyroelongated triacontaditeron ... 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
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 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(pi/n))+1/(1-cos(pi/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/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
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 1.224745 80, 480, 640, 280, 42
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
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
pid pentagon - icosidodecahedron duoprism 1.828016 150, 450, 490, 225, 37
pike pentagon-icosahedron duoprism 1.275976 60, 210, 262, 135, 25
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
..., 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
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) 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 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 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
... triangular,tetrahedral duoantiprism ... 24, 132, 248, 174, 36
... tetrahedral - hexagon-prismantiprismoid ... 48, 192, 308, 204, 42
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 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) 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 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
siddy small dodekicosahedron 1.721489 60, 120, 32
... 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) 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
topax pteroprismated hexateron 1.190238 60, 270, 330, 135, 21
tot truncated triacontiditeron, truncated pentacross 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: 731


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 6D
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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 pentacomb, 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
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* 1.224745 160, 1440, 2880, 2160, 636, 76
braxh birectified hexeractic honeycomb
bril (old: driss) birectified heptapeton, 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 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
dijak (alt.: taccahin) (mono-)diminished icosiheptaheptacontidipeton, tac atop hin 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
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
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) 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 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
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
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
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) 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 d/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
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
... tetradecapeton dual 0.774597 14, 84, 280, 490, 420, 140
... 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
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) 1 60, 480, 1120, 1200, 576, 76
ram rectified pentacontitetrapeton, Gosset polypeton 02,2,1, Voronoi cell of lattice E6* 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
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 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 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) 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 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
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
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
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 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
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: 426


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 7D
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Acronym Name Circumradius Face vector
..., 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 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
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
... 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
grohp great-rhombihexahedron prism 0.890446 48, 120, 84, 20
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
guposaz great petated hepteractihecatonicosoctaexon 1.242133 896, 5376, 14560, 22400, 20328, 10192, 2186
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
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
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) 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
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
papaid, pap || id, K-4.142 pentagonal-antiprism atop icosidodecahedron 3.077684 40, 130, 124, 34
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
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 1.414214 756, 12096, 44352, 70560, 48384, 11592, 758
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 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) 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
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 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) 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 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
tattoc tritruncated octaexon 1.854050 280, 980, 1400, 1050, 448, 112, 16
taz truncated hecatonicosoctaexon, truncated heptacross 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
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
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
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
trippen triangle - pentachoron duoprism-prism, vertex figure of buffy 0.991632 30, 105, 175, 175, 111, 44, 10
... Fxo xfo3oox5xxx&#zxt 300, 840, 828, 258
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) 0.707107 14, 84, 280, 560, 672, 448, 128

Count of actually available polytopes: 217


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----
 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 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) 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
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
kadify 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
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
recto rectified octeract, rectified hexadecazetton 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) 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)
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) 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
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 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
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: 114


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----
 9D
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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 1.224745 672, 12096, 48384, 102816, 133056, 102144, 41472, 7056, 530
breday birectified decayotton, Gosset polytope 06,2 1.024695 120, 1260, 3360, 4620, 4032, 2310, 840, 180, 20
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
gripa (old: gripalgrip) grip alterprism, grip atop inverted grip, medial spid-first segment of spat 1.870829 120, 360, 400, 190, 32
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
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 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) 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 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) 0.707107 18, 144, 672, 2016, 4032, 5376, 4608, 2304, 512

Count of actually available polytopes: 33


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 10D
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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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