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 circumradii are explicitly given - are also available in an (accordingly) numerically sorted order.



---- 2D ----


Acronym Name Circumradius
... hyperbolic [10,8,4,6] tiling with tetragonal Coxeter domain
... 2hexat (?)
... 2hoha (?)
... 2srothat (?)
... 2that (?)
... 2that+∞{3} (?)
... 2toxat (?)
... hyperbolic [(33,4)4] tiling
... 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
depat hyperbolic order 10 pentagonal tiling 0.206652 i
ditatha ditrigonary trigonal hemiapeirogonal tesselation, alternate triangular tiling
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
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
hisquat hyperbolic order 6 square tiling 0.5 i
huht hexahexagonal tiling
... hyperbolic tetrapentagonal tiling of family o3o4o5*a 0.438176 i
... hyperbolic order 3 tritetragonal tiling 0.728238 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
... 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
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
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
... hyperbolic snub tritritetragonal tiling, hyperbolic snub tiling of family o3o3o4*a
... hyperbolic snub trigonal-horocyclic tiling, hyperbolic snub triapeirogonal tiling
... hyperbolic snub tetrapentagonal tiling
... hyperbolic snub pentapentagonal tiling
satsa squariapeirotruncated squariapeirogonal 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
... hyperbolic snub di-horocyclic tiling
sirthet small rhombitriheptagonal tiling, hyperbolic rhombitriheptagonal tiling 2.728895 i
snasquat snub square 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
squat square tiling, 2D hypercubical honeycomb2), 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
srotoct (old: sirtoct) hyperbolic (small) rhombitrioctagonal tiling 2.096343 i
... 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
tocat hyperbolic order 3 truncated octagonal tiling 2.947161 i
toct hyperbolic trioctagonal tiling 1.553774 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 triangular tiling, Delone complex of hexagonal lattice A2
tutrip two trip cupolaic blend, gyrated blend of 2 digonal cupola, Phillips head 0.763763
tutut two tut cupolaic blend, gyrated blend of 2 truncated tetrahedra 1.172604
... 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 order 4 tritetragonal tiling, hyperbolic ditetragonal tritetratrigonal tiling, hyperbolic alternated order 4 hexagonal tiling 0.408248 i
... hyperbolic tripentagonal tiling of family o3o4o5*a 0.357770 i
... hyperbolic rectified ditetragonary tritetragonal tiling, cantic order 4 hexagonal tiling 1.060082 i
... hyperbolic dipentagonal tiling of family o3o4o5*a 0.956676 i
... hyperbolic shieldotritetragonal tiling, hyperbolic tritetratrigonal tiling, cantic octagonal tiling 1.446026 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: 150



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---- 3D ----


Acronym Name Circumradius
... triangle hecatonicosahedron
... dodeca-augmented rhombicuboctahedron
... external blend of 12 raded-1-10-5-5 edge facetings
... external blend of 20 sidtid-0-3-3-3 edge facetings
... 24 face equihedral toroid
... t24-s6-n8 2.431352
... 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))]
2n/2-p 2n-gonal prism of winding number 2 sqrt[1/4+1/(4 sin2(π/n))]
2n/d-p 2n/d-prism, 2n-prism with winding number d sqrt[1/4+1/(4 sin2(π d/2n))]
... 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
... pentagonal butterfly wedge, blend of 2 pentagonal pyramids, half of blend of 2 pentagonal antiprisms 0.951057
... 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
... triaconta-augmented rhombicosidodeahedron ...
... 32 face equihedral toroid
... triangle triacontahexahedron
... 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
... 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}
... Leonardo polyhedron of type {4,5;31}
... 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}
... 6doe (?) 1.401259
... 6gissid (?) 0.535233
... squippy-teddi-G3 toroid ...
..., 6Q3-2S3-gyro parallelly that dissected rich
..., 6Q3-2S3-ortho (un)gyrated 6Q3-2S3-gyro
... 6tet (?) 0.612372
... a3b3c, general variation of truncated octahedron sqrt[(3a2+4b2+3c2+4ab+2ac+4bc)/8]
... a3b4c, general variation of great rhombicuboctahedron sqrt[2a2+4b2+3c2+4ab+(2ac+4bc)sqrt(2)]/2
... 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
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
auhip, J54 augmented hexagonal prism
aupip, J52 augmented pentagonal prism
auteddi, J64 augmented tridiminished icosahedron
autic, J66 augmented truncated cube
autid, J68 augmented truncated dodecahedron
autip, J49 augmented triangular prism
autut, J65 augmented truncated tetrahedron
auwaco, J87 augmented sphenocorona
bagydrid, J79 bigyrate diminished rhombicosidodecahedron 2.232951
bamich biambocubic honeycomb
batatoh bitruncated alternated-cubic honeycomb, bitruncated tetrahedral-octahedral honeycomb, quarter cubic honeycomb
batch bitruncated cubic honeycomb, truncated-octahedral honeycomb, Voronoi complex of body-centered cubic (bcc) lattice
bauco bi-augmented cuboctahedron, 4fold rhombohedron ...
baupip, J53 biaugmented pentagonal prism
bautic, J67 biaugmented truncated cube
bautip, J50 biaugmented triangular prism
... cubically-diminished dodecahedron, bi-tetrahedrally-diminished dodecahedron 1.401259
bilbiro, J91 bilunabirotunda
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
bithon bitetrahedral honeycomb
bobipyr bowtie bipyramid, crossed tetragonal bipyramid, bowtie (line-)tegum 0.707107
cabisch cantic bisnub cubic honeycomb
cadditradid complex (ditrigonary) rhombidodecadodecahedron 0.866025
caquitpica cubatiquasitrunciprismated cubatiapeiratic honeycomb
casch cantic snub cubic honeycomb
chexah hyperbolic cubic-hexagonal-tiling honeycomb, bitruncated order 4 hexagonal-tiling honeycomb, bitruncated order 6 cubic honeycomb 1.870829 i
cho cubohemioctahedron, rhomballelohedron 1
... cho+4{6/2} (?) 1
chon cubic honeycomb, 3D hypercubical honeycomb3), Voronoi complex of primitive cubical lattice, Delone complex of primitive cubical lattice
... cubically truncated rhombic dodecahedral honeycomb
cid small complex icosidodecahedron 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
... (ico derived) tridpy variant, o3m4o3o cell
... (tes derived) tridpy variant, o4m3o3o cell
... (hi derived) tridpy variant, o5m3o3o cell
... (ex derived) pedpy variant, o3m3o5o cell
cotco cuboctatruncated cuboctahedron, cubitruncated cuboctahedron 1.322876
cube (alt: squip) cube, hexahedron, 3D measure-polytope3), geochor(id), square prism, triangular antitegum, Voronoi cell of primitive cubical lattice, Delone cell of primitive cubical lattice, terminally chamfered tetrahedron, surtegmated tetrahedron 0.866025
... cubically truncated rhombic dodecahedron, chamfered octahedron
cutpica cubatitrunciprismated cubatiapeiratic honeycomb
... d3o3x, variation of cuboctahedron 2.661453
dap, 10-ap decagonal antiprism 1.674505
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
desided disnub icosidodecadodecahedron, compound of 2 sided 1.126898
did dodecadodecahedron, great dodecadodecahedron 1
... 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
dird dirhimbidodecahedron, compound of 12 pip 0.986715
dirid, J76 diminished rhombicosidodecahedron 2.232951
dis disnubihedron, compound of 12 tet 0.612372
disco disnub cuboctahedron, compound of 2 snic
disdi-verf vertex figure of disnub disicositetrachoron 0.866025
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
... ditdid+gidtid (?) 0.866025
ditoh ditetrahedral-octahedral honeycomb
ditra ditriangular trapezoprism sqrt[(a+b)2+c2]/2
ditrah hyperbolic distriangular-tiling honeycomb 2.075910 i
dittec ditruncated cube, truncated truncated cube, expanded ambiated tic sqrt[(7+4 sqrt(2))y2+(24+16 sqrt(2))y+(24+16 sqrt(2))]/2
dittet ditruncated tetrahedron, truncated truncated tetrahedron, expanded ambiated tut sqrt[(11y2+36y+36)/8]
ditti ditrigonal icosahedron, vertex figure of idhi 1.401259
dittoe ditruncated octahedron, truncated truncated octahedron, expanded ambiated toe sqrt[(5y2+9y sqrt(2)+9)/2]
doe dodecahedron, cosmohedron, Goldberg polyhedron GP(1,0) 1.401259
... dodecahedrically truncated rhombic triacontahedron, chamfered icosahedron
doehon hyperbolic order 4 dodecahedral honeycomb 0.899454 i
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
dro dirhombioctahedron, compound of 8 trip 0.763763
dudsi dual of D-stellation of icosahedron, D-faceting of dodecahedron, vertex figure of paphicki 0.866025
e icosiicosahedron, compound of 10 tet 0.612372
ebauco elongated bi-augmented cuboctahedron, 4fold elongated rhombohedron, bi-augmented pexco ...
editoh elongated ditetrahedral-octahedral honeycomb
epcu, J20 elongated pentagonal cupola
epedpy, J16 elongated pentagonal dipyramid
epeppy, J9 elongated pentagonal pyramid
epgybro, J43 elongated pentagonal gyrobirotunda
epgycuro, J41 elongated pentagonal gyrocupolarotunda
epigybcu, J39 elongated pentagonal gyrobicupola
epobcu, J38 elongated pentagonal orthobicupola
epobro, J42 elongated pentagonal orthobirotunda
epocuro, J40 elongated pentagonal orthocupolarotunda
epro, J21 elongated pentagonal rotunda
erich parallelly that elongated rich
esch edge-snub cubic honeycomb
escu, J19 elongated square cupola, diminished small rhombicuboctahedron 1.398966
esquidpy, J15 elongated square dipyramid
esquigybcu, J37 elongated square gyrobicupola, pseudorhombicuboctahedron, Miller's solid 1.398966
esquipy, J8 elongated square pyramid
etcu, J18 elongated triangular cupola
etidpy, J14 elongated trigonal dipyramid
etigybcu, J36 elongated triangular gyrobicupola
etobcu, J35 elongated triangular orthobicupola
etoh elongated tetrahedral-octahedral honeycomb, elongated alternated cubic honeycomb
etoph elongated-triagonal prismatic honeycomb
etripy, J7 elongated triangular pyramid
... expanded dodeca-augmented great rhombicuboctahedron ...
exrad expanded rhombic dodecahedron
exrhote expanded rhombic triacontahedron
extoh expanded octahedral-tetrahedral honeycomb
... f v10o, variation of decagonal prism, hull of 10/3-prism 1.286277
... f v3o, variation of triangular prism, vertex figure of rectified great grand hecatonicosachoron 0.884212
... f v5o, variation of pentagonal prism, vertex figure of righi 0.964832
... f x3o, variation of triangular prism, vertex figure of rectified hecatonicosachoron 0.993902
... f x4o, variation of cube 1.074481
... f x5/2o, variation of 5/2-prism, vertex figure of raghi 0.964832
... f x5o, variation of pentagonal prism 1.173932
... f3o3x, variation of cuboctahedron 1.327129
... f3o4x, variation of small rhombicuboctahedron 1.789732
... f3o5x, variation of srid, hull of siid, hull of quit gissid 2.785428
... f3v5v, variation of grid, hull of idtid 3.236068
... f3x5o, variation of ti, hull of tigid, hull of gaddid 3.036797
... f3x5x, variation of great rhombicosidodecahedron, hull of quitdid 4.341518
gabirch great birhombatocubic honeycomb
gabreth great birhombitetrahedral honeycomb
gacid great complex icosidodecahedron 0.587785
gacoca great cubaticubatiapeiratic honeycomb
gacquitpica great cubatiquasitrunciprismated cubatiapeiratic honeycomb
gactipeca great cubatitrunciprismated cubatiapeiratic honeycomb
gad great dodecahedron, faceted icosahedron, vertex figure of fix 0.951057
gaddid great dodekicosidodecahedron 0.716891
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
gaqrich great quasirhombated cubic honeycomb
gaquapech great quasiprismated cubic honeycomb
gaquatid great quasitruncated icosidodecahedron, stellatruncated icosidodecahedron 1.020684
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
getdoca (old: gotactictosquath) great tetradicubatiapeiratic honeycomb, great tetrahedral cubic tomocubic tomosquare tiling honeycomb
getit cadoca great tritrigonary cubatidicubatiapeiratic honeycomb
gibil biro great bilunabirotunda
gicdatrid great complex (ditrigonary) rhombicosidodecahedron 0.866025
gid great icosidodecahedron 0.618034
... 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
giddy great dodekicosahedron 1.134229
... giddy+12{10/2} (?) 1.134229
... giddy+20{6/2} 1.134229
gidhei great dodecahemicosahedron, small dodecahemiicosahedron (but not sidhei) 1
gidhid great dodecahemidodecahedron 0.618034
gidisdrid great disnub dirhombicosidodecahedron, Skilling's figure 0.707107
gidpicdoh hyperbolic great disprismated cubical-dodecahedral honeycomb, hyperbolic omnitruncated order 5 cubical honeycomb, hyperbolic omnitruncated order 4 dodecahedral honeycomb 4.248159 i
gidrid great dirhombicosidodecahedron, great snub disicosidisdodecahedron, Miller's monster 0.707107
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
gifodib sidtid faceting sidtid-2-10-20-0 (i.e. with 10(=d) {3}, 20(=i) {4}, and 2(=b) {5/2}) 0.866025
giid great icosicosidodecahedron 1.134229
gike great icosahedron, retrosnub tetrahedron, retrosnub tetratetrahedron, edgified penta-stellahedron, vertex figure of gax 0.587785
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
gird great rhombidodecahedron 0.716891
... gird+12{10/4} (?) 0.716891
... gird+20{6/2} (?) 0.716891
girsid great (inverted) retrosnub icosidodecahedron, azathoth
gisdid great snub dodekicosidodecahedron, shub-niggurath 0.707107
giship tristrophic heptagrammic prism, heptagrammic prism of winding number 3, great heptagrammic prism, great stellated heptagonal prism 0.716257
gisid great inverted snub icosidodecahedron, great vertisnub icosidodecahedron, cthulhu
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
githawro great triangular hebesphenorotunda
gobath great biambotetrahedral honeycomb
gocco great cubicuboctahedron 0.736813
gosid great snub icosidodecahedron, tsathoggua
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 rhombicosidodecahedron (but not qrid), truncated icosidodecahedron, omnitruncated icosahedron, omnitruncated dodecahedron 3.802395
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+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
gybef, J26 gyrobifastegium
gyeditoh gyroelongated ditetrahedral-octahedral honeycomb
gyepabro, J48 gyroelongated pentagonal birotunda
gyepcu, J24 gyroelongated pentagonal cupola
gyepibcu, J46 gyroelongated pentagonal bicupola
gyepip, J11 gyroelongated pentagonal pyramid, diminished icosahedron
gyepro, J25 gyroelongated pentagonal rotunda
gyerich parallelly that elongated gyrich
gyescu, J23 gyroelongated square cupola
gyesp, J10 gyroelongated square pyramid
gyesqidpy, J17 gyroelongated square dipyramid
gyesquibcu, J45 gyroelongated square bicupola
gyetaph gyroelongated triangular-prismatic honeycomb
gyetcu, J22 gyroelongated triangular cupola
gyetibcu, J44 gyroelongated triangular bicupola
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
gyrich gyrated rectified cubical honeycomb
gyrid, J72 gyrated rhombicosidodecahedron 2.232951
gytoh gyrated tetrahedral-octahedral honeycomb, gyrated alternated cubic honeycomb
gytoph gyrated triangular prismatic honeycomb
hachon hyperbolic order 6 cubical honeycomb 0 i
hap, 6-ap hexagonal antiprism 1.087664
hawmco, J89 hebesphenomegacorona
hedhon hyperbolic order 6 dodecahedral honeycomb 0 i
hep heptagonal prism 1.256179
hexah hyperbolic order 3 hexagonal-tiling honeycomb 1.414214 i
hicu hexagonal cupola ∞   i.e. flat in euclidean space
hihexah hyperbolic order 6 hexagonal-tiling honeycomb 0 i
hiktut hexakis truncated tetrahedron 1.172604
hip hexagonal prism, Voronoi cell of unit-stacked hexagonal lattice 1.118034
hiph hexagonal prismatic honeycomb, Voronoi complex of unit-stacked hexagonal lattice
hippy, 6pyr (degenerate) hexagonal pyramid ∞   i.e. flat in euclidean space
hirki hemirhombichiro-icosahedron, compound of 5 thah 0.707107
... ho oh&#q, narrower variant of digonal antiprism 1.767767
... ho3oh&#q, narrower variant of trigonal antiprism, hemiation of hip 1.118034
hog dhidicup verf vertex figure of hog dhidicup 0.730749
hoha hexagonal hemiapeirogonal tesselation
hudsi dual of H-stellation of icosahedron, H-faceting of dodecahedron, vertex figure of paphacki, huitzilopochtli 0.866025
... (infinite series of) hyperbolic uniform honeycombs with pyritohedral vertex figure
id icosidodecahedron, rectified icosahedron, rectified dodecahedron 1.618034
... id+seihid+sidhid (?) 1.618034
iddei icosidisicosahedron, compound of 5 oho 1
ided icosidodecadodecahedron 1.322876
idisdid invertidisnub dodecadodecahedron, compound of 2 isdid
idtid icosidodecatruncated icosidodecahedron, icositruncated dodecadodecahedron 2
ike   (alt.: snit) icosahedron, snub tetrahedron, snub tetratetrahedron, snub triangle antiprism, hydrohedron, gyroelongated pentagonal bipyramid, vertex figure of ex 0.951057
... ike+3gad (?) 0.951057
... icosahedrally truncated rhombic triacontahedron, chamfered dodecahedron, Goldberg polyhedron GP(2,0)
ikhon hyperbolic order 3 icosahedral honeycomb 0.509376 i
isdid inverted snub dodecadodecahedron, vertisnub dodecadodecahedron, nyarlathotep
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
... dual of uniform n-gonal prism, n-gonal dipyramid
mabaud, J60 metabiaugmented dodecahedron
mabauhip, J56 metabiaugmented hexagonal prism
mabautid, J70 metabiaugmented truncated dodecahedron
mabgyrid, J74 metabigyrated rhombicosidodecahedron 2.232951
mabidrid, J81 metabidiminished rhombicosidodecahedron 2.232951
mabirch medial birhombatocubic honeycomb
magydrid, J78 metagyrate diminished rhombicosidodecahedron 2.232951
mesdi-verf vertex figure of medial snub disicositetrachoron 0.866025
mibdi, J62 metabidiminished icosahedron 0.951057
mibkid metabikis dodecahedron, (subsymmetrically) metabistellated-dodecahedron, dual of mibdi
... mono lowered small rhombicuboctahedron ...
... mono lowered truncated cube ...
n-ap n-gonal antiprism sqrt[(3-2 cos(π/n))/(8-8 cos(π/n))]
n-azedip n-gonal - apeirogonal duoprism
n-p n-gonal prism sqrt[1/4+1/(4 sin2(π/n))]
n/2-ap n/2 antiprism sqrt[(3-2 cos(2π/n))/(8-8 cos(2π/n))]
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))]
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))]
n/d-p n/d-prism, n-prism with winding number d sqrt[1/4+1/(4 sin2(π d/n))]
n/d-py n/d-gonal pyramid 1/sqrt[4-1/sin2(πd/n)]
... noble {9,3} modwrap within srid 2.232951
... hyperbolic o3o3o4s4*a tesselation
... hyperbolic o3o3o4x4*a tesselation 0.5 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
... o3β4o (?) ...
... o3β4x (?) ...
... o3β5o (?) ...
... o3β5x (?) ...
... hyperbolic o3x3x3o4*a tesselation 1.189207 i
... hyperbolic cyclotruncated tetrahedral-icosahedral honeycomb 0.786151 i
... o3x4q, variation of truncated cube, hull of sno 2.121320
... o3x4u, variation of truncated cube 2.613126
... hyperbolic o3x4x3o4*a tesselation 0.944355 i
... hyperbolic o3x4x3o5*a tesselation
... hyperbolic o3x5x3o5*a tesselation
... 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)
... o5/2f5x variation of truncated great dodecahedron 2.478019
... o5/2β5o (?) ...
... o5/2β5x (?) ...
... o5x3o5β (?) ...
... hyperbolic o8o4x *b3x tesselation 0.321797 i
oap, 8-ap octagonal antiprism 1.375549
... (hi derived) truncated tridpy variant, o2o3o symmetric co relative ...
... (ico derived) truncated tridpy variant, o2o3o symmetric co relative ...
... (tes derived) truncated tridpy variant, o2o3o symmetric co relative ...
oct (alt.: trap, tatet) octahedron, rectified tetrahedron, tricross3), tetratetrahedron, aerochor(id), trigonal antiprism, 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
... oct+6{4} (?) 0.707107
... octahedrally truncated rhombic dodecahedron, chamfered cube
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
odsnic octadiminished snub cube, chiral 4fold dodecahedron-like barrel, vertex figure of octsnich 1.343713
ogpy, 8/3-pyr octagrammic pyramid 0.594604
oho octahemioctahedron, allelotetratetrahedron 1
... oho+8{3} 1
op octagonal prism, bidiminished small rhombicuboctahedron 1.398966
... oqo3ooq&#xt, cubera (cube chimera), (fully) mono-truncated cube 0.866025
... truncated pedpy variant, o2o5o symmetric co relative 1.203002
... vertex figure of ope 0.816497
... 20 thawroes toroid
... octagonal Leonardo style "polyhedron of renaissance", vertex figure of lamina-trunc(o8o4xb3x) 1.847759
... p12-h4
... pentagonal antidipyramid, pentagonal antitegum, pentagonal kiteohedron, dual of pap, axial bi-kis-doe, deca-truncated sissid
pabaud, J59 parabiaugmented dodecahedron
pabauhip, J55 parabiaugmented hexagonal prism
pabautid, J69 parabiaugmented truncated dodecahedron
... partially bi-expanded hyperbolic order 8 triangular tiling, partially bi-contracted hyperbolic shieldotritetragonal tiling
pabextet partially bi-expanded tetrahedron
pabextut partially bi-expanded truncated tetrahedron
pabgyrid, J73 parabigyrated rhombicosidodecahedron 2.232951
pabidrid, J80 parabidiminished rhombicosidodecahedron 2.232951
pac girco partially (mono-)contracted great rhombicuboctahedron ...
... partially contracted hyperbolic shieldotritetragonal tiling
... partially contracted hyperbolic x4o3x3o3*b tesselation
... partially contracted hyperbolic x4o3x3x3*b tesselation
pacop partially Stott contracted octagonal prism
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 ...
padex snic partially dodeca-expanded snub cube
pagydrid, J77 paragyrate diminished rhombicosidodecahedron 2.232951
pakid pentakis dodecahedron, apiculated dodecahedron
pap pentagonal antiprism, para-bidiminished icosahedron 0.951057
paqrich prismated quasirhombated cubic honeycomb
... para bi lowered truncated cube ...
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 cube partially tetrahedrally-expanded cube, tetrahedrally truncated cube, chamfered tetrahedron, partially tri-expanded tetrahedron
patex sirco partially tetrahedrally-expanded small rhombicuboctahedron, tetrahedrally lowered small rhombicuboctahedron, partially tri-expanded truncated tetrahedron ...
pd{3,5,3} partial diminishing (old: truncation) of hyperbolic order 3 icosahedral tesselation 0.509376 i
pechon hyperbolic order 5 cubic honeycomb 0.555893 i
pecu, J5 pentagonal cupola 2.232951
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
pegybcu, J31 pentagonal gyrobicupola
pegycuro, J33 pentagonal gyrocupolarotunda
peppy, 5pyr, J2 pentagonal pyramid 0.951057
pero, J6 pentagonal rotunda, half of icosidodecahedron 1.618034
... 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 ...
pexrich partially expanded rectified cubic honeycomb
pextet partially (edge-)expanded tetrahedron
pextich partially expanded truncated cubic honeycomb
pextoe partially (mono-)expanded truncated octahedron ...
pextoh partially expanded tetrahedral-octahedral honeycomb
pextut partially (edge-)expanded truncated tetrahedron
phexah hyperbolic order 5 hexagonal-tiling honeycomb 0.381966 i
phexdo partially hexa-expanded dodecahedron
phexid partially hexa-expanded icosidodecahedron
phexik partially hexa-expanded icosahedron
pip pentagonal prism, 5-p, vertex figure of rox 0.986715
pobcu, J30 pentagonal orthobicupola
pobro, J34 pentagonal orthobirotunda 1.618034
pocuro, J32 pentagonal orthocupolarotunda
pox snic partially octa-expanded snub cube
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
pysnic pyritosnub cube, pyritohedral sirco variant, edge-alternated girco 2.317611
pystid pyritohedrally stellated icosidodecahedron
... q x3o, variation of triangular prism, vertex figure of rectified tesseract 0.912871
... q x4o, variation of cube, vertex figure of rectified cubic honeycomb 1
... q x5o, variation of pentagonal prism 1.106168
... q x6o, variation of hexagonal prism 1.224745
... q x8o, variation of octagonal prism 1.485633
... q3o3x, variation of cuboctahedron 1.215958
... q3o4x, variation of small rhombicuboctahedron, hull of tisso 1.658312
... q3o5x, variation of srid 2.601518
... q3x3o, variation of truncated tetrahedron, triangle-snub small rhombicuboctahedron 1.398966
... q3x4x, variation of girco, hull of quitco 2.564844
... qo3oo&#x, shallower variant of trigonal pyramid, vertex pyramid of cube 0.866025
... qo3oq&#x, shallower variant of trigonal antiprism, medial segment of cube 0.866025
qrid quasi rhombicosidodecahedron, great rhombicosidodecahedron (but not grid) 0.716891
quequapech quasiquasiprismated cubic honeycomb
querco quasirhombicuboctahedron, great rhombicuboctahedron (but not girco) 0.736813
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
quit gissid quasitruncated great stellated dodecahedron, great stellated truncated dodecahedron, great stellatruncated dodecahedron 0.657550
quit sissid quasitruncated small stellated dodecahedron, small stellated truncated dodecahedron, small stellatruncated dodecahedron 0.852911
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
quitdid quasitruncated dodecadodecahedron, stellatruncated dodecadodecahedron 1.658312
quith quasitruncated hexahedron, stellated truncated hexahedron, stellatruncated cube 0.579471
... rhombic enneacontahedron
rad (old: rhode) rhombic dodecahedron, Voronoi cell of face-centered cubic (fcc) lattice, terminally chamfered cube, terminally chamfered octahedron, surtegmated cube, surtegmated octahedron
raded rhombidodecadodecahedron 1.322876
... edge faceting raded-1-10-5-5 1.322876
radh rhombic dodecahedral honeycomb, Voronoi complex of face-centered cubic (fcc) lattice
rah rhombihexahedron, compound of 3 cube 0.866025
rahrie rhombihyperhombicosicosahedron, compound of 5 socco 1.398966
rapescu retrograde pentagonal cuploid, retrograde pentagonal semicupola 0.866025
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
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
rath hyperbolic rectified (order 6) tetrahedral honeycomb 1 i
ratricu retrograde trigonal cupola, 3/2-cupola 0.707107
rebatch rectified bitruncated cubic honeycomb
rebtatoh rectified bitruncated tetrahedral-octahedral honeycomb
recta rectangular alterprism, rectangular trapezoprism sqrt[c2+(a+b)2/2]/2
retic (alt.: amtic) rectified/ambiated truncated cube 3.414214
retoe (alt.: amtoe) rectified/ambiated truncated octahedron 2.121320
retrip (alt.: amtrip) rectified/ambiated trip, kernel of trip and m m3o, o2o3o symmetric co relative 0.816497
retut (alt.: amtut) rectified/ambiated truncated tetrahedron 2.661453
rhom rhombihedron, compound of 5 cube 0.866025
rhote (old: rattic) rhombic triacontahedron, terminally chamfered dodecahedron, terminally chamfered icosahedron, surtegmated dodecahedron, surtegmated icosahedron
... ri+12{10/2} (?) 1.322876
... ri+12{10/4} (?) 1.322876
rich rectified cubic honeycomb
ridatha rectified ditetratihemiapeiratic honeycomb
riddoh hyperbolic rectified order 4 dodecahedral honeycomb 1.272020 i
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
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 (?) ...
... β3/2β3x3*a (?) ...
... β3o4β (?) ...
... β3o5β (?) ...
... hyperbolic s3s4o4o tesselation ... i
... hyperbolic s3s4o4x tesselation ... i
... β3x4β (?) ...
... β3x5β (?) ...
... hyperbolic alternated small prismated order-4 square tiling honeycomb
... hyperbolic o3o4s4o tesselation
... family of (generally hyperbolic) s4oPo4s tesselation
... β5/2o5β (?) ...
... β5/2x5β (?) ...
... s60-r60-p12-h30
sabirch small birhombatocubic honeycomb
saddid small dodekicosidodecahedron 2.232951
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 semicupolaically faceted icosahedron 0.951057
scufgi semicupolaically faceted great icosahedron 0.587785
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
serch snub rectified cubic honeycomb
seside small snub icosicosidodecahedron, snub disicosidodecahedron, holosnub icosahedron, hastur 1.458190
shappy, 7/2-pyr small heptagrammic pyramid 0.650389
shexah hyperbolic order 4 hexagonal-tiling honeycomb 0.707107 i
ship bistrophic heptagrammic prism, heptagrammic prism of winding number 2, small heptagrammic prism, small stellated heptagonal prism 0.811783
si snub icosahedron, compound of 10 oct (but not gissi) 0.707107
sicdatrid small complex (ditrigonary) rhombicosidodecahedron 0.866025
siddid (old: siided) snub dodecadodecahedron, chaugnar faugn
sidditdid small ditrigonary dodekicosidodecahedron, small dodekified icosidodecahedron 1.721489
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
sided snub icosidodecadodecahedron, dagon 1.126898
sidhei small dodecahemicosahedron, great dodecahemiicosahedron (but not gidhei) 1
sidhid small dodecahemidodecahedron 1.618034
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
... sidtid+ditdid (?) 0.866025
... sidtid+ditdid+gidtid (?) 0.866025
... sidtid+gidtid (?) 0.866025
... edge faceting sidtid-0-3-3-3 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
siid small icosicosidodecahedron 1.721489
..., s∞o2o3x6s ...
..., s∞o2s3s6s full snub triangular prismatic honeycomb
..., s∞o2s3s6x edge-snub triangular prismatic honeycomb
..., s∞o2s4s4s full snub square prismatic honeycomb
..., s∞o2s4s4x edge-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
... 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
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
... 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
sladit small lanceal ditriacontahedron, strombic hexecontahedron, deltoidal hexecontahedron, tetragonal hexecontahedron
snadow, J84 snub disphenoid, snub digonal antiprism
snathaph snub trigonal-hexagonal prismatic honeycomb
sne snub icosiicosahedron, compound of 5 ike 0.951057
snic snub cube, snub cuboctahedron 1.343713
snich, s4s3s4s (full) snub cubical honeycomb, snub bicubic honeycomb
snid snub dodecahedron, snub icosidodecahedron 2.155837
snisquap, J85 snub square antiprism
snit pyritohedron, pyritosnub tetrahedron, o2o2o symmetric ike variant, vertex figure of hyperbolic cube + n-prism honeycomb sqrt[a2+c2]
snit pyritohedron, pyritosnub tetrahedron, vertex alternated toe 1.581139
sno snub octahedron, compound of 4 oct 0.707107
snu snubihedron, compound of 6 tet (but not sis) 0.612372
so stella octangula, compound of 2 tet 0.612372
sobath small biambotetrahedral honeycomb
socco small cubicuboctahedron 1.398966
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
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
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
squigybcu, J29 square gyrobicupola
squippy, 4pyr, J1 tetragonal pyramid, half of oct 0.707107
squobcu, J28 square orthobicupola
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
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+8{6/2} (?) 1.398966
srothaph (old: rothaph) (small) rhombitriangular-hexagonal prismatic honeycomb
stacu pentagrammic cupola, star cupola 0.866025
stap bistrophic pentagrammic antiprism, stellar antiprism, 5/2-antiprism 0.656431
stappy, 5/2-pyr pentagrammic pyramid, stellated pentagonal pyramid 0.587785
starp (old: restap) tristrophic pentagrammic antiprism, stellar retroprism (retrograde stellar antiprism), 5/3-antiprism 0.587785
stiddip (tristrophic) decagrammic prism, stellated decagonal prism, 10/3-prism, 10-prism with winding number 3 0.794963
stip stellated pentagonal prism, 5/2-prism, 5-prism with winding number 2, vertex figure of raggix 0.725530
stiscu pentagrammic cuploid, star semicupola 0.866025
stop (old: sop) (tristrophic) octagrammic prism, stellated octagonal prism, 8/3-prism, 8-prism with winding number 3 0.736813
stut cadoca small tritrigonary cubatidicubatiapeiratic honeycomb
... rhombical dodeca-augmented snub-dodecahedral variant, rhombi-propello-icosahedron
... icosa-expanded rhombic enneacontahedron
... rhombical octa-augmented truncated-octehedral variant
... expanded octa-augmented truncated-octehedral variant
... rhombical hexa-augmented snub-cubical variant, rhombi-propello-octahedron
tabatch truncated bitruncated-cubic-honeycomb
tabtatoh truncated bitruncated tetrahedral-octahedral honeycomb
tagyrid, J74 trigyrated rhombicosidodecahedron 2.232951
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 trireplinished great icosahedron 0.587785
tassiph truncated square prismatic honeycomb
tatoh truncated tetrahedral-octahedral honeycomb, truncated alternated cubic honeycomb, cantic cubic honeycomb
taud, J61 triaugmented dodecahedron
tauhip, J57 triaugmented hexagonal prism
tautid, J71 triaugmented truncated dodecahedron
tautip, J51 triaugmented trigonal prism
te truncated icosiicosahedron, compound of 10 tut 1.172604
teddi, J63 tridiminished icosahedron, ursahedron, vertex figure of sadi 0.951057
teddoe tetrahedrally diminished dodecahedron, vertex figure of pd{3,5,3} 1.401259
tedrid, J83 tridiminished rhombicosidodecahedron, magnaursahedron 2.232951
tekah tetrakis hexahedron, apiculated cube
tepcus tetrapod-cut-sirco 1.398966
tepdid tripentadiminished icosidodecahedron 1.618034
tet tetrahedron, 3D simplex3), 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 0.612372
thah tetrahemihexahedron, vertex figure of tho, triangular crossed cuploid 0.707107
thaph truncated-hexagonal prismatic honeycomb
thawro, J92 triangular hebesphenorotunda
thiph triangular-hexagonal prismatic honeycomb
thon hyperbolic order 6 tetrahedral honeycomb 0 i
ti truncated icosahedron, buckyball, Goldberg polyhedron GP(1,1) 2.478019
tic truncated cube, truncated hexahedron 1.778824
tich truncated cubic honeycomb
tid truncated dodecahedron 2.969449
tiddoh hyperbolic truncated (order 4) dodecahedral honeycomb 2.246127 i
tiggy truncated great icosahedron, great truncated icosahedron 1.053292
tigid truncated great dodecahedron 1.876844
tih hyperbolic truncated order 3 icosahedral honeycomb 2.082108 i
tikit triakis tetrahedron, apiculated tetrahedron
tikko triakis octahedron, apiculated octahedron
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
titdi tri-trigonally diminished icosahedron, (subsymmetrically) tristellated-dodecahedron, tri-kis-dodecahedron, dual of teddi, vertex figure of tridex
tobcu, J27 triangular orthobicupola, vertex figure of gytoh 1
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 1.581139
topfu two-op-fusion 1.398966
... toroidal pentagrammic bicuploid, star semicupolaic diabolo
... toroidal tiler
totratip hyperbolic truncated order 8 triangle tiling prism 2.220806 i
trah hyperbolic order 3 triangle-tiling honeycomb 0 i
tricu, J3 triangular cupola, half of cuboctahedron 1
tridpy (alt.: trit), J12 trigonal dipyramid, (line-)triangle-tegum
trip, 3-p triangular prism, digonal cupola, Delone cell of unit-stacked hexagonal lattice, vertex figure of rap 0.763763
trirp (degenerate) trigonal retroprism, retrograde trigonal antiprism ∞   i.e. flat in euclidean space
trirp (variant) vertex figure of faceted rectified pentachoron, taller trigonal retroprism (3/2 antiprism) variant 0.763763
... truncated triangular prism, expanded ambiated trip sqrt[(7y2+16y+16)/12]
tupip orthogonal blend of pentagonal prisms, vertex figure of sadsadox 0.986715
tuquith blend of 2 quasitruncated cubes 0.579471
tustip orthogonal blend of pentagagramic prisms, vertex figure of gadsadox 0.725530
tut truncated tetrahedron, cantic cube 1.172604
tutic blend of 2 truncated cubes 1.778824
twip dodecagonal prism 1.995508
... u x3o, variation of triangular prism, vertex figure of rectified hecatonicosachoron 1.154701
... u x4o, variation of cube 1.224745
... u x5o, variation of pentagonal prism 1.312862
... u x6o, variation of hexagonal prism 1.414214
... u3o3x, variation of cuboctahedron 1.541104
... u3o4x, variation of small rhombicuboctahedron 2.040640
... u3x3o, variation of truncated tetrahedron 1.732051
... u3x4o, variation of truncated octahedron 2.236068
... v f3o, variation of triangular prism, vertex figure of rasishi 0.983956
... v f5/2o, variation of 5/2-prism, vertex figure of ragashi 0.905040
... v x3o, variation of triangular prism, vertex figure of rectified great grand stellated hecatonicosachoron 0.654847
... v x5o, variation of pentagonal prism, vertex figure of ragishi 0.905040
... v3o3x, variation of cuboctahedron, vertex figure of gadtaxady 0.820211
... v3o5f, variation of srid, hull of tiggy 1.704262
... v3x3o, variation of truncated tetrahedron, vertex figure of sidtaxhi 0.975835
... v3x5f, variation of grid, hull of gaquatid 4.323687
... axially trigonal variant of pentagonal rotunda ...
... w x4o, variation of cube 1.398966
... w x8o, variation of octagonal prism, hull of 8/3-prism 1.778824
... w3x3o, variation of truncated tetrahedron 1.973010
... w3x4x, variation of girco, hull of cotco 3.193704
waco, J86 sphenocorona
wamco, J88 sphenomegacorona
wavicoca sphenoverted cubaticubatiapeiratic honeycomb
... x f3o, variation of triangular prism 1.059565
... x f5/2o, variation of 5/2-prism, vertex figure of rofix 0.986715
... x q3o, variation of triangular prism, vertex figure of rectified icositetrachoron 0.957427
... x u3o, variation of triangular prism 1.258306
... x v5o, variation of pentagonal prism, vertex figure of rigfix 0.725530
... x3(-x)5f, variation of grid 1.618034
... x3/2β3x (?) ...
... x3f4o, variation of truncated octahedron, hull of siddo, hull of passipsido 2.176251
... x3f5o, variation of ti, hull of raded, hull of kri 3.463334
... hyperbolic x3o3o3x4*a tesselation 1.553774 i
... hyperbolic x3o3o3x5*a tesselation 1.272020 i
... hyperbolic x3o3o4o3*a tesselation 0.511081 i
... hyperbolic x3o3o5o3*a tesselation 0.250437 i
... hyperbolic x3o3x3o4*a tesselation 1.429970 i
... hyperbolic x3o3x3o5*a tesselation 1.118425 i
... hyperbolic x3o4o3x5*a tesselation
... hyperbolic x3o4o4o4*a tesselation 0 i
... x3o4q, variation of small rhombicuboctahedron 1.732051
... hyperbolic x3o4x3o4*a tesselation 1.045866 i
... hyperbolic x3o4x3o5*a tesselation 0.919229 i
... hyperbolic x3o5x3o5*a tesselation
... hyperbolic x3o6o3o6*a honeycomb, hyperbolic triangular-tiling - hexagonal-tiling honeycomb 0 i
... x3q3o, variation of truncated tetrahedron 1.442951
... x3β3o (?) ...
... x3β4o (?) ...
... x3β5o (?) ...
... x3u3o, variation of truncated tetrahedron 1.837117
... x3u4o, variation of truncated octahedron 2.549510
... x3v3o, variation of truncated tetrahedron, vertex figure of dattady 0.935414
... x3w3o, variation of truncated tetrahedron 2.120453
... x3w4o, variation of truncated octahedron, hull of rah, hull of snu 2.956796
... hyperbolic x3x3o3o4*a tesselation 1.391625 i
... hyperbolic x3x3o3o5*a tesselation 1.072098 i
... hyperbolic x3x3o3x4*a tesselation 2.256021 i
... hyperbolic x3x3o3x5*a tesselation 1.816256 i
... x3x3u, variation of truncated octahedron 2.091650
... hyperbolic x3x3x3o4*a tesselation 2.085865 i
... hyperbolic x3x3x3o5*a tesselation 1.601395 i
... hyperbolic x3x3x3x4*a tesselation 2.942253 i
... hyperbolic x3x3x3x5*a tesselation 2.339260 i
... hyperbolic x3x4o3o4*a tesselation, cyclotruncated octahedral-cubic honeycomb 1 i
... hyperbolic x3x4o3o5*a tesselation 0.869999 i
... hyperbolic x3x4o3x5*a tesselation
... hyperbolic x4x4o *b3x tesselation, hyperbolic runcicantic o3o4o4x tesselation 2.090770 i
... x3x4q, variation of great rhombicuboctahedron 2.645751
... hyperbolic x3x4x3o4*a tesselation 1.599084 i
... hyperbolic x3x4x3o5*a tesselation
... hyperbolic x3x4x3x4*a tesselation 2.197368 i
... hyperbolic x3x4x3x5*a tesselation
... hyperbolic x3x5o3o5*a tesselation
... hyperbolic x3x5x3x5*a tesselation, hyperbolic omnitruncated dodecahedral-icosahedral honeycomb 1.798907 i
... hyperbolic x4o3o4o3*a tesselation, cubic-octahedral honeycomb 0.377964 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 ... i
... hyperbolic x4x3o8o tesselation 0.594604 i
... hyperbolic x4x3x8o tesselation 1.864101 i
... hyperbolic x4x4o4o4*a tesselation 0.353553 i
... 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
... p60-r60, 41st stellation of ti
... expansion of 41th stellation of truncated icosahedron
... xo oq&#q, tetrahedron with one shorter edge, vertex figure of tisdip 0.836660
... xo ox&#h, longer variant of digonal antiprism, vertex figure of deca 0.935414
... xo ox&#k, longer variant of digonal antiprism, vertex figure of cont 0.989219
... xo ox&#q, longer variant of digonal antiprism, vertex figure of triddip 0.790569
... xo3oo&#q, longer variant of trigonal pyramid, vertex figure of tepe 0.774597
... xo3ox&#h, longer variant of trigonal antiprism, cyclo-hexadiminished co, vertex figure of batatoh 1
... xo3ox&#q, longer variant of trigonal antiprism, vertex figure of spid 0.866025
... vertex figure of small prismated icositetrachoron 0.541196
... pentagonal rhombic barrel
... higher digonal cupola, vertex figure of srip 0.906327
... vertex figure of cope 0.894427

Count of actually available polytopes: 873



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---- 4D ----


Acronym Name Circumradius
(2,2n)-pap dyad - 2n-gon prismantiprismoid, s2s2s-2n-x, edge-alternated square - 4n-gon duoprism ...
(n,2m)-pap n-gon - 2m-gon prismantiprismoid, s-n-s-2-s-2m-x, edge-alternated 2n-gon - 4m-gon duoprism ...
... mono-augmented trigonal mibdi-laced wedge ...
10,n-dip decagon - n-gon duoprism sqrt[(3+sqrt(5))/2+1/(4 sin2(π/n))]
..., 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))]
... (1,4)-expanded bited ...
... 1/10-luna of hexacosachoron 1.618034
2,n-dap digon - n-gon duoantiprism, hemiated square - 2n-gon duoprism sqrt[A2/2+B2/(4 sin2(π/2n))]
... 2affic (?) 1.414214
... 2affidhi (?) 2.236068
... 2cont (?) 3.414214
... 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
... 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))]
2n,m-dip 2n-gonal - m-gonal duoprism sqrt[1/(4 sin2(π/2n))+1/(4 sin2(π/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
3,n-dip, K-4.175 triangle - n-gon duoprism, n-gon - n-prismatic wedge sqrt[1/3+1/(4 sin2(π/n))]
... general variant of triddap sqrt[(a2+b2)/3]
..., {3} || gybef {3} || gyrobifastegium ...
... 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
4,2n-dip square - 2n-gon duoprism sqrt[1/2+1/(4 sin2(π/2n))]
4,n-dip, K-4.177 square - n-gonal duoprism sqrt[1/2+1/(4 sin2(π/n))]
... tetracontadisdiminished ex 1.618034
... tetracontadisdiminished sidpixhi 5.236068
... 4D corner hypercubera 1
... 4pen+160{3} (?) 0.632456
... 4/10-luna of hexacosachoron 1.618034
5,n-dip pentagon - n-gon duoprism sqrt[(5+sqrt(5))/10+1/(4 sin2(π/n))]
..., K-4.146 pentagon - pentagonal-rotunda wedge, {5} || pero 3.077684
... pentadiminished 2/10-luna of hexacosachoron 1.618034
..., 5Y4-3T-3Q3-T3 ...
..., 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))]
..., 6Q4-2T parallelly squobcu dissected pacratoh
... 6tes (?) 1
... general 7-2-stepprism sqrt(A2+B2)
8,n-dip octagon - n-gonal duoprism sqrt[(2+sqrt(2))/2+1/(4 sin2(π/n))]
... triangular duoexpandoprism sqrt[(a2+3b2)/3]
... terminally chamfered hexadecachoron
... chamfered hexadecachoron
... tetracontoctachoron-derived Gévay polychoron ...
afdec antifrustic distetracontoctachoron 1.414214
affic antifrustary tetracontoctachoron 1.414214
affidhi antifrustary dishecatonicosachoron 2.236068
affip antifustric prismatochoron, compound of 16 hiddip 1.414214
affixthi antifrustic hexacositrishecatonicosachoron 2.236068
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]
... aoc3ooo3cao *b3oca&#zd sqrt[(a2+ac+c2)/2]
apid (alt.: bamid) antiprismatodecachoron, biambodecachoron, triangle based biambodecachoron 0.774597
arsdod depabdirox around-symmetrical dodecadiminishing of deep parabidiminished rox 3.077684
arse aurap around-symmetrically expanded augmented rectified pentachoron
arse biscrahi bistratic icosidodecahedron-first subsegment of small rhombihexacosachoron, around-symmetrically expanded biscrahi 6.073594
arspabd biscrox around-symmetrically parabidiminished bistratic icosahedron-first cap of rectified hexacosachoron 3.077684
arsted biscrox around-symmetrically tridiminished bistratic icosahedron-first cap of rectified hexacosachoron 3.077684
arsted diddidex around-symmetrical tridiminishing of (axial) duo-disdodeca-icosa-diminished hexacosachoron 1.618034
aubautipip augmented biaugmented-triangular-prism prism
aurap augmented rectified pentachoron
auteddipe augmented-tridiminished-icosahedron prism ...
autipip augmented-triangular-prism prism ...
autodip augmented 3-8-duoprism ...
autpen augmented truncated pentachoron ...
... vertex figure of biprismatododecateron 0.816497
badhidy (old: buthi) blendic dishecatonicosa-dishecatonicosachoron, compound of tigaghi and quit sishi 2
badohi blendic dishecatonicosachoron 2
bamic (old: apic) biambotetracontoctachoron, antiprismatotetracontoctachoron, triangle based biambotetracontoctachoron 1.732051
baticot bitruncated icositetrachoric tetracomb, small tetracontaoctachoric tetracomb
batitit bitruncated tesseractic tetracomb
bauautipip biaugmented augmented-triangular-prism prism ...
baucubaike bi-augmented cubaike
baudeca biaugmented decachoron
bautipip biaugmented-triangular-prism prism
... BAVFfxoo xFofxFVo3xxFxooxo5xooxFfoV&#zx
... vertex figure of biprismatointercepted dodecateron 0.816497
bhidtex bi-hecatonicosidiminished truncated hexacosichoron 4.643523
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
bicypdex (alt.: bicypaugap) bi-cyclopentadiminished hexacosachoron, bi-cyclopentaaugmented great antiprism 1.618034
bicypdrahi (bistratic) bi-cyclopentadiminished rectified hexacosachoron 4.534568
bicypdrox (bistratic) bi-cyclopentadiminished rectified hexacosachoron 3.077684
bicyte ausodip bicyclotetraugmented square-octagon duoprism ...
bicyte gysrit bicyclotetragyrated small rhombitesseract 1.847759
bideca (old: dudeca) bidecachoron, decachoron dual, bi-apiculated pentachoron 0.816497
bidex bi-icositetradiminished hexacosachoron 1.618034
bidoctaco, {4} || co, K-4.28 square atop cuboctahedron, bidiminished octaco, square first rotunda of cytau tes 1
bidrap, K-4.8 bidiminished rectified pentachoron, antiduowedge, square - tetrahedral wedge, digonal gyrobicupolaic ring, {4} || tet, line || ortho trip 0.774597
bidsid pixhi bi-icositetra-diminished small disprismatohexacosihecatonicosachoron 5.236068
bidsrip bidiminished small rhombated pentachoron 1.183216
... bilbiro wedge ...
bimtec bimesotruncatotetracontoctachoron sqrt[3a2+4ab sqrt(2)+3b2]
bimted (old: bimtid) bimesotruncatodecachoron sqrt[(3a2+4ab+3b2)/5]
bipec biprismatotetracontoctachoron sqrt[a2+ab sqrt(2)+b2]
biped biprismatodecachoron sqrt[(2a2+ab+2b2)/5]
bipgy srit bipara(bi)gyrated small rhombitesseract, pseudo cantellated tesseract 1.847759
birgax bi-icositetra-replinished grand hexacosachoron 0.618034
biscex bistratic vertex-first cap of hexacosachoron 1.618034
biscpoxic bistratic vertex-first cap of poxic
biscrahi bistratic icosidodecahedron-first cap of rectified hecatonicosachoron 4.534568
biscrox bistratic icosahedron-first cap of rectified hexacosachoron 3.077684
biscsrico bistratic cuboctahedron-first cap of small rhombated icositetrachoron 2.613126
biscsrip bistratic trip-cap of srip, {3}-diminished small rhombated pentachoron 1.183216
bitach bitruncatocubic honeycomb, tegum sum of 2 inverted (x,y)-tichs
bitapna bitrigonal antiprismattic enenehexachoro, 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)
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]
bitefa bitegmic hecatontetracontatetrachoron, compound of 12 ico in spic army, compound of 2 kitefa 1
bithi blendic trishecatonicosachoron 2
bithit bitruncated hexadecachoric tetracomb, bitruncated demitesseractic tetracomb, runcicantic tesseractic tetracomb
bricot birectified icositetrachoric tetracomb, birectified demitesseractic tetracomb, runcic tesseractic tetracomb
... BxxFxfofx3oooxxxFFF3xBxfFxxof *b3xxBxfFfxo&#zx
... vertex figure of cellibiprismatohexateron 0.816497
... vertex figure of cellidishexateron 0.816497
cagoraht (old: gicaroht) celligreatorhombated hexadecachoric tetracomb (great cellirhombated hexadecachoric tetracomb), runcicantic icositetrachoric tetracomb
cagratit (old: gicartit) celligreatorhombated tesseractic tetracomb (great cellirhombated tesseractic tetracomb), great rhombitesseractic-prismatotesseractic tetracomb, stericantitruncated tesseractic tetracomb
cagricot (old: gicaricot) celligreatorhombated icositetrachoric tetracomb (great cellirhombated icositetrachoric tetracomb), runcicantic hexadecachoric tetracomb
capicot celliprismated icositetrachoric tetracomb, great prismatotetracontaoctachoric tetracomb
capirsit celliprismatorhombisnub ico tetracomb
capoht celliprismated demitesseractic tetracomb, tomoicositetrachoric-diprismatotesseractic 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
... longer antiduowedge, vertex figure of cellirhombated dodecateron 0.953463
caricot (old: scaricot) (small) cellirhombated icositetrachoric tetracomb, great disicositetrachoric tetracomb
cartit (old: scartit) (small) cellirhombated tesseractic tetracomb, small rhombitesseractic-prismatotesseractic tetracomb, stericantellated tesseractic tetracomb
... vertex figure of cellihemidodecateron 0.866025
chi chirohecatonicosachoron, chiral compound of 5 ico 1
chont hyperbolic (order 3) cubic-honeycomb tetracomb 0.5 i
chope cubohemioctahedron prism 1.118034
chopy, pt || cho (degenerate) cubohemioctahedron pyramid ∞   i.e. flat in euclidean space
... augmented axially-octahedral ursachoron ofxo3xooo4oooo&#xt ...
coaescu, co || escu, K-4.62 cuboctahedron atop elongated square cupola 1.447009
coaop, co || op, K-4.63 cuboctahedron atop octagonal-prism 1.447009
coasirco, co || sirco, K-4.61 cuboctahedron atop small rhombicuboctahedron 1.447009
coatic, K-4.129 cuboctahedron atop truncated cube, cuboctahedral cap of small rhombated icositetrachoron 2.613126
coaticbicu coatic bicupola
coatobcu coatoe bicupola, equatorially contracted rectified icositetrachoron
coatoe, co || toe, K-4.95 cuboctahedron atop truncated octahedron, cuboctahedral cap of rectified icosatetrachoron 1.732051
coatotum bistratic co-cap of prip, tut-diminished prip, Stott expansion of tip, (co,toe)-based tutsachoron, (co,toe)-based tutism 1.612452
coatut, co || tut, K-4.48 cuboctahedron atop truncated tetrahedron, cuboctahedral cap of small rhombated pentachoron 1.183216
coatutu expanded axially-tetrahedral ursachoron, (co,tut)-based ursulate 1.328131
cont tetracontoctachoron, octagonny, bitruncated icositetrachoron 3.414214
contit tetracontoctachoric tetracomb, lamina-truncate of hyperbolic o3x4x3o8o tesselation 0.594604 i
cope, K-4.43 cuboctahedron prism 1.118034
copy, pt || co (degenerate) cuboctahedron pyramid ∞   i.e. flat in euclidean space
coqroc tetracontoctiquasirhombated tetracontoctachoron 1.325654
cotcope cuboctatruncated-cuboctahedron prism, cubitruncated-cuboctahedron prism 1.414214
croc tetracontoctirhombated tetracontoctachoron 3.200413
cubaco, cube || co, K-4.35 cube atop cuboctahedron, cubical cupola 1.031784
cubaike, cube || ike, K-4.21 cube atop icosahedron 1
cubasirco, cube || sirco, K-4.71 cube atop small rhombicuboctahedron, cubical cap of small disprismatotesseractihexadecachoron 1.485633
cubatic, cube || tic (degenerate) cube atop truncated cube ∞   i.e. flat in euclidean space
... pyrithohedral cube-doe-bilbiro honeycomb
cubpy, K-4.26 cubical pyramid, vertex-pyramid of ico 1
cute (old: cubdipy) cubical (line-)tegum, cubical bipyramid ...
cydadex cyclical decadiminishing of ex 1.618034
cypit cyclopentachoric tetracomb, pentachoric-dispentachoric tetracomb, Delone complex of lattice A4
cytau tes cyclotetraaugmented tesseract, cyclotetradiminished icositetrachoron 1
cyte cubau sodip cyclotetra cubaugmented sodip ...
cyte gysrit cyclotetragyrated small rhombitesseract 1.847759
cyte opau sodip cyclotetra octagon-prism-augmented sodip ...
cyted spic cyclotetradiminished small prismatotetracontoctachoron 1.847759
cyted srit cyclotetradiminished small rhombitesseract, cyclotetraugmented octagonal duoprism 1.847759
cythdex cyclical triangularily-hexagonally diminished hexacosachoron 1.618034
cytid rico cyclotridiminished rectified-icositetrachoron, metatridiminished rectified-icositetrachoron 1.732051
cytid srico cyclotridiminished small rhombated icositetrachoron 2.613126
cytopit cyclotruncated pentachoric tetracomb, small truncated-pentachoric tetracomb
dahi dishecatonicosachoron 3
dahiquatady dishecatonicosiquasitruncated dishecatonicosachoron 4.134026
dahitady dishecatonicositruncated dishecatonicosachoron 2.431014
damibdrox deep metabidiminished rectified hexacosachoron 3.077684
dapabdi poxic (alt.: hau sircope) deep parabidiminished poxic, hexa-augmented sircope
dapabdi spic deep parabidiminished small prismatotetracontoctachoron, hexa-gyro-augmented truncated-cube prism 1.847759
dappip, K-4.96 decagonal-antiprism prism 1.747560
dard tipady diretroditetrahedronary prismatodishecatonicosachoron 1.414214
dastop dodeca-star toroidi-prism 0.707107
... dastop + 2x 2did (?) 0.707107
datap ditetrahedronary prismatochoron, compound of 100 hiddip 1.414214
datcathi ditetrahedronary coincidic trishecatonicosachoron 1.414214
dattady ditetrahedronary dishecatonicosachoron 1.414214
dattathi ditetrahedronary trishecatonicosachoron 1.414214
... DCBAVFfxoo xxxFofxFVo3xoxxFxooxo5ofxooxFfoV&#zx
deca decachoron, bitruncated pentachoron, equatorial cross-section of (vertex first) q-pent 1.414214
dedip (old: dadip) decagon-decagon duoprism 2.288246
... vertex figure of dodecabiprismatohemidodecateron 0.866025
... did atop 3doe (?) 1.414214
dida raded, did || raded dodecadodecahedron atop rhombidodecadodecahedron 1.336349
didadoe did atop doe 1.414214
didamibdrox diminished deep metabidiminished rectified hexacosachoron 3.077684
diddatigid, did || tigid dodecadodecahedron atop truncated great dodecahedron, did-first cap of sirfix 4.352502
diddip dodecadodecahedron prism 1.118034
didhi dodecahedronary dishecatonicosachoron 1
didpy, pt || did (degenerate) did pyramid ∞   i.e. flat in euclidean space
dihipap dyad-hexagonal prismantiprismoid, s2s2s6x, edge-alternated sitwadip ...
... mono-diminished vertex-first rotunda of hexacosachoron 1.618034
... diminished thawro-wedged 1/6-luna of hexacosachoron, {6},ike-wedge, ike,thawro,thawro-multiwedge ...
dippit disprismatotesseract 1.485633
diquitdi disicositetraquasitruncated disicositetrachoron 1.608038
dirico diminished rectified icosatetrachoron 1.732051
disdi disnub disicositetrachoron 1
dispap dyad-square prismantiprismoid, s2s2s4x, edge-alternated sodip ...
distadedip decagon-decagram duoprism 1.732051
ditdap digon-triangle duoantiprism, hemiated shiddip sqrt[A2/2+B2]
ditdi disicositetratruncated disicositetrachoron 2.326846
ditdidap ditrigonary-dodecadodecahedron antiprism 0.951057
ditdiddip ditrigonal-dodecadodecahedron prism 1
dithix ditrigonary hecatonicosihexacosichoron 1.732051
dittadphi ditetrahedronary disprismatohecatonicosachoron 1.414214
dittady ditrigonary dishecatonicosachoron 1
... dittady+dox (?) 1
dittafady ditetrahedrofissary dishecatonicosachoron 1.414214
ditusna disicosahedronary tetrasnubbachoron, compound of 20 ex in rahi army, compound of 2 kidisna 1.618034
doaid, doe || id, K-4.77 dodecahedron atop icosidodecahedron, dodecahedral cupola 1.618034
doasrid, doe || srid, K-4.152 dodecahedron atop small rhombicosidodecahedron, dodecahedral cap of small disprismatohexacosihecatonicosachoron 5.236068
doasridaid doe atop srid atop id
doc distetracontoctachoron 2.449490
dod honho disoctidishemioctintercepted hemioctachoron 1
... rico-derived polychoron incorporating does 2.802517
..., doe || 6-dim-id || f-ike || doe axially-pyritohedral (2,24,12,6)-diminishing of ex 1.618034
doh honho disoctihemihexadekintercepted hemioctachoron 1
dohitipady dishecatonicositruncated prismatodishecatonicosachoron 4.472136
dope, K-4.74 dodecahedron prism 1.487792
dopix dodecahedronary prismatohexacosachoron, compound of 60 spid 1
dox (old: gex) dodecahedronary hexacosachoron (great hexacosachoron), compound of 25 ico 1
duhd decahemidecachoron, copyropodichoron 1
duspid small-prismated-decachoron dual, crystalic icosachoron
dutip truncated-pentachoron dual, apiculated pentachoron, tetrakis pentachoron
dygytpuf, K-4.13 dyadic gyrotegmipucofastegium, 3-prism atop reflected ortho 3-prism 0.866025
ebdah hithi exoblendic dishemihecatonicostrishecatonicosachoron 2
ebuthi exotic blendic tetrishecatonicosachoron 2
ecubedpy elongated cubical bipyramid, hexadiminished icositetrachoron 1
ecubpy elongated cubical pyramid, heptadiminished icositetrachoron 1
efdit xithi exofissary ditrigonal hexacositrishecatonicosachoron 1.732051
eikedpy elongated icosahedral bipyramid
eikepy elongated icosahedral pyramid
eocta sirco elongated octasirco ...
eoctaco elongated octaco
eoctatut elongated octatut
eoctpy elongated octahedral pyramid, diminished pex hex
epipdapy elongated pentagonal-prismatic bipyramid ...
epippy elongated pentagonal-prismatic pyramid ...
escupe, K-4.68 elongated-square-cupola prism 1.485633
esircoatic elongated sircoatic, diminished srit
esquippidpy elongated square-pyramidal bipyramid, esquidpy-wedge, half of partially (mono-)expanded hex
esquipuf elongated square pucofastegium, square atop octagon-prism atop octagon-prism
esquipyp elongated square-pyramidal-prism, elongated-square-pyramid prism, external blend of square-pyramidal prism and tesseract
etedpy elongated tetrahedral bipyramid
etepe elongated tetrahedral-prism, elongated-triangular-pyramid prism, external blend of tetrahedral prism and (triangle,square)-duoprism
etepy elongated tetrahedral pyramid
etetaco elongated tetaco ...
etripdapy elongated trigonal-prismatic bipyramid ...
etrippy elongated trigonal-prismatic pyramid ...
etripuf elongated trigonal pucofastegium ...
etutatoe elongated tutatoe ...
... ex+fix (?) 1.618034
... ex+gohi+120id (?) 1.618034
ex, pT hexacosachoron, 600-cell, hydrochoron, tetraplex, polytetrahedron 1.618034
... FAxoAFxoxx3FxAAoxFxox oxofofxFof3ooxofxfoFf&#zx
... FAxoFFxoox3foFFxofoxo oxofofxFof3ooxofxfoFf&#zx
... FAxoFFxxox3foFFxofxxo oxofofxFof3ooxofxfoFf&#zx
... FAxoFFxxox3foFFxofxxo xoxFxFoAxF3oxxofxFoFf&#zx
... vertex figure of facetospinopenteractidishexadecateron 0.919866
... Ffxo oxFx3xfox5xoxx&#zx
... Ffxo xofo3ofox5xoxx&#zx
... vertex figure of facetoinverted decahexadecateron 0.919866
firgaghi faceted rectified great grand hecatonicosachoron 1.070466
firgogishi facetorectified great grand stellated hecatonicosachoron 0.661585
firp faceted rectified pentachoron, retropyrohemiperichoron, vertex figure of dah, tetrahedral cuploid 0.774597
... firp+rap+15{4} (?) 0.774597
firsashi faceted rectified small stellated hecatonicosachoron 2.802517
firt facetorectified tesseract 1.224745
... fix+gahi+120id (?) 1.618034
fix, pI icosahedral hecatonicosachoron, faceted hexacosichoron, polyicosahedron 1.618034
... fooo3xxoF3xfxo *b3oxFo&#zx
... triacontapenta-diminished hexacosachoron, fooo5ofxo xofx5oxox&#zx 1.618034
frico facetorectified icositetrachoron 1.732051
frogfix faceted rectified great faceted hexacosichoron 0.726543
frox faceted rectified hexacosichoron 3.077684
... frox+600 2thah (?) 3.077684
fry facetorectified hecatonicosachoron 4.534568
... dodeca-diminished equatorial tetrastratic segment of rox 3.077684
... Fxo oxf3xox5xfo&zxt
... equatorial tetrastratic segment of rectified hexacosachoron 3.077684
... Fxox3xoxf3oFxx *b3oxfo&#zx
... Fxxox5ofxfo xofox5oxofx&#zx
... Fxxx3xxoF3xfxo *b3oxFo&#zx
... Fxxx5ofxo xofx5oxox&#zx
gabbadipady great blendic disprismatodishecatonicosachoron 2
gabbathi great blendic trishecatonicosachoron 2
... vertex figure of great biprismatodiscellipenteract 1.118034
gabippady (old: gabbippady) great blendic prismatodishecatonicosachoron 2
gabred great birhombatodecachoron sqrt[(2a2+2ab+3b2)/5]
gabric great birhombatotetracontoctachoron sqrt[a2 + 2 sqrt(2) ab + 3b2]
gacdupthix small capped dipentary tetrishecatonicosahexacosichoron 1.328131
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
gadatady grand ditetrahedral dishecatonicosachoron 0.874032
gadathiphi grand ditetrahedronary hecatonicosaprismatohecatonicosachoron 0.874032
... 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
gaddip great-dodecahedron prism 1.074481
gaddit thix grand ditrigonal trishecatonicosihexacosachoron 1.732051
... vertex figure of great dispinocellirhombated penteract 0.907821
gadixady great dishexacosadishecatonicosachoron 3.139124
gadixhix (old: gixhix) great dodecahedronary hexacosahemihexacosachoron, compound of 25 ihi (but not sadixhix) 1
gadpy great-dodecahedral pyramid, vertex cap of fix 1.618034
gadsadox great disnub dihexacosachoron 0.726543
gadtap great ditetrahedronary prismatochoron, compound of 36 stadidip 0.874032
gadtaxady grand ditetrahedronary hexacosadishecatonicosachoron 0.874032
gadtaxhi great ditetrahedronary hexacosihecatonicosachoron 0.874032
gadtef pixady great ditetrahedronary exofissary prismatohexacosadishecatonicosachoron 0.874032
gadtifady (old: gadtafady) great ditetrahedronarofissary dishecatonicosachoron 0.874032
gaedit pathi grand exoditetrahedronary prismatotriakishecatonicosachoron 0.874032
... vertex figure of great facetosphenary penteract 0.776106
... gaghi+didhi (?) 1
... gaghi+idhi (?) 1
... gaghi+paphacki+sridaphi (?) 1
... gaghi+sridixhi (?) 1
gaghi, gapD great grand hecatonicosachoron, greatened aggrandized polydodecahedron 1
gahfipto great hexadecafeceted prismatotesseractioctachoron 0.890446
... gahi+gohi (?) 1.618034
gahi, apD grand hecatonicosachoron, aggrandized polydodecahedron 1.618034
ganbathi great spinoblendic trishecatonicosachoron 2
ganbippady great spinoblendic prismatodishecatonicosachoron 2
... vertex figure of great spinocelliprismated penteract 0.920055
gap great antiprism, grand antiprism, pentagonal double antiprismoid (but not: great duoantiprism), bicyclical decadiminishing of ex 1.618034
... dual of great antiprism ...
gapript great pseudorhombated prismatotesseract 0.765367
... gapript+16 2thah (?) 0.765367
gapthi grand prismatotriakishecatonicosachoron 2.400819
gaqri great quasirhombated icositetrachoron 1.230739
gaqrigafix great quasirhombated great faceted hexacosachoron 1.080363
gaqrigaghi great quasirhombated great grand hecatonicosachoron 1.679184
gaqrigagishi great quasirhombated great grand stellated hecatonicosachoron 1.179024
gaqrigashi great quasirhombated great stellated hecatonicosachoron 2.700333
gaqrigohi great quasirhombated great hecatonicosachoron 2
gaqript grand quasirhombated prismatotesseract 0.765367
gaqrisashi great quasirhombated small stellated hecatonicosachoron 5.018002
gaqrit great quasirhombated tesseract 1.401594
gaquapac great quasiprismatotetracontoctachoron 1.127864
gaquatiddip great-quasitruncated-icosidodecahedron prism 1.136572
gaquidapixhi great quasidisprismatohexacosihecatonicosachoron 1.581630
gaquidipdy grand quasidisprismatodishecatonicosachoron 1.695697
gaquidphihi great quasidisprismatohecatonicosihecatonicosachoron 4.242641
gaquidpoth great quasidisprismatotesseractihexadecachoron 1.938391
gaquipadah great quasiprismatodishexadecachoron 0.890446
garawv hixhi great retrosphenoverted hecatonicosihexacosihecatonicosachoron 1.054256
gard tadhix grand retroditetrahedronary dishecatonicosihexacosachoron 0.874032
gardatady grand retroditetrahedral dishecatonicosachoron 0.874032
... gardatady+1440{5} 0.874032
gardatathi grand retroditetrahedronary trishecatonicosachoron 0.874032
gardtapaxhi grand retroditetrahedronary hexacosidishecatonicosachoron 0.874032
gardtaxady grand retroditetrahedronary hexacosidishecatonicosachoron 0.874032
garpit grand rhombated dishexadecachoron 1.847759
garpop grand rhombated prismatopentachoron 1.183216
gashi, aspD grand stellated hecatonicosachoron, aggrandized stellated polydodecahedron 0.618034
... vertex figure of great pteroprismated penteract 0.837186
... gax+gashi+120gid (?) 0.618034
... gax+gofix (?) 0.618034
gax, apT grand hexacosachoron, aggrandized polytetrahedron 0.618034
geedatepthi great exoditetrahedrary prismatotrishecatonicosachoron 1.414214
gefdit dixdy great exofissary ditrigonal dihexacosadihecatonicosachoron 1.732051
gefidtethi great exofissary ditetrahedronary tetrakishecatonicosachoron 0.874032
gefirdit xethi great exofissary retroditetrahedronary hexacositrishecatonicosachoron 1.414214
gefradit thix great exofissary retroditetrahedronary triakishecatonicosihexacosachoron 0.874032
gefridit xethi great exofissary retroinverted ditetrahedronary hexacositrishecatonicosachoron 1.414214
getit dixady great tritrigonal dihexacosidihecatonicosachoron 1.136572
getit phiddix great tritrigonal prismatohecatonicosidishexacosachoron 1.136572
getit pixady great tritrigonal prismatohexacosidihecatonicosachoron 1.136572
getit thix great tritrigonal trishecatonicosihexacosachoron 1.136572
getit xethi great tritrigonal hexacositrishecatonicosachoron 1.136572
ghahoh great hexadecahemihexadecachoron 1
ghihi great hecatonicosihecatonicosachoron 0.854102
ghipady great hecatonicosiprismatodishecatonicosachoron 4.087567
gibricot great birhombated icositetrachoric tetracomb, great grand prismatodisicositetrachoric tetracomb
gic great tetracontoctachoron, octagrammy 0.585786
gichado great cubihexadecadisoctachoron 1.174172
gico great icositetrachoron, stella prismata, compound of 3 tes 1
... gico+8co+16 2thah (?) 1
gid thipady great ditrigonary hecatonicosiprismatodishecatonicosachoron 4.087567
gid tipathi great ditrigonal prismatotriakishecatonicosachoron 2.920251
gidard tipady great diretroditetrahedronary prismatodishecatonicosachoron 1.414214
giddatady great ditetrahedronary dishecatonicosachoron 1.414214
giddic great distetracontoctachoron 0.765367
giddip great-icosidodecahedron prism 0.794963
giddit thix great ditrigonal trishecatonicosihexacosachoron 1.732051
gidditdiddip great-ditrigonary-dodekicosidodecahedron prism 1.239546
gidditdy great ditrigonary dishecatonicosachoron 1.732051
gidditpix great ditrigonary prismatohexacosichoron 1.732051
gidhiquit paddy great dishecatonicosaquasitruncated prismatodishecatonicosachoron 2.140933
gidipthi great dipental trishecatonicosachoron 1.328131
gidpith great disprismatotesseractihexadecachoron, great prismated tesseract, omnitruncated tesseract 3.498949
gidpixathi great dipentagonal hexacositrihecatonicosachoron 1.328131
gidpixhi great disprismatohexacosihecatonicosachoron, omnitruncated hecatonicosachoron, omnitruncated hexacosachoron 12.786651
gidriddip great-dirhombicosidodecahedron prism, great-snub-disicosidisdodecahedron prism, prism of Miller's monster 0.866025
gidthidy hi great ditrigonal hecatonicosadishecatonicosihecatonicosachoron 1.732051
gidthixhi great ditrigonary hecatonicosihexacosihecatonicosachoron 3.139124
gidtidap great-ditrigonary-icosidodecahedron antiprism 0.951057
gidtiddip great-ditrigonary-icosidodecahedron prism 1
gidtixhi great ditrigonary hexacosihecatonicosachoron 1
... gidtixhi+dox (?) 1
gifdahihox great fissary dodecahedronary hecatonicosihemihexacosachoron 1
giidip great-icosicosidodecahedron prism 1.239546
gik vadixady great skewverted dishexacosidishecatonicosachoron 2.013884
gik vipathi great skewverted prismatotriakishecatonicosachoron 2.828427
gik vixathi great skewverted hexacositriakishecatonicosachoro 2.013884
gikagid, gike || gid great icosahedron atop great icosidodecahedron, great icosahedral cap of rectified grand hexacosachoron, great-icosahedral cupola 0.726543
gikepy great-icosahedral pyramid, vertex cap of gax 0.618034
gikkiv datapixady great skewverted ditrigonary prismatohexacosadishecatonicosachoron 2.013884
gikviphado great skewverted prismatohexadecadisoctachoron 1.414214
... vertex figure of great prismated biprismatopenteract 0.837186
gipdohiny great pental dishecatonicosaintercepted hecatonicosachoron 0.726543
gipe great-icosahedron prism 0.771681
giphado great prismatohexadecadisoctachoron 1.082392
giphatit great prismated demitesseractic tetracomb, great diprismatodemitesseractic tetracomb, steriruncicantic tesseractic tetracomb
giphiddix great prismatohecatonicosadishexacosachoron 1.624598
giphidy great prismated hecatonicosadishecatonicosachoron 1.348948
giphihix great prismatohecatonicosahecatonicosahexacosachoron 1.893038
giphixhi great prismatohecatonicosihexacosihecatonicosachoron 2.920251
gippapivady great pentagrammal antiprismatoverted dishecatonicosachoron 0.726543
gippic great prismatotetracontoctachoron, omnitruncated icositetrachoron 5.169905
gippict great prismated icositetrachoric tetracomb
gippid great prismatodecachoron, omnitruncated pentachoron, Voronoi cell of lattice A4* 2.236068
gippittit great prismated tesseractic tetracomb, great diprismatotesseractic tetracomb, runcicantitruncated tesseractic tetracomb
gippixady great prismatohexacosadishecatonicosachoron 1.207883
gippixhihy great prismatohexacosihecatonicosihecatonicosachoron 1.021064
giprapivady great pentagonal retroprismatoverted dishecatonicosachoron 1.902113
gipriphi great pseudorhombated prismatohecatonicosachoron 0.799575
... gipriphi+600 2thah (?) 0.799575
gipthi great prismatotriakishecatonicosachoron 3.531591
gipti great prismatotriakisicositetrachoron 1.938391
giqragashi great quasirhombated grand stellated hecatonicosachoron 2
girc great retrotetracontoctachoron 0.765367
gircope, K-4.125 great-rhombicuboctahedron prism 2.370932
girfaddic great retrofrustic distetracontoctachoron 1.414214
girfix great rhombated faceted hexacosachoron 7.404918
girfixthi great retrofrustic hexacositrishecatonicosachoron 2.236068
girpdi great rhombiprismic disicosatetrachoron 1.938391
girpdo great rhombiprismatodisoctachoron 1.174172
girpith great rhombiprismated tesseractihexadecachoron 1.082392
girpixhi great rhombiprismic hexacosahecatonicosachoron 1.021064
girsiddip great-(inverted)-retrosnub-icosidodecahedron prism
gisdiddip great-snub-dodekicosidodecahedron prism
gisdipthi great stellated dipental trishecatonicosachoron 1.328131
... gishi+gashi (?) 0.618034
gishi, gspD great stellated hecatonicosachoron, greatened stellated polydodecahedron 0.618034
gisiddip great-inverted-snub-icosidodecahedron prism
gisp great swirlprism 0.618034
gissidagid, gissid || gid great stellated dodecahedron atop great icosidodecahedron, great stellated dodecahedral cupola 0.692924
gissidagike great stellated dodecahedron antiprism, great icosahedron antiprism, taller great stellated dodecahedron atop great icosahedron 0.662791
gissiddip great-stellated-dodecahedron prism 0.732444
gissidpy great-stellated-dodecahedral pyramid, vertex cap of gaghi 0.591923
gissidragike great stellated dodecahedron retroprism, great icosahedron retroprism, narrower great stellated dodecahedron atop great icosahedron 0.618034
git thixady great tritrigonal hecatonicosihexacosidishecatonicosachoron 1.136572
gitphi great tripesic hecatonicosachoron 0.874032
gitpodady great (intersected) tripesic dodecahedronary dishecatonicosachoron 1
gittifcoth great tesseractifaceted cubitesseractihexadecachoron 0.890446
gittith great tesseractitesseractihexadecachoron 0.890446
gixathi great hexacositriakishecatonicosachoron 3.804226
gixhi great hexacosihecatonicosachoron 1.244649
gixhidy great hexacosihecatonicosadishecatonicosachoron 1.464888
gixhihy great hexacosihecatonicosihecatonicosachoron 0.763932
gixipady great hexacosiprismatodishecatonicosachoron 1.624598
gnappoth great spinoprismatotesseractihexadecachoron 0.890446
goccope great-cubicuboctahedron prism 0.890446
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
gogishi, gaspD great grand stellated hecatonicosachoron, greatened aggrandized stellated polydodecahedron 0.540182
gohi, gpD great hecatonicosachoron, greatened polydodecahedron 1.618034
gohihix great hecatonicosihecatonicosihexacosachoron 1.464888
gohiny great hecatonicosintercepted hecatonicosachoron 0.661585
gondip great octagonal spinoduoprism 0.890446
goquidipdy great quasidisprismatodishecatonicosachoron 6.566933
gosiddip great-snub-icosidodecahedron prism
gotdatixhi great toroidoditrigonary hexacosihecatonicosachoron 1.732051
gotditpix great toroidoditrigonary prismatohexacosichoron 1.732051
gotto great trisoctachoron, great triakisoctachoron 1.224745
grad tathi great retroditetrahedronary trishecatonicosachoron 1.414214
graggix great rhombated grand hexacosachoron 1.658546
graghi great rhombated grand hecatonicosachoron 4.550627
grahi great rhombated hecatonicosachoron, cantitruncated hecatonicosachoron 11.252107
graphi grand retropental hecatonicosachoron 0.726543
grawv ditathi great retrosphenoverted ditrigonary triakishecatonicosachoron 2.093315
grawv hidy great retrosphenoverted hecatonicosadishecatonicosachoron 1.589926
grawv hixhi great retrosphenoverted hecatonicosihexacosihecatonicosachoron 1.513868
grawvathi great retrosphenoverted triakishecatonicosachoron 2.572554
grawvixady great retrosphenoverted hexacosadishecatonicosachoron 2.036148
grico great rhombated icositetrachoron, cantitruncated icositetrachoron 4.299451
gricot great rhombated icositetrachoric tetracomb, great prismatodisicositetrachoric tetracomb
..., xFoFx3xxxxx5xofox&#xt   (F=ff=x+f) bilunabirotundic great rhombicosidodecahedron prism
gridaphi great retroinverted dodecahedronary prismatohecatonicosachoron 1
griddip, K-4.150 great-rhombicosidodecahedron prism 3.835128
gridixhi great retroinverted dodecahedronary hexacosahecatonicosachoron 1
gridtathi great retroinverted ditetrahedronary trishecatonicosachoron 1.414214
grip great rhombated pentachoron, cantitruncated pentachoron 1.843909
gripady great rhombiprismic dishecatonicosachoron 1.207883
griphi great retropental hecatonicosachoron 1.175571
grit great rhombated tesseract, cantitruncated tesseract 3.005916
grittit great prismatotesseractic tetracomb, cantitruncated tesseractic tetracomb
grix great rhombated hexacosachoron, cantitruncated hexacosachoron 9.124101
gudap (old: gedap) great duoantiprism, (old: great double antiprism) (but not: great antiprism) 1
guti great tetrakisicositetrachoron 2.326846
gwav ditathi great sphenoverted ditrigonary triakishecatonicosachoron 2.036148
gwavathi great sphenoverted triakishecatonicosachoron 1.027486
gwavixady great sphenoverted hexacosadishecatonicosachoron 0.799575
gyautisdip gyro-augmented 3-4-duoprism ...
gybeffip gybef prism
gyepipa pero, K-4.140 gyroelongated pentagonal pyramid atop pentagonal rotunda 3.077684
gyepippip gyroelongated-pentagonal-pyramid prism 1.074481
gypasp great pyramidic swirlprism 0.618034
gyprip gyrated prip 1.612452
gyspid (alt: tetacobcu) gyrated small prismatodecachoron, orthobicupola of runcinated pentachoron, tetaco orthobicupola 1
haddet demidistesseract, compound of 2 hex 0.707107
hadedip hexagon - decagon duoprism 1.902113
haf, K-4.46 hexagonal antifastegium, hexagon - hap wedge, {6} || gyro hip 1.130454
hagy gircope hexa-gyro-augmented gircope
happip, K-4.53 hexagonal-antiprism prism 1.197085
hatho hemitesseractihemioctachoron 0.707107
hau gircope hexa-augmented gircope
hau ticcup hexa-(ortho-)augmented ticcup
haucope hexa-augmented cope
hautope hexa-augmented tope
... external blend of the hebesphenomegacorona-prism and a cube-pyramid, cubic-pyramid-augmented hebesphenomegacorona-prism
hedip heptagonal-heptagonal duoprism 1.629715
... hex+8oct (?) 0.707107
hex, K-4.2 (alt: octit, trapt) hexadecachoron, tetracross4), 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
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 3.702459
... hi dimpled in by 120 ikadoes ...
hibbit hexagonal duoprismatic tetracomb, Voronoi complex of bihexagonal lattice A2×A2
hiddip hexagonal-hexagonal duoprism, Voronoi cell of lattice A2×A2 1.414214
hidhi hecatonicosa-diminished hecatonicosachoron 3.702459
hidicau pretasto hexadeca-diminished icositetra-augmented pentagonorhombic-trisnub-trisoctachoron
hihiquatady hecatonicosihecatonicosiquasitruncated dishecatonicosachoron 3.605551
hinhi hecatonicosintercepted hecatonicosachoron 2.802517
hinnit hexadekintercepted tesseract 1.224745
hippyp hexagon-pyramidal prism, line || hip ∞   i.e. flat in euclidean space
histodip hexagon - octagram duoprism 1.137055
... vertex figure of hexadecateron 0.774597
hitte hyperbolic (order 3) hecatonicosachoric tetracomb 2.301105 i
hitwadip hexagon - dodecagon duoprism 2.175328
hixady hecatonicosihexacosidishecatonicosachoron 3
hixquathix hecatonicosihexacosaquasitruncated hecatonicosihexacosachoron 2.174739
hixquitixhi hecatonicosihexacosiquasitruncated hexacosihecatonicosachoron 2.351141
hixquitphix hecatonicosihexacosiquasitruncated prismatohecatonicosihexacosachoron 2.483382
hixtaphix hecatonicosihexacositruncated prismatohecatonicosihexacosachoron 7.735167
hixthix hecatonicosihexacositruncated hecatonicosihexacosachoron 6.186316
hixtixhi hecatonicosihexacositruncated hexacosihecatonicosachoron 3.804226
hocucup hollow cubic cupoliprism, six tepe blend, "coord-planes squares star" atop "coord-planes squares star" 0.790569
hoddated ex (shallow-)hexa-octa-diminished deep-tetra-diminished hexacosachoron 1.618034
hodho hexadecoctidishemioctachoron 1
hodip hexagon - octagon duoprism 1.645329
hog dhidicup hollow gidhid cupoliprism 0.732444
hoh honho hexadecoctihemihexadekintercepted hemioctachoron 1
hohoh hexadecoctihemihexadecachoron 1
hossdap hollow small stellated dodecahedral antiprism, pseudo sissid atop pseudo sissid 0.707107
... hossdap + 2 2sissid (?) 0.707107
hot thibbit hexagonal-omnitruncated-trihexagonal duoprismatic tetracomb
... vertex figure of hexadecasphenohexadecateron 0.957427
huhoh hexadecahemihexadecachoron 1
icau pretasto icositetra-augmented pentagonorhombic-trisnub-trisoctachoron
icau prissi icositetra-augmented prismatorhombisnub icositetrachoron
ico icositetrachoron, 24-cell, xylochoron, octaplex, rectified hexadecachoron, birectified tesseract, 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
... 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
... id - srid - F-ike - ti tower, thawro'd rox ...
idasrid, id || srid, K-4.131 icosidodecahedron atop small rhombicosidodecahedron, icosidodecahedron cupola, ike-first supra-cap of rox 3.077684
idasridati id atop srid atop ti
idati, id || ti, K-4.158 icosidodecahedron atop truncated icosahedron, icosidodecahedral cap of small rhombated hexacosachoron 6.073594
iddip, K-4.90 icosidodecahedron prism 1.693527
idhi invertidodecahedronary hecatonicosachoron 1
ididdip icosidodecadodecahedron prism 1.414214
idim sidpixhi icosa-diminished small disprismatohexacosihecatonicosachoron 5.236068
idimex spid-diminished ex, icosidiminished ex 1.618034
idimsrahi icosa-diminished small rhombated hecatonicosachoron 6.735034
idimsrix icosa-diminished small rhombated hexacosachoron 6.073594
idprahi icositetra-diminished prismatorhombated hecatonicosachoron 8.278950
idprix icositetra-diminished prismatorhombated hexacosachoron 9.744610
idsid pixhi icositetra-diminished small disprismatohexacosihecatonicosachoron 5.236068
idsrahi icositetra-diminished small rhombated hecatonicosachoron 6.735034
idsrix icositetra-diminished small rhombated hexacosachoron 6.073594
idtiddip icosidodecatruncated-icosidodecahedron prism, icositruncated-dodecadodecahedron prism 2.061553
ihi icositetrahemiicositetrachoron 1
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
ikadoe (alt.: ikap), ike || doe, K-4.78 icosahedron atop dodecahedron, icosahedral antiprism, dodecahedral antiprism, segment of vertex-first hexacosachoron 1.618034
ikaid, ike || id, K-4.137 icosahedron atop icosidodecahedron, icosahedral cap of rectified hexacosachoron, icosahedral cupola 3.077684
... (1,0,8,12,0)-diminished vertex-first-rotunda of ex, (subsymmetrical) icosiena -diminished vertex-first rotunda of hexacosachoron 1.618034
... (1,0,4,12,0)-diminished vertex-first-rotunda of ex, heptadeca-diminished vertex-first rotunda of hexacosachoron 1.618034
ikepy, K-4.84 icosahedral pyramid, vertex cap of hexacosachoron 1.618034
iktum bistratic icosahedron-first cap of truncated hexacosachoron, ike-based tutsatope, ike-based tutism 4.643523
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
ini icositetrintercepted icositetrachoron 1.732051
inpac icositetraintercepted prismatotetracontaoctachoron 1.847759
... inpac+72{4} (?) 1.847759
ipe, K-4.36 icosahedron prism 1.074481
ipixady invertopental hexacosadishecatonicosachoron 3.077684
iquatoc icositetraquasitruncated tetracontoctachoron 2
iquatpic icositetraquasitruncated prismatotetracontoctachoron 2.828427
iquipadah inverted quasiprismatodishexadecachoron 1.485633
... vertex figure of invertiretrolepidoteron 0.912871
... vertex figure of invertiretrohexadecalepidohemipenteract 0.912871
isdiddip inverted-snub-dodecadodecahedron prism
ite (old: it, older: ikedpy) (line-)ikosahedron-tegum, icosahedral bipyramid
... vertex figure of spikifacetospinodishexadecateron 0.951190
kavahto skewverted hexadecatrisoctachoron 1.414214
kavipathi skewverted prismatotrishecatonicosachoron 2.828427
kaviphdit skewverted prismatohexadecadistesseract 1.414214
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
lifpipixhi polar facetopental prismatohexacosahecatonicosachoron 3.077684
... lamina-truncate of hyperbolic x3x4x338o tesselation 1.864101 i
... great-rhombated-pentachoron dual
... small-rhombated-pentachoron dual
mabred medial birhombatodecachoron sqrt[(2a2+2ab+3b2)/5]
mabric medial birhombatotetracontoctachoron sqrt[a2 + 2 sqrt(2) ab + 3b2]
mardatathi medial retroditetrahedral triakishecatonicosachoron 1.414214
mesdi medial snub disicositetrachoron 1
mibdiadoe, mibdi || doe, K-4.82 metabidiminished icosahedron atop dodecahedron, metabidiminished segment of vertex-first hexacosachoron 1.618034
mibdip metabidiminished-icosahedron prism 1.074481
mibdipy, K-4.87 metabidiminished-icosahedral pyramid 1.618034
mibdirit metabidiminished rectified tesseract, wedge-diminished rectified tesseract, bistratic cuboctahedron based wedge 1.224745
middit thix medial ditrigonal trishecatonicosihexacosachoron 1.732051
mif pixady circumfacetopental hexacosadishecatonicosachoron 0.726543
mipthi medial prismatotriakishecatonicosachoron 3.199386
mix medial hexacosachoron, mete-star, compound of 120 pen 0.632456
mohiny medial hecatonicosintercepted hecatonicosachoron 1.070466
mrawv hixhi medial retrosphenoverted hecatonicosihexacosihecatonicosachoron 3.963358
mriphi medial retropental hecatonicosachoron 1.902113
n,m-dip n-gon - m-gon duoprism sqrt[1/(4 sin2(π/n))+1/(4 sin2(π/m))]
n,n-dip n-gon - n-gon duoprism 1/(sqrt(2)*sin(π/n))
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))]
n-appip, K-4.176 n-antiprism prism sqrt[(5-4 cos(π/n))/(8-8 cos(π/n))]
n-appy n-antiprismatical pyramid sqrt[(2-2 cos(π/n))/(5-6 cos(π/n))]
n-apt (line-)n-antiprismatic tegum, n-antiprismatic bipyramid, n-pyramidal antiprism
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))]
... n-fold dissected cubic polytwister, n-fold dissected cubiter, cubiswirlic 6n-choron ...
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))]
n-cufbil n-gonal cupofastegia biluna
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))]
... n-fold dissected dodecahedron polytwister, n-fold dissected doter, dodecaswirlic 12n-choron ...
... n-fold dissected great-dodecahedral polytwister, n-fold dissected gaditer, great-dodecaswirlic 12n-choron ...
n-gytpuf n-gonal gyrotegmicupolafastegium, n-cupola atop inverted gyrated n-cupola, 2n-prismatic gyrated bi-wedge
... n-fold dissected icosahedral polytwister, n-fold dissected ikter, icosaswirlic 20n-choron ...
... (n,m)-double antiprismatoid ...
n-m-det (n,m)-ditetragoltriate ...
... n-fold dissected octahedral polytwister, n-fold dissected octer, octaswirlic 8n-choron ...
n-pidpy n-prismatic bipyramid
n-pipy n-prism pyramid, general vertex pyramid of o-3-x-3-o-n-o 1/sqrt[3 - 1/sin2(π/n)]
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)]
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-tepuf n-gonal tegmipucofastegium, n-cupola atop inverted ortho n-cupola, 2n-prismatic ortho bi-wedge
... n-fold dissected tetrahedral polytwister, n-fold dissected tetter, tetraswirlic 4n-choron ...
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))]
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))]
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))]
n/d-appip n/d-antiprism prism sqrt[(5-4 cos(π d/n))/(8-8 cos(π d/n))]
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))]
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))]
n/d-pyp n/d-pyramidal prism, line || n/d-prism sqrt[1/4+1/(4-1/sin2[π d/n])]
... vertex figure of spinotriacontaditeron 0.912871
... n/d-grammic retroantiprismatic hemiantiprism 0.707107
nipdip spinoprismatodispentachoron 1
nipixady intercepted invertopental hexacosadishecatonicosachoron 3.077684
... omni-pecu-augmented (10,10)-duoprism
... omni-pecu-augmented (10,20)-duoprism
... omni-pippy-augmented (5,10)-duoprism
... omni-pippy-augmented (5,20)-duoprism
... omni-pecu-gyroaugmented (10,10)-duoprism
... omni-pecu-gyroaugmented (10,20)-duoprism
... hyperbolic order 3 small-stellated-hecatonicosachoral tetracomb 0.242934 i
... o3o3β4o (?) ...
... o3o3β4x (?) ...
... o3o3β5o (?) ...
... o3o3β5x (?) ...
... hyperbolic great-hecatonicosachoral tetracomb 0.393076 i
... o3β3o4β (?) ...
... o3β3o5β (?) ...
... o3β3β3o (?) ...
... o3β3β4o (?) ...
... o3β3β4β (?) ...
... o3β3β5o (?) ...
... o3β3β5β (?) ...
... o3β3x3o (?) ...
... o3β3x4o (?) ...
... o3β3x4β (?) ...
... o3β3x4x (?) ...
... o3β3x5o (?) ...
... o3β3x5β (?) ...
... o3β3x5x (?) ...
... o3β4o3o (?) ...
... o3β4β3o (?) ...
... o3β4x3o (?) ...
... o3x3β4o (?) ...
... o3x3β5o (?) ...
... hyperbolic o3x4x3o8o tesselation 0.594604 i
... hyperbolic birectified order 5 hecatonicosachoric tetracomb 0.747674 i
... icositetrachoron-derived Gévay polychoron, rectified o3m4o3o ...
... tesseract-derived Gévay polychoron, rectified o4m3o3o ...
... hecatonicosachoron-derived Gévay polychoron, rectified o5m3o3o ...
oaf, K-4.58 octagonal antifastegium, octagon - oap wedge, {8} || gyro op 1.409438
oappip, K-4.65 octagonal-antiprism prism 1.463603
... augmented axially-tetrahedral ursachoron ofxo3xooo3oooo&#xt ...
... oxFxofx3xooxFxo3ofxfooo&#xt   (F=ff=x+f)
... oxFxoo3xooxFx3ofxfox&#xt   (F=ff=x+f)
... oxFxofx3xfoxFxo3ooxfooo&#xt   (F=ff=x+f)
... oxFxoo3xfoxFx3ooxfox&#xt   (F=ff=x+f)
octaco, K-4.29 octahedron atop cuboctahedron, half of icositetrachoron (its oct-first rotunda), rectified octahedron-pyramid 1
octacube (alt.: octap), oct || cube, K-4.15 octahedron atop cube, octahedral antiprism, cubical antiprism, vertex figure of icoap 0.879465
octasirco, oct || sirco, K-4.107 octahedron atop small rhombicuboctahedron, octahedral cap of small prismatotetracontoctachoron 1.847759
octasircoacube oct atop sirco atop cube
octatoe, oct || toe (degenerate) octahedron atop truncated octahedron ∞   i.e. flat in euclidean space
octatricu, oct || tricu, K-4.30 octahedron atop trigonal cupola, 2/6-luna of icositetrachoron 1
octatut, oct || tut, K-4.52 octahedron atop truncated tetrahedron, octahedral cap of small rhombated pentachoron 1.183216
... octatut,tricuf-blend
octatutbicu octatut bicupola ...
octpy, K-4.3 octahedral pyramid, half of hex (its vertex-first rotunda) 0.707107
octsnich hyperbolic octahedral - snub-cubic honeycomb 0.380999 i
octu axially-octahedral ursachoron ofx3xoo4ooo&#xt, oct-based ursulate, vertex figure of s3s4o3o4o 1.144123
octum octahedron-first rotunda of truncated hexadecachoron, oct-based tutsatope, oct-based tutism 1.581139
odedip octagon-decagon duoprism 2.079697
odho octidishemioctachoron 1
... octa-diminished thawro-wedged 2/6-luna of hexacosachoron ...
odip octagon-octagon duoprism 1.847759
odipt octagonal-duoprismatic tetracomb 0.321797 i
... oFfoo3ooxxF3Fxoxo3ooffx&#zx
... oFFxx3xxoof3fooxo3ooffx&#zx
... oFFxx3xxoof3fooxx3xxFFo&#zx
... oFFxx3xxoxf3Fxxox3oofFx&#zx
ofiddady omnifacetododecahedronary dishecatonicosachoron 1
... ofoxFxo3xxFxoox3xoofxfo&#xt   (F=ff=x+f)
ofpipixhi omnifacetopental prismatohexacosahecatonicosachoron 0.726543
... oFxFox5AxFoFx2oxofox5ooxofx&#zx
... oFxx3xxof3foxo3oofx&#zx
... axially pyritohedral octa-diminishing of telex, hexa-diminishing of oofoo3oxoxo5xooox&#xt
... oFxxox5Fofxfo oxofox5ooxofx&#zx
... oFxxx5Fofxo oxofx5ooxox&#zx
oh octahemihexadecachoron 1
ohope octahemioctahedron prism 1.118034
ohopy, pt || oho (degenerate) octahemioctahedron pyramid ∞   i.e. flat in euclidean space
ohuhoh octihexadecahemihexadecachoron 1
omfapaxady omnicircumfacetopental hexacosadishecatonicosachoron 0.726543
ondip octagonal spinoduoprism 1.485633
... medial tetrastratic segment of telex
... ooofxfooo3xoxxoxxox5ofxofoxfo&#xt
... ooofxxFfooFoofo3oxFxoFxxxFooFxx3xfoxFoofFxxFoox&#xt
... ooofxxFfooFxofx3oxFxoFxxxFoxFxo3xfoxFoofFxxfooo&#xt
... oooxfxooo3xoxoxoxox5ofxfofxfo&#xt
... ooxf3xfox3oxFx&#xt
opatic, op || tic, K-4.106 octagonal prism atop truncated cube 1.847759
ope, K-4.11 (alt: dytpuf) octahedron prism, vertex figure of rat, dyadic tegmipucofastegium 0.866025
... pentachoron-derived Gévay polychoron, rectified o3m3o3o 1.095445
... hexacosachoron-derived Gévay polychoron, rectified o3m3o5o 6.412847
ostodip octagon-octagram duoprism 1.414214
otathisbit omnitruncated-trihexagonal-square duoprismatic tetracomb
otbaquitit octagonnally tetrablended quasitruncated tesseract 0.615370
otbott octagonnally tetrablended truncated tesseract 2.149726
otcypit omnitruncated cyclopentachoric tetracomb, great-prismatodecachoric tetracomb, Voronoi complex of lattice A4*
otwadip octagon - dodecagon duoprism 2.332200
owau prit   (alt.: pox spic, alt.: phic prico) octa-augmented prismatorhombated tesseract, partially octa-expanded small prismated (dis)icositetrachoron, partially hexadeca-contracted prismatorhombated icositetrachoron
owaudope omni-augmented dodecahedral-prism
... oxFxofo3xfoxFxx3ooxfoox&#xt   (F=ff=x+f)
... oxofofoxo3oofoxofoo5xxoxxxoxx&#xt
... oxofxfooo3xxxxoxxox5ooxofoxfo&#xt
... oxofxfoxo3xxFxoxFxx5xxoxFxoxx&#xt
... oxofxfoxo3xxxxoxxxx5ooxofoxoo&#xt
... oxoofooxo3oofxoxfoo5xxoxxxoxx&#xt
... oxoxfxooo3xxxoxoxox5ooxfofxfo&#xt
... oxoxfxoxo3xxxoxoxxx5ooxfofxoo&#xt
... oxqw wxwx3ooxx4qwox&#zx
... oxqwQ wxwxx3ooxxx4qwoxo&#zx
... proh-cap augmented bistratic prit-cap ...
... oxwQ wxoo3xxxx4oxxo&#zx ...
... point atop tet atop co
... oct atop tut atop toe
... oxxFxoAFxxFoxFx3xofxxFoooFxxfox3xFxoFxxFAoxFxxo&#xt
pabdico parabidiminished icositetrachoron, hexa-augmented tesseract 1
pabdiproh parabidiminished prismatorhombated hexadecachoron, tristratic tic-first central segment of proh 2.613126
pabdirico parabidiminished rectified icosatetrachoron, bistratic co-first central segment of rico, axis-orthogonal partial Stott expanded rit 1.732051
pabex thex partially biexpanded truncated hexadecachoron, partially bicontracted prismatorhombated tesseract ...
pabexrico partially bi-expanded rico, partially bi-contracted proh
pabexrit partially bi-expanded rit, partially bi-contracted tat
pabextah partially bi-expanded tesseractihexadecachoron, partially bi-contracted great rhombated tesseract
pabextico partially bi-expanded tico, partially bi-contracted gidpith
pac gidpith partially (mono-)contracted gidpith
pac grit partially (mono-)contracted great rhombated tesseract
pacprit partially (mono-)contracted prit ...
pacproh partially (mono-)contracted proh
pacsid pith (alt: cuba sircobcu) partially (mono-) contracted sidpith, partially expanded quawros, cubasirco bicupola
pacsrit partially (mono-)contracted small rhombated tesseract ...
pactat partially (mono-)contracted tat
padedip pentagon - decagon duoprism 1.828016
padiap prismatic double inverted antiprism, pentagrammic double antiprismoid 0.618034
padohi prismatodishecatonicosachoron 2.497212
paf, K-4.22 pentagonal antifastegium, pentagon - pap wedge, {5} || gyro pip 1
pahtex prit partially demitesseractic-expanded prit, partially demitesseractic-contracted gidpith
pahtex sidpith partially demitesseractic-expanded sidpith, partially demitesseractic-contracted proh
pahtex srit partially demitesseractic-expanded srit, partially demitesseractic-contracted grit
pahtex tes partially demitesseractic-expanded tesseract, partially demitesseractic-contracted truncated tesseract, hexadecachorally truncated tesseract
paltite prismatoaltitruncated ico tetracomb
... dodecaswirlic triacosihexacontachoron, thirtyfold dissected dodecahedral polytwister, thirtyfold dissected doter ...
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
paphacki pentagon-prismatic heptacosicosachoron, great prismasaurus (also: great prismosaurus) 1
paphicki pentagram-prismatic heptacosicosachoron, small prismasaurus (also: small prismosaurus) 1
pappip, K-4.39 pentagonal-antiprism prism 1.074481
pappy pentagon-antiprismatical pyramid 1.618034
papvixhi pentagonal prismatoverted hexacosahecatonicosachoron 1.902113
paqri prismatoquasirhombated icositetrachoron 1.938391
paqrigafix (old: paquerfix) prismatoquasirhombated great facetted hexacosachoron 1.878261
paqrigagishi (old: paqrahi) prismatoquasirhombated great grand stellated hecatonicosachoron 1.207883
paqrigshi (old: paqraghi) prismatoquasirhombated great stellated hecatonicosachoron (prismatoquasirhombated grand hecatonicosachoron) 3.199386
paqrit prismatoquasirhombated tesseract 1.174172
pataht prismatotruncated demitesseractic tetracomb, prismatodiprismatodisicositetrachoric tetracomb
paticot prismatotruncated icositetrachoric tetracomb, small diprismatodisicositetrachoric tetracomb
pautpen penta-augmentated truncated pentachoron ...
paw, K-4.133, {10} || pap antipentawedge, decagon - pentagonn-antiprismatic wedge, pentagonal gyrobicupolaic ring, {10} || pap, {5} || gyrated pecu 3.077684
pecuf, K-4.154 pentagonal cupofastegium, decagon - pentagon-prismatic wedge, pentagonal orthobicupolaic ring, {10} || pip, {5} || pecu, 2/5-luna of stawros 5.236068
pecupe pentagonal-cupola prism, pentagonal-prism atop decagonal-prism 2.288246
pedap pentagonal duoantiprism ...
pedip pentagon-pentagon duoprism 1.203002
pedisna pental disnubbachoron, compound of 12 ex in rox army, compound of 2 kepisna 1.618034
pedpedip pentadiminished pentagonal duoprism 1.203002
pen, K-4.1 pentachoron, 4D simplex4), 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
pennit hyperbolic order 5 pentachoric tetracomb 0.393076 i
peppia pero, K-4.139 pentagonal-pyramid atop pentagonal-rotunda 3.077684
peppyp, K-4.38 pentagon-pyramidal prism, J2 prism, line || pip 1.074481
pepuf, K-4.165 pentagonal pucofastegium, pentagon - decagon-prismatic wedge, pentagonal magnabicupolaic ring, {5} || dip, {10} || pecu, {5}-first cap of srahi 6.735034
perope, K-4.92 pentagonal-rotunda prism 1.693527
pesc (old: peppypy), K-4.86 pentagon scalene, pentagon-pyramidal pyramid, line atop fully orthogonal pentagon, 5 tet rosette 1.618034
pex hex partially (mono-)expanded hex, partially contracted quawros
pex thex partially (mono-)expanded thex ...
pexic partially (mono-)expanded icositetrachoron ...
pexrico partially (mono-)expanded rico
pexrit partially (mono-)expanded rit
pextah partially (mono-)expanded tesseractihexadecachoron
pextico partially (mono-)expanded tico
phiddip pentagon hexagon duoprism 1.312862
phitte hyperbolic order 5 hecatonicosachoric tetracomb 0.206652 i
phud prismatohemidecachoron 1
pibhaki pentagonal-bipyramidal heptacosiicosachoron, rectified-hexacosachoron dual, surtegmated hecatonicosachoron
pibox srico partially bi-octa-expanded small rhombitetracontoctachoron
pibox tico partially bi-octa-expanded truncated icositetrachoron
picnut prismatocubiintercepted tesseract 0.890446
pikap (alt.: snittap) pyritohedral icosahedral antiprism, snub-tetrahedral antiprism, non-uniform alternation of tope ...
pinnip prismatointercepted pentachoron, retropyroinvertirectichoron, vertex figure of han 0.774597
... pinnip+5 2thah (?) 0.774597
pinnipdip pentaintercepted prismatodispentachoron, prismatopentaintercepted dispentachoron 1.183216
... pinnipdip+15{4} (?) 1.183216
pinpith prismatointercepted prismatotesseractihexadecachoron 1.847759
... pinpith+48{4} 1.847759
pinpixhi prismatointercepted prismatohexacontahecatonicosachoron 6.735034
... pinpixhi+1800{4} (?) 6.735034
piphid prismatopentahemidecachoron, copyrofacetoretropodichoron 1
... piphid+10tet (?) 1
pippindip prismatopentintercepted dispentachoron 1.183216
pippy, K-4.141 pentagonal-prismatic pyramid, vertex pyramid of the rectified hexacosachoron 3.077684
pirgaghi prismatorhombated great grand hecatonicosachoron 1.893038
pirghi prismatorhombated great hecatonicosachoron 4.917351
pirhatit prismatorhombated demitesseractic tetracomb, great prismatodemitesseractic tetracomb, steriruncic tesseractic tetracomb
pirpop pseudorhombated prismatopentachoron 1.183216
... pirpop+5 2thah (?) 1.183216
pirshi prismatorhombated (small) stellated hecatonicosachoron 5.515107
pistadedip pentagon - decagram duoprism 1.051462
pistodip pentagon - octagram duoprism 1.008216
pitest hyperbolic order 5 tesseractic tetracomb 0.242934 i
pithatit prismatotruncated demitesseractic tetracomb, small prismatodemitesseractic tetracomb, stericantic tesseractic tetracomb
pittip prismatotriakispentachoron 1.612452
poc gippic partially octa-contracted great prismatotetracontoctachoron
poc prico   (alt.: phex spic) partially octa-contracted prismatorhombated icositetrachoron, partially hexadeca-expanded small prismated (dis)icositetrachoron ...
poccont partially octa-contracted tetracontoctachoron
pocsric   (alt.: phixic) partially octa-contracted small rhombated icositetrachoron, partially hexadeca-expanded icositetrachoron, octa-augmented truncated tesseract ...
... pocuro wedge ...
podip pentagon - octagon duoprism 1.559075
potatit prismatotruncated tesseractic tetracomb, small tomocubic-diprismatotesseractic tetracomb, runcitruncated tesseractic tetracomb
pox prico partially octa-expanded prismatorhombated icositetrachoron
pox rico partially octa-expanded rectified icositetrachoron
pox srico partially octa-expanded small rhombated icositetrachoron
pox tico partially octa-expanded truncated icositetrachoron
poxic   (alt.: phic srico, alt.: owau sidpith) partially octa-expanded icositetrachoron, partially hexadeca-contracted small rhombated icositetrachoron, octa-augmented small diprismated tesseractithexadecachoron ...
prahi prismatorhombated hecatonicosachoron, runcitruncated hexacosachoron 8.278950
prap vixhi pentagonal retroprismatoverted hexacosahecatonicosachoron 1.175571
prarsi prismatorhombiretrosnub icositetrachoron 1.328131
pretasto pentagonorhombic trisnub trisoctachoron
prico prismatorhombated icositetrachoron, runcitruncated icositetrachoron 3.498949
pricot prismatorhombated icositetrachoric tetracomb, great diprismatodisicositetrachoric tetracomb
prip prismatorhombated pentachoron, runcitruncated pentachoron 1.612452
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
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
prittit prismatorhombated tesseractic tetracomb, rhombitesseractic-diprismatotesseractic tetracomb, runcicantellated tesseractic tetracomb
prix prismatorhombated hexacosichoron, runcitruncated hecatonicosachoron 9.744610
proh prismatorhombated hexadecachoron, prismatotruncated tesseract, runcitruncated tesseract 2.613126
... (0,0,0,12,0)-diminished vertex-first-rotunda of ex, dodeca-diminished vertex-first rotunda of hexacosachoron 1.618034
pta cubaike cube-augmented cubaike 1
ptaika cube ike-augmented cubaike
pybiscrox pyritohedral bistratic icosahedron-first cap of rectified hexacosachoron 3.077684
pysna s2s3s4x, pyritosnub alterprism, edge-alternated great-rhombicuboctahedronal prism, edge-snub octahedral hosochoron ...
pysnet s3s3s4x, pyritosnub tesseract, edge-alternated great diprismated tesseractihexadecachoron, edge-snub hexadecachoron ...
... q x3o3o, variation of tetrahedron prism, vertex figure of rectified penteract 0.935414
... qo3oo3oo&#x, shallower variant of tetrahedral pyramid, vertex pyramid of tes 1
... qo3oq3oo&#x, shallower variant of rap, segment of tes 1
qragishi (old: qraghi) quasirhombated grand stellated hecatonicosachoron 1.662508
qrico quasirhombated icositetrachoron 1.082392
qriddip quasi-rhombicosidodecahedron prism 0.874032
qrigfix (old: querfix) quasirhombated great faceted hexacosachoron 1.027486
qrigogishi (old: qrahi) quasirhombated great grand stellated hecatonicosachoron 0.799575
qrit quasirhombated tesseract 0.765367
... vertex figure of quasicellated penteractitriacontiditeron 1.118034
quad pagaxhi quasidisprismatogrand hexacosihecatonicosachoron 0.874032
quadippady quasidisprismatodishecatonicosachoron, Unholey Terror 1.414214
quawros quadratic ({8} || cube-)wedge rosette, bridge cyclotetraaugmented tesseract, ring-augmented tesseract, cube || {8} || cube, {4} || squobcu || {4}
quercope quasirhombicuboctahedron prism 0.890446
quidex quatro-icositetradiminished hexacosachoron, tristellatododecahedral enneacontahexachoron, dual of sadi
quidpith (old: qippith) quasi(dis)prismatotesseractihexadecachoron 0.890446
quidpixhi quasidisprismatohexacosihecatonicosachoron 0.763932
quipdohi quasiprismatodishecatonicosachoron 1.328131
quiphi quasiprismatohecatonicosachoron 0.726543
quippic quasiprismatotetracontoctachoron 0.765367
quippirfix quasiprismatorhombated faceted hexacosachoron 3.531591
quippirgashi quasiprismatorhombated grand stellated hecatonicosachoron 1.348948
quippirgax quasiprismatorhombated grand hexacosachoron 1.021064
quippirghi quasiprismatorhombated grand hecatonicosachoron 2.400819
quiproh quasiprismatorhombated hexadecachoron 1.082392
quit gashi quasitruncated grand stellated hecatonicosachoron 0.953850
quit gishi quasitruncated great stellated hecatonicosachoron 0.953850
quit gissiddip quasitruncated-great-stellated-dodecahedron prism 0.826058
quit gogishi quasitruncated great grand stellated hecatonicosachoron 0.677481
quit sishi quasitruncated small stellated hecatonicosachoron 2
quit sissiddip quasitruncated-small-stellated-dodecahedron prism, small-stellated-truncated-dodecahedron prism 0.988665
quitcope quasitruncated-cuboctahedron prism 1.174172
quitdiddip quasitruncated-dodecadodecahedron prism 1.732051
quithip quasitruncated-hexahedron prism 0.765367
quitit quasitruncated tesseract 0.615370
... vertex figure of retrocellitriacontadiahexadecateron 0.912871
... vertex figure of retrodishexadecateron 0.774597
radatathi retroditetrahedronary dishecatonicosachoron 1.414214
radeda tigid, raded || tigid rhombidodecadodecahedron atop truncated great dodecahedron 2.363565
radiddip (old: radedip) rhombidodecadodecahedron prism 1.414214
rafficdi retrofrustic tetracontoctadisicositetrachoron 1.414214
raffixthi retrofrustic hexacositrishecatonicosachoron 2.236068
ragaghi rectified great grand hecatonicosachoron 1.070466
ragashi rectified grand stellated hecatonicosachoron 1.175571
raggix rectified grand hexacosachoron 0.726543
raghi rectified grand hecatonicosachoron 1.902113
ragishi rectified great stellated hecatonicosachoron 1.175571
rahi rectified hecatonicosachoron 4.534568
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
rappisdi retroantiprismatosnub disicositetrachoron 1
... rappisdi+mesdi+288{4} (?) 1
rapsady retroantiprismatosnub dishecatonicosachoron 1.618034
rasdi retrosnub icositetrachoron, retrosnub disicositetrachoron 0.618034
rasishi rectified small stellated hecatonicosachoron 2.802517
... vertex figure of retrotriacontidicellihemitriacontaditeron 0.866025
ratho rectified tesseractihemioctachoron 1
rathotathibit rhombitrihexagonal-omnitruncated-trihexagonal duoprismatic tetracomb
... vertex figure of retrosphenary cellihexateron 0.921954
rawvathi retrosphenoverted triakishecatonicosachoron 2.689994
rawvatoth retrosphenoverted tesseractitesseractihexadacachoron 1.847759
rawvaty retrosphenoverted triakisicositetrachoron 2.613126
rawvhiddix retrosphenoverted hecatonicosadishexacosachoron 1.258409
rawvhitto retrosphenoverted hexadecatesseractioctachoron 1.732051
rawvid tixady retrosphenoverted ditrigonary hexacosadishecatonicosachoron 5.330704
rawvtip retrosphenoverted triakispentachoron 1.183216
recont rectified tetracontoctachoron 6.754807
redeca rectified decachoron 2.828427
... cuboctahedral retro-cuploid 1
respic rectified small prismated tetracontoctachoron 3.557647
respid rectified small prismated decachoron 1.732051
retdip (old: retriddip) rectified triddip 1.290994
rico rectified icosatetrachoron, cantellated hexadecachoron, hexadecachoron-derived Gévay polychoron 1.732051
... rico-cap augmented thex-rotunda ...
ricot rectified icositetrachoric tetracomb
ridatathi retroinverted ditetrahedral triakishecatonicosachoron 1.414214
ridditdy retroditrigonary dishecatonicosachoron 1.732051
ridimex (alt.: idimrox) rectified icosidiminished hexacosachoron, icosidiminished rectified hexacosachoron 3.077684
ridtidohi rectified ditrigonary dishecatonicosachoron 1.732051
rigfix rectified great faceted hexacosichoron 0.726543
riggidtixhi rectified great ditrigonary hexacosihecatonicosachoron 1.732051
righi rectified great hecatonicosachoron 1.902113
rigogishi rectified great grand stellated hecatonicosachoron 0.661585
... vertex figure of retropenteractihexadecateron 0.774597
ripahi retroinverted prismatohecatonicosachoron 4.534568
... ripahi+600 2thah (?) 4.534568
ripdip rhombiprismato dispentachoron 1.612452
risadi (alt.: idrox) rectified snub icositetrachoron, icositetradiminished rectified hexacosachoron 3.077684
rissidtixhi rectified small ditrigonary hexacosihecatonicosachoron 1.732051
rit rectified tesseract, rectified octachoron, birectified hexadecachoron, runcic tesseract 1.224745
rithsithbit rhombitrihexagonal-simotrihexagonal duoprismatic tetracomb
rittit rectified tesseractic tetracomb, quartertesseractic tetracomb
rixhi retroinverted hexacosahecatonicosachoron 3.077684
rofix rectified faceted hexacosichoron 3.077684
... vertex-first rotunda of hexacosachoron 1.618034
rox rectified hexacosachoron 3.077684
... rox+720pip (?) 3.077684
... β3o3o4β (?) ...
... β3o3o5β (?) ...
... β3o3β3o (?) ...
... β3o3β4β (?) ...
... β3o3β4x (?) ...
... β3o3β5o (?) ...
... β3o3β5β (?) ...
... β3o3β5x (?) ...
... β3o4o3β (?) ...
... β3o4β3o (?) ...
... β3β3o3β (?) ...
... β3β3o4β (?) ...
... β3β3o5β (?) ...
... β3β3β3o (?) ...
... β3β3β3x (?) ...
... β3β3β5o (?) ...
... β3β3β5x (?) ...
... β3β3x3β (?) ...
... β3β3x4β (?) ...
... β3β3x5β (?) ...
... β3β3x *b3o (?) ...
... alternated truncated hyperbolic order 4 icositetrachoral tetracomb
... β3β4o3β (?) ...
... β3β4β3o (?) ...
... β3β4β3x (?) ...
... β3β4x3β (?) ...
... β3x3o4β (?) ...
... β3x3o5β (?) ...
... β3x3β3o (?) ...
... β3x3β3x (?) ...
... β3x3β4β (?) ...
... β3x3β4x (?) ...
... β3x3β5o (?) ...
... β3x3β5β (?) ...
... β3x3β5x (?) ...
... β3x3x3β (?) ...
... β3x3x4β (?) ...
... β3x3x5β (?) ...
... β3x4β3o (?) ...
... β3x4β3x (?) ...
... β3x4x3β (?) ...
... octahedra-alternated faceting of scartit
... s4x2s4x (?) ...
sabbadipady small blendic disprismatodishecatonicosachoron 2
sabbathi small blendic trishecatonicosachoron 2
sabippady (old: sabbippady) small blendic prismatodishecatonicosachoron 2
sabred small birhombatodecachoron sqrt[(2a2+2ab+3b2)/5]
sabric small birhombatotetracontoctachoron sqrt[a2 + 2 sqrt(2) ab + 3b2]
sad phiddix small dipentary hecatonicosadishexacosachoron 2.497212
saddiddip small-dodekicosidodecahedron prism 2.288246
sadi   (alt.: idex) snub icositetrachoron, snub disicositetrachoron, semistruncated icositetrachoron, icositetradiminished hexacosachoron, snub rhombatohexadecachoron 1.618034
sadit snub icositetrachoric tetracomb, Gosset's non-Wythoffian tetracomb
sadixady small dishexacosadishecatonicosachoron 1.773668
sadixhix (old: sixhix) small dodecahedronary hexacosahemihexacosachoron, compound of 25 ihi (but not gadixhix) 1
sadsadox small disnub dihexacosachoron 3.077684
sadtap small ditetrahedronary prismatochoron, compound of 36 dedip 2.288246
sadtef pixady small ditetrahedronary exofissary prismatohexacosadishecatonicosachoron 2.288246
sadtifady small ditetrahedronarofissary dishecatonicosachoron 2.288246
sanbathi small spinoblendic trishecatonicosachoron 2
sanbippady small spinoblendic prismatodishecatonicosachoron 2
sand tathi small intercepted ditetrahedronary trishecatonicosachoron 2.288246
saquid paxhi small quasidisprismatohexacosihecatonicosachoron, Holey Terror 2.288246
sazdideta square antitrapezary disicositetratidistesseratiapeiratic tetracomb
scadupthix small capped dipentary tetrishecatonicosahexacosichoron 2.497212
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
... hyperbolic honeycomb with seed point at edge of right-angled octahedron domain
seedatepthi small exoditetrahedrary prismatotrishecatonicosachoron 1.414214
sefdit dixdy small exofissary ditrigonal dihexacosadihecatonicosachoron 1.732051
sefidtethi small exofissary ditetrahedronary tetrakishecatonicosachoron 2.288246
sefradit thix small exofissary retroditetrahedronary triakishecatonicosihexacosachoron 2.288246
sesidip small-snub-icosicosidodecahedron prism 1.541531
sgysrahi swirl-gyrated small rhombated hecatonicosachoron, swirl-gyrated cantellated hecatonicosachoron 6.735034
shafipto small hexadecafaceted prismatotesseractioctachoron 1.485633
... shafipto+32tet (?) 1.485633
shahoh small hexadecahemihexadecachoron 1
shasc small heptagrammic scalene, small-heptagrammic-pyramidal pyramid, line atop fully orthogonal small heptagramm 0.658240
shiddip, K-4.54 square - hexagon duoprism 1.224745
shihi small hecatonicosihecatonicosachoron 5.854102
shihix small hecatonicosihecatonicosihexacosachoron 2.975584
shinhi small hecatonicosintercepted hecatonicosachoron 4.534568
shipady small hecatonicosiprismatodishecatonicosachoron 1.814331
shitte hyperbolic order 4 hecatonicosachoric tetracomb 0.899454 i
sibricot small birhombated icositetrachoric tetracomb, grand prismatodisicositetrachoric tetracomb
sichado small cubihexadecadisoctachoron 2.370932
sid pippady small dipentary prismatodishecatonicosachoron 2.497212
sid thipady small ditrigonary hecatonicosiprismatodishecatonicosachoron 1.814331
sid tipathi small ditrigonary prismatotriakishecatonicosachoron 4.179968
siddapady small disprismatodishecatonicosachoron 2
siddatady small ditetrahedral dishecatonicosachoron 2.288246
siddic small distetracontoctachoron 1.847759
siddiddip snub-dodecadodecahedron prism
siddit paxhi small ditetrahedronary hexacosidishecatonicosachoron 2.288246
siddit thix small ditrigonal trishecatonicosihexacosachoron 1.732051
sidditdiddip small-ditrigonary-dodekicosidodecahedron prism 1.792631
sidditdy small ditrigonary dishecatonicosachoron 1.732051
sidditpix small ditrigonary prismatohexacosichoron 1.732051
sidhiquit paddy small dishecatonicosaquasitruncated prismatodishecatonicosachoron 5.605034
sididdip snub-icosidodecadodecahedron prism
sidipthi small dipental trishecatonicosachoron 2.497212
... sidpippady+120 2sissid (?) 2.497212
sidpith small disprismatotesseractihexadecachoron, runcinated tesseract, small prismated tesseract 1.485633
sidpixathi small dipentagonal hexacositrihecatonicosachoron 2.497212
sidpixhi small disprismatohexacosihecatonicosachoron, runcinated hecatonicosachoron, runcinated hexacosachoron 5.236068
sidrebcu stellidodecahedral rectibicupola, orbiform bistratc stack of small stellated dodecahedron atop pseudo dodecadodecahedron atop great dodecahedron 1.064815
sidsrahi swirl-diminished small rhombated hecatonicosachoron, swirl-diminished cantellated hecatonicosachoron 6.735034
sidtaxady small ditetrahedronary hexacosidishecatonicosachoron 2.288246
sidtaxhi small ditetrahedronary hexacosihecatonicosachoron 2.288246
sidthidy hi small ditrigonal hecatonicosadishecatonicosihecatonicosachoron 1.732051
sidthixhi small ditrigonary hecatonicosihexacosihecatonicosachoron 1.773668
sidtidap small-ditrigonary-icosidodecahedron antiprism 0.951057
sidtiddip small-ditrigonary-icosidodecahedron prism 1
sidtixhi small ditrigonary hexacosihecatonicosachoron 1
... sidtixhi+dox (?) 1
sifdahihox small fissary dodecahedronary hecatonicosihemihexacosachoron 1
siida (alt.: siidcup) small icosicosidodecahedral alterprism, small icosicosidodecahedral cupoliprism, closer siid atop siid 1.765796
siidip small-icosicosidodecahedron prism 1.792631
sik vadixady small skewverted dishexacosidishecatonicosachoron 4.684471
sik vipathi small skewverted prismatotriakishecatonicosachoron 2.828427
sik vixathi small skewverted hexacositriakishecatonicosachoro 4.684471
siphado small prismatohexadecadisoctachoron 2.613126
siphatit small diprismatodemitesseractic tetracomb, steric tesseractic tetracomb
siphidy small prismated hecatonicosadishecatonicosachoron 4.917351
sipthi small prismatotriakishecatonicosachoron 1.878261
sipti small prismatotriakisicositetrachoron 3.498949
sirc small retrotetracontoctachoron 1.847759
sirco aticu expanded axially-octahedral ursachoron, (sirco,tic)-based ursulate 1.806144
sircoa gircotum bistratic cap of prismatorhombated tesseract, rhombicuboctahedral rotunda, (sirco,girco)-based tutschoron, (sirco,girco)-based tutism 2.370932
sircoagirco, sirco || girco (degenerate) small rhombicuboctahedron atop great rhombicuboctahedron ∞   i.e. flat in euclidean space
sircoatic, sirco || tic, K-4.100 small rhombicuboctahedron atop truncated cube, small-rhombicuboctahedral cap of small rhombated tesseract 1.847759
sircoatoe, sirco || toe, K-4.75 small rhombicuboctahedron atop truncated octahedron 1.582890
sircope, K-4.66 small-rhombicuboctahedron prism, medial (cube-first) subsegment of sidpith 1.485633
sirdatady small retroditetrahedral dishecatonicosachoron 2.288246
... sirdatady+1440{5/2} 2.288246
sirdop small rhombidispentachoron 1.183216
sirdtapady small retroditetrahedronary prismatodishecatonicosachoron 2.288246
... sirdtapady+600 2tet (?) 2.288246
sirdtaxady small retroditetrahedronary hexacosidishecatonicosachoron 2.288246
sirfix small rhombated faceted hexacosachoron 4.352502
sirfixthi small retrofrustic hexacositrishecatonicosachoron 2.236068
sirgaghi small rhombated great grand hecatonicosachoron 1.513868
sirgashi small rhombated grand stellated hecatonicosachoron 1.589926
sirgax small rhombated grand hexacosachoron 1.054256
sirghi small rhombated great hecatonicosachoron 3.387054
sirpaxhi small rhombiprismic hexacosahecatonicosachoron 9.744610
sirpdi small rhombiprismic disicosatetrachoron 3.498949
sirpdo small rhombiprismatodisoctachoron 2.370932
sirphinady small inverted retropental hecatonicosaintercepted dishecatonicosachoron 3.077684
sirpith small rhombiprismated tesseractihexadecachoron 2.613126
sirsashi small rhombated small stellated hecatonicosachoron 3.963358
sirsiddip small-(inverted)-retrosnub-icosicosidodecahedron prism 0.766294
sisdipthi small stellated dipental trishecatonicosachoron 2.497212
... 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
sisp small swirlprism 1.618034
sissid || 3doe (degenerate) sissid atop 3doe ∞   i.e. flat in euclidean space
sissidadid, sissid || did small stellated dodecahedron atop dodecadodecahedron, small-stellated-dodecahedral cupola 1.064815
sissidadoe (degenerate) sissid atop doe ∞   i.e. flat in euclidean space
sissidagad, sissid || gad small stellated decahedron atop great dodecahedron, sissid antiprism, gad antiprism 1
sissidaraded, sissid || raded small stellated dodecahedron atop rhombidodecadodecahedron, sissid-first cap of padohi 2.497212
sissiddip small-stellated-dodecahedron prism 0.771681
sissidpy small-stellated-dodecahedral pyramid, vertex cap of unit gofix, vertex cap of v-scaled gohi 0.618034
sistodip square - octagram duoprism 0.890446
sistople (old: stodop) square-octagram plus-prism, octagram diorthoprism, compound of 2 sistodip 1.485633
sit thixady small tritrigonal hecatonicosihexacosidishecatonicosachoron 3.835128
sitphi small tripesic hecatonicosachoron 2.288246
sitpodady small (intersected) tripesic dodecahedronary dishecatonicosachoron 1
sitwadip square - dodecagon duoprism 2.057195
six fipady small hexacosafaceted prismatodishecatonicosachoron 5.236068
sixathi small hexacositriakishecatonicosachoron 2.351141
... six fipady+1200tet (?) 5.236068
sixhidy small hexacosihecatonicosadishecatonicosachoron 2.975584
sixhihy small hexacosihecatonicosihecatonicosachoron 5.236068
sixipady small hexacosiprismatodishecatonicosachoron 6.881910
skiv datapixady small skewverted ditrigonary prismatohexacosadishecatonicosachoron 4.684471
skiviphado small skewverted prismatohexadecadisoctachoron 1.414214
snahi s3s3s5s, snub hecatonicosachoron, non-uniform alternation of gidpixhi ...
snappoth small spinoprismatotesseractihexadecachoron 1.485633
snet s3s3s4s, snub tesseract, non-uniform alternation of gidpith ...
sni (old: snico) / snoc s3s4s3s, (fully) snubbed icositetrachoron (but not sadi) / snubbed tetracontoctachoron, non-uniform alternation of gippic ...
sniccap s2s3s4s, snub-cubic antiprism, non-uniform alternation of gircope ...
sniccup, K-4.60 snub-cube prism, snub-cuboctahedron prism 1.433724
sniddap s2s3s5s, snub-dodecahedral antiprism, non-uniform alternation of griddip ...
sniddip, K-4.110 snub-dodecahedron prism, snub-icosidodecahedron prism 2.213060
snip / snad s3s3s3s, snub pentachoron / snub decachoron, non-uniform alternation of gippid ...
sobcated small bicuntitruncated decachoron, general variant of expanded decachoron, general variant of expanded bideca sqrt[(2a2+3ab+3b2+2ac+4bc+3c2)/5]
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]
soccope small-cubicuboctahedron prism 1.485633
socdip stellated-octagonal duoprism, compound of 4 tes in odip army 1
sodip, K-4.70 square - octagon duoprism 1.485633
sody small deckishecatonicosachoron, compound of 10 ex in hi army, compound of 2 spohi 1.618034
sophi small prismatohecatonicosachoron 3.077684
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
... hexaconta-sphenated id-first deep parabidiminished rahi ...
sphiddix small prismatohecatonicosadishexacosachoron 6.881910
sphihix small prismatohecatonicosahecatonicosahexacosachoron 5.515107
sphixhi small prismatohecatonicosihexacosihecatonicosachoron 4.179968
spic small prismatotetracontoctachoron, runcinated icositetrachoron, expanded icositetrachoron 1.847759
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
spidrico swirlprismatodiminished rectified icositetrachoron, 24-diminished rectified icositetrachoron 1.732051
spidrox (alt.: hidrox) swirlprismatodiminished rectified hexacosachoron, 120-diminished rectified hexacosachoron 3.077684
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
spixady small prismatohexacosadishecatonicosachoron 8.278950
spixhihy small prismatohexacosihecatonicosihecatonicosachoron 9.744610
spohi small pentishecatonicosachoron, chiral compound of 5 ex in hi army 1.618034
sporaggix swirlprismatoreplenished rectified grand hexacosachoron 0.726543
sprapivady small pentagonal retroprismatoverted dishecatonicosachoron 3.077684
spriphi small pseudorhombated prismatohecatonicosachoron 6.735034
... spriphi+600 2thah (?) 6.735034
spript small pseudorhombated prismatotesseract 1.847759
... spript+16 2thah (?) 1.847759
spysp small pyramidic swirlprism 1.618034
squacufbil square-cupofastegia biluna, rotunda of quawros, square atop squobcu
squacupe, K-4.69 square-cupola prism, cube atop octagonal prism 1.485633
squadedip, K-4.97 square - decagon duoprism 1.765796
squaf, K-4.14 square antifastegium, square - squap wedge, {4} || gyro cube, bidiminished octahedral antiprism 0.879465
... cubiswirlic heptacontidichoron, twelvefold dissected cubic polytwister, twelvefold dissected cubiter 1.538189
... external blend of the square-antiprism prism and 2 cube-pyramids, cubic-pyramid-biaugmented square-antiprism prism
... external blend of the square-antiprism prism and 2 squap-pyramids, squap-pyramid-biaugmented square-antiprism prism
squappip, K-4.19 square-antiprism prism 0.962692
squappy square-antiprismatical pyramid 0.879465
squapt (line-)square-antiprismatic tegum, square-antiprismatic bipyramid, square-pyramidal antiprism
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
... squashed hexaconta-sphenated id-first deep parabidiminished rahi ...
squaw, K-4.64, {8} || squap antitetrawedge, octagon - square-antiprismatic wedge, square gyrobicupolaic ring, {8} || squap, {4} || gyrated squacu 1.447009
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
squipdip, K-4.42 square-pentagon duoprism 1.106168
squippia squacu, K-4.109 square pyramid atop square cupola 1.847759
squippiaco, K-4.31 square-pyramid atop cuboctahedron 1
squippiatricu, K-4.32 square-pyramid atop triangular-cupola 1
squippyal cube, K-4.16 squippy atop gyro cube 0.879465
squippyp, K-4.12 square-pyramidal prism, J1 prism, line || cube, digonal magnabicupolaic ring 0.866025
squipuf, K-4.105 square pucofastegium, square - octagon-prismatic wedge, square magnabicupolaic ring, {4} || op, {8} || squacu, square-cap of srit 1.847759
sradditdahix small retroditetrahedronary dishecatonicosihexacosachoron 2.288246
sraghi small rhombated grand hecatonicosachoron 2.689994
srahi small rhombated hecatonicosachoron, cantellated hecatonicosachoron 6.735034
srawv ditathi small retrosphenoverted ditrigonary triakishecatonicosachoron 3.294556
srawv hidy small retrosphenoverted hecatonicosadishecatonicosachoron 3.387054
srawv hixhi small retrosphenoverted hecatonicosihexacosihecatonicosachoron 6.073594
srawvathi small retrosphenoverted triakishecatonicosachoron 4.352502
srawvixady small retrosphenoverted hexacosadishecatonicosachoron 6.735034
srico small rhombated icositetrachoron, cantellated icositetrachoron 2.613126
sricot small rhombated demitesseractic tetracomb, small prismatodisicositetrachoric tetracomb
..., xFoFx3ooooo5xofox&#xt   (F=ff=x+f) bilunabirotundic rhombicosidodecahedron prism, castellated rhombicosidodecahedral prism
srida gridtum bistratic srid-cap of prahi, (srid,grid)-based tutsachoron, (srid,grid)-based tutism 8.278950
sridaphi small retroinverted dodecahedronary prismatohecatonicosachoron 1
sridati, srid || ti, K-4.126 small-rhombicosidodecahedron atop truncated-icosahedron 2.485450
sridatid, K-4.159 small rhombicosidodecahedron atop truncated dodecahedron, small-rhombicosidodecahedral cap of small rhombated hecatonicosachoron 6.735034
sridatidu expanded axially-icosahedral ursachoron, (srid,tid)-based ursulate 3.077684
sriddip, K-4.111 small-rhombicosidodecahedron prism 2.288246
sridixhi small retroinverted dodecahedronary hexacosahecatonicosachoron 1
srip small rhombated pentachoron, cantellated pentachoron 1.183216
sripady small rhombiprismic dishecatonicosachoron 8.278950
sriphi small retropental hecatonicosachoron 3.077684
srit small rhombated tesseract, cantellated tesseract 1.847759
srittit small rhombitesseractic tetracomb, cantellated tesseractic tetracomb
srix small rhombated hexacosachoron, cantellated hexacosachoron 6.073594
stadidip decagram-decagram duoprism 0.874032
stafe stellar (pentagrammal) antifastegium, pentagram - stap wedge, {5/2} || gyro stip 0.535857
stapedit ({5/2},{5})-duotegum, tegum product of a pentagon and a pentagram
stappip pentagramic-antiprism prism 0.825168
stappyp pentagram-pyramidal prism, line || stip 0.771681
stardedip pentagram - decagon duoprism 1.701302
stardip pentagram-pentagram duoprism 0.743496
starodip pentagram - octagon duoprism 1.408368
starpedip (old: stipdip, starpendip) pentagram-pentagon duoprism, stellar (pentagonal) pentagonal diprism 1
stasc (old: stappypy) stellar scalene, pentagrammic scalene, pentagram-pyramidal pyramid, line atop fully orthogonal pentagram, 5 tet two-step rosette 0.618034
stastidedip pentagram - decagram duoprism 0.811393
stastodip pentagram - octagram duoprism 0.754511
stawros pentagrammic ({10} || pip-)wedge rosette, bridge cyclopentaaugmented starpedip, ring-augmented starpedip
sted stellated decachoron, compound of 2 pen 0.632456
stefacoth small tesseractifaceted cubitesseractihexadecachoron 1.485633
steth small tesseractitesseractihexadecachoron 1.485633
stico (old: sico) stellated icositetrachoron, stella tegmata, compound of 3 hex 0.707107
stippy stellated-pentagonal prismatic pyramid, vertex pyramid of the rectified grand hexacosachoron 0.726543
sto small trisoctachoron, small triakisoctachoron 1.224745
... sto+16tet (?) 1.224745
stoc stellated tetracontoctachoron, compound of 2 ico 1
stodatixhi small toroidoditrigonary hexacosihecatonicosachoron 1.732051
stodip octagram-octagram duoprism 0.765367
stoditpix small toroidoditrigonary prismatohexacosichoron 1.732051
stut dixady small tritrigonal dihexacosidihecatonicosachoron 3.835128
stut phiddix small tritrigonal prismatohecatonicosidishexacosachoron 3.835128
stut pixady small tritrigonal prismatohexacosidihecatonicosachoron 3.835128
stut thix small tritrigonal trishecatonicosihexacosachoron 3.835128
stut xethi small tritrigonal hexacositrishecatonicosachoron 3.835128
suti small tetrakisicositetrachoron 1.608038
swav ditathi small sphenoverted ditrigonary triakishecatonicosachoron 2.572554
swavathi small sphenoverted triakishecatonicosachoron 2.093315
swavixady small sphenoverted hexacosadishecatonicosachoron 3.294556
tabene trigonal-bipyramidal enneacontahexachoron, rectified-icositetrachoron dual, surtegmated icositetrachoron
tadeca truncated decachoron sqrt(2y2+7y+7)
taggix truncated grand hexacosachoron 1.199039
taghi truncated grand hecatonicosachoron 3.477092
tah tesseractihexadecachoron, bitruncated tesseract, bitruncated hexadecachoron, runcicantic tesseract 2.121320
tahi triakishecatonicosachoron 2
tastic truncated stellated tetracontoctachoron, compound of 2 truncated icositetrachora 2.645751
tat truncated tesseract 2.149726
tatriddip truncated triangular duoprism sqrt[(2y2+5x+5)/3]
tattit truncated tesseractic tetracomb
tau ope tetra-augmented ope
tau tope tetra-augmented tope
tautipip triaugmented-triangular-prism prism
tautisdip triaugmented 3,4-duoprism ...
teddi adoe, teddi || doe, K-4.83 tridiminished-icosahedron atop dodecahedron, triminished segment of vertex-first hexacosachoron 1.618034
teddi aid, teddi || id, K-4.147 tridiminished icosahedron atop icosidodecahedron 3.077684
teddipe tridiminished-icosahedron prism 1.074481
teddipy, K-4.88 tridiminished-icosahedral pyramid 1.618034
tehipau tuttip hip-wise tetra-augmented tuttip
telex vertex first tele-elongated hexacosachoron
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
teppix (old: dattix) tripesic hexacosachoron, compound of 60 deca 1.414214
tes (alt.: squadip), K-4.20 tesseract, octachoron, "hypercube", 4D measure-polytope4), 8-cell, geoter(id), square duoprism, vertex figure of icot 1
test tesseractic tetracomb, 4D hypercubical honeycomb4), Voronoi complex of C4 lattice, Delone complex of C4 lattice
tetaco altut tetrahedron atop cuboctahedron atop inverted truncated tetrahedron ...
tetaco ausrip tetaco-augmented srip
tetaco, tet || co, K-4.23 tetrahedron atop cuboctahedron, tetrahedral rotunda of small prismatodecachoron 1
tetacoaoct octahedron atop (pseudo) cuboctahedron atop tetrahedron 1
tetaltut, tet || inv. tut (degenerate) tetrahedron atop inverted truncated tetrahedron, (degenerate) tetrahedron atop alternate truncated tetrahedron ∞   i.e. flat in euclidean space
tetatricu, tet || tricu, K-4.24 tetrahedron atop trigonal cupola, 0.290215-luna of small prismatodecachoron 1
tetatut, K-4.56 tetrahedron atop truncated tetrahedron, tetrahedral cap of rectified tesseract 1.224745
tete (old: tedpy) (line-)tetrahedron-tegum, tetrahedral bipyramid
tetripau tuttip trip-wise tetra-augmented tuttip
tetu axially-tetrahedral ursachoron ofx3xoo3ooo&#xt, tet-based ursulate, vertex figure of sadit 1
tewau thawrorh tetra-augmented thawro rhombochoron ...
tex truncated hexacosachoron 4.643523
thahp tetrahemihexahedral prism, vertex figure of rhohid 0.866025
thaquitoth tesseractihexadecaquasitruncated tesseractihexadecachoron 1.338990
thaquitpath tesseractihexadecaquasitruncated prismatotesseractihexadecachoron 1.608038
thatoth tesseractihexadecatruncated tesseractihexadecachoron 1.790840
thatpath tesseractihexadecatruncated prismatotesseractihexadecachoron 2.326846
... thawro pyrite, octa-diminishing of id - srid - F-ike - ti tower ...
... thawro wedge ...
thawrorh thawro rhombochoron ...
... thawro-wedged 1/6-luna of hexacosachoron ...
... thawro-wedged 2/6-luna of hexacosachoron ...
thex truncated hexadecachoron, cantic tesseract 1.581139
thext truncated hexadecachoric tetracomb, truncated demitesseractic tetracomb, cantic tesseractic tetracomb
thi truncated hecatonicosachoron 8.218334
thiddip, K-4.47 triangle - hexagon duoprism, hexagon - hip wedge 1.154701
tho tesseractihemioctachoron, octahemioctachoron, vertex figure of hehad 0.707107
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
tibbic triangular-bipyramidal chilliadiacosichoron, rectified-hecatonicosachoron dual, surtegmated hexacosachoron
tibbid (alt.: durap) triangular-bipyramidal decachoron, rectified-pentachoron dual, surtegmated pentachoron, joined pentachoron
tibbit triangular-bipyramidal triacontadichoron, rectified-tesseract dual, surtegmated hexadecachoron
... expanded augmented axially-octahedral ursachoron ofx3xoo4xxx&#xt
tica gircobcu ticagirco bicupola
ticagirco, K-4.128 truncated cube atop great rhombicuboctahedron, truncated-cubical cap of prismatorhombated hexadecachoron, cuboctahedral supra-cap of small rhombated icositetrachoron 2.613126
ticcup, K-4.99 truncated-cube prism 1.847759
tico truncated icositetrachoron, cantitruncated hexadecachoron 2.645751
ticont truncated tetracontoctachoron sqrt[(6+4 sqrt(2))y2+(23+16 sqrt(2))y+(23+16 sqrt(2))]
ticot truncated icositetrachoric tetracomb
... expanded augmented axially-icosahedral ursachoron ofxo3xooo5xxxx&#xt
... triaconta-sphenated id-first tristratic sub-cap of rahi ...
tidagrid, tid || grid, K-4.173 truncated dodecahedron atop great rhombicosidodecahedron, truncated-dodecahedral cap of prismatorhombated hexacosichoron 9.744610
tiddip, K-4.130 truncated-dodecahedron prism 3.011250
tidimex (alt.: idimtex) truncated icosidiminished hexacosachoron, icosidiminished truncated hexacosachoron 4.643523
tidox (old: togex) truncated dodecahedronary-hexacosachoron (truncated great hexacosachoron), compound of 25 tico 2.645751
tidtes tetra-diminished tesseract 1
tidtidohi truncated ditrigonary dishecatonicosachoron 2.645751
tiffix truncated faceted hexacosichoron 4.643523
tigaghi truncated great grand hecatonicosachoron 2
tigfix truncated great faceted hexacosichoron 1.199039
tiggidtixhi truncated great ditrigonary hexacosihecatonicosachoron 2.645751
tiggipe truncated-great-icosahedron prism 1.165943
tighi truncated great hecatonicosachoron 3.477092
tigiddip truncated-great-dodecahedron prism 1.942303
... vertex figure of triacontadipenteract 0.935414
tip (alt: tettum) truncated pentachoron, tet-based tutsatope, tet-based tutism 1.264911
tipe, K-4.127 truncated-icosahedron prism 2.527959
tisadi (alt.: idtex) truncated snub icositetrachoron, icositetradiminished truncated hexacosachoron 4.643523
tiscsrix tristratic icosidodecahedron-first cap of small rhombihexacosachoron 6.073594
tisdip, K-4.18 triangle - square duoprism, square - cube wedge, vertex figure of nit 0.912871
tispic truncated small prismated tetracontoctachoron sqrt[(2+sqrt(2))y2+(7+4 sqrt(2))y+(7+4 sqrt(2))]
tispid truncated small prismated decachoron sqrt(y2+3y+3)
tissidtixhi truncated small ditrigonary hexacosihecatonicosachoron 2.645751
tistadip triangle - pentagram duoprism, pentagram - stip wedge 0.780850
tisted truncated stellated decachoron, compound of 2 truncated pentachora 1.264911
tisthit triangular-simotrihexagonal tetracomb
tistodip triangle - octagram duoprism, octagram - stop wedge 0.791345
titho truncated tesseractihemioctachoron 1.581139
titwadip triangle - dodecagon duoprism, dodecagon - twip wedge 2.016280
toagirco, toe || girco, K-4.149 truncated octahedron atop great rhombicuboctahedron, truncated octahedral cap of prismatorhombated icositetrachoron 3.498949
toagircoatic toe atop girco atop tic
toatic, toe || tic, K-4.98 truncated octahedron atop truncated cube 1.785406
tobcuatut, tobcu || tut, K-4.49 triangular-orthobicupola atop truncated-tetrahedron 1.183216
tobcupe, K-4.44 triangular-orthobicupola prism 1.118034
todip, K-4.59 triangle - octagon duoprism, octagon - op wedge 1.428440
todithix toroidoditrigonary hecatonicosihexacosichoron 1.732051
todtixhi toroidal ditrigonal hexacosihecatonicosachoron 1.732051
... vertex figure of topax 0.907485
tope, K-4.89 truncated-octahedron prism 1.658312
tosot thibbit tomosquare-omnitruncated-trihexagonal duoprismatic tetracomb
tracufbil triangular-cupofastegia biluna, {3} || tricu || {3}, 0.419569-luna of gyspid 1
traddet triangular antiditetragoltriate sqrt[(a22+b22)/3]
tradedip, K-4.94 triangle - decagon duoprism, decagon - dip wedge 1.717954
traf, K-4.6 triangular antifastegium, triangle oct wedge, {3} || gyro trip, {3} || oct, (vertex-) diminished rap 0.774597
... icosaswirlic hexacosachoron, thirtyfold dissected icosahedral polytwister, thirtyfold dissected ikter ...
... octaswirlic enneacontahexachoron, twelvefold dissected octahedral polytwister, twelvefold dissected octer 1.255926
trapedip, K-4.34 triangle - pentagon duoprism, pentagon - pip wedge 1.028076
trateddi, {3} || teddi, K-4.33 {3} atop teddi, teddi based wedge 1
traw, K-4.27 trigonal antitriwedge, hexagon - octahedral wedge, triangular gyrobicupolaic ring, {6} || oct, {3} || gyrated tricu, 1/6-luna of ico 1
tribbit triangular duoprismatic tetracomb, Delone complex of bihexagonal lattice A2×A2
tricuatut, tricu || tut, K-4.50 triangular-cupola atop truncated-tetrahedron 1.183216
tricuf, K-4.25 trigonal cupofastegium, hexagon - triangle-prismatic wedge, triangle orthobicupolaic ring, {6} || trip, {3} || tricu, 0.209785-luna of small prismatodecachoron 1
tricupe, K-4.45 triangular-cupola prism, triangular prism atop hexagonal prism 1.118034
triddap triangle duoantiprism, hemiated hiddip 1.414214
triddep triangular duoexpandoprism, expanded triddip, tegum sum of 2 alternated thiddips 1.154701
triddet triangular ditetragoltriate sqrt[(a2+b2)/3]
triddip, K-4.10 triangle-triangle duoprism, triangle - trip wedge, vertex figure of dot, Delone cell of lattice A2×A2 0.816497
triddit triangle duotegum, dual of triangle duoprism, 6-2-stepprism 1.060660
tridex tri-icositetradiminished hexacosachoron, tetragonal-antiwedge heptacontadichoron 1.618034
tridico (alt.: cytid ico) (cyclo)tridiminished ico 1
tridpyp triangular-bipyramid prism, tetrahedral prism bicupola, external blend of 2 tetrahedral prisms
..., trip || gybef triangular prism || gyrobifastegium ...
trippy, K-4.7 trigonal-prismatic pyramid, vertex pyramid of the rectified pentachoron 0.774597
tript trigonal-prismatic (line-)tegum, trigonal-prismatic dipyramid ...
tripuf, K-4.51 trigonal pucofastegium, triangle - hexagon-prismatic wedge, trigonal magnabicupolaic ring, {3} || hip, {6} || tricu, {3}-first cap of srip 1.183216
trisqdip trisquare duoprism, compound of 9 tes in twaddip army 1
tritep (alt: dycufbil) (line-)triangle-tegum prism, triangular-bipyramidal prism, dyadic cupofastegia biluna
turap two rectified-pentachoron cupolaic blend 0.774597
... expanded augmented axially-tetrahedral ursachoron ofxo3xooo3xxxx&#xt
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
tutatobcu tutatoe orthobicupola
tutatoe augrip tutatoe-augmented grip
tutatoe gybcu tutatoe gyrobicupola
tutatoe, tut || toe, K-4.76 truncated tetrahedron atop truncated octahedron, truncated-tetrahedral cap of prismatorhombated pentachoron, tetrahedral canticupola 1.612452
tuttip, K-4.57 truncated-tetrahedron prism 1.274755
twaddip dodecagonal-dodecagonal duoprism 2.732051
twagy griddip twelve-gyro-augmented great-rhombated-icosidodecahedral prism
twagy tiddip twelve-gyro-augmented truncated-icosidodecahedral prism
twau doaid deep mono-diminished rotunda of ex, 12-augmented doe || id 1.618034
twau griddip twelve-(ortho-)augmented great-rhombated-icosidodecahedral prism
twau iddip twelve-augmented icosidodecahedral-prism
twau sridati twelve-augmented sridati
twau sriddip twelve-augmented sriddip
twau tiddip twelve-(ortho-)augmented truncated-icosidodecahedral prism
twau tipe twelve-augmented truncated-icosahedral prism
... external blend of the sphenocorona-prism and a cube-pyramid, cubic-pyramid-augmented sphenocorona-prism
wavathi sphenoverted triakishecatonicosachoron 1.662508
wavaty sphenoverted triakisicositetrachoron 1.082392
wavdatixady sphenoverted ditrigonary hexacosadishecatonicosachoron 1.258409
wavhiddix sphenoverted hecatonicosadishexacosachoron 5.330704
wavitoth sphenoverted tesseractitesseractihexadecachoron 0.765367
... wx ox3xx4oo&#zx
... wx ox3xx4xx&#zx
... hyperbolic pentagrammic-order hexacontachoric tetracomb 0.393076 i
... x3o3o5v, variation of small disprismatohexacosihecatonicosachoron 3.835128
... hyperbolic hex-ex tetracomb 0.171780 i
... x3o3β4o (?) ...
... x3o3β4x (?) ...
... x3o3β5o (?) ...
... x3o3β5x (?) ...
... hyperbolic order 4 icositetrachoral tetracomb 0 i
... x3o4q3o, variation of small rhombated icositetrachoron 3.316625
... x3o4β3o (?) ...
... x3o4s4o (?) ...
... hyperbolic order 5 faceted-hexacosichoral tetracomb, hyperbolic order 5 icosahedral-hecatonicosachoral tetracomb, hyperbolic ridged pentachoric tetracomb 0.393076 i
... x3β3o3o (?) ...
... x3β3o3β (?) ...
... x3β3o3x (?) ...
... x3β3o4o (?) ...
... x3β3o4β (?) ...
... x3β3o4x (?) ...
... x3β3o5o (?) ...
... x3β3o5β (?) ...
... x3β3o5x (?) ...
... x3β3β3x (?) ...
... x3β3β4o (?) ...
... x3β3β4β (?) ...
... x3β3β4x (?) ...
... x3β3β5o (?) ...
... x3β3β5β (?) ...
... x3β3β5x (?) ...
... x3β3x4β (?) ...
... x3β3x5β (?) ...
... x3β4o3o (?) ...
... x3β4o3β (?) ...
... x3β4o3x (?) ...
... x3β4β3x (?) ...
... x3x3β3o (?) ...
... x3x3β4o (?) ...
... x3x3β5o (?) ...
... truncated hyperbolic order 4 icositetrachoral tetracomb 1.414214 i
... x3x4β3o (?) ...
... hyperbolic x3x4x3x8o tesselation 1.864101 i
... tesseractic tetracomb
... xAFxx3ooxxF3Fxoxo3ooffx&#zx
... xFfoo3xoxxF3fxoxo3ooffx&#zx
... xFfxo3xoxoF3fxooo3oofFx&#zx
... xfofxxfoFxfxo3ooxxoFxFoxxoo3oxfxFofxxfofx&xt (F=ff=x+f)
... xfooo5xofxo oxofx5ooxox&#zx, icosapentadiminished ex
... trigonal mibdi-laced wedge 1
xhi hexacosihecatonicosachoron, bitruncated hecatonicosachoron, bitruncated hexacosachoron 7.579634
xhidy hexacosihecatonicosadishecatonicosachoron 3
xithi hexacositriakishecatonicosachoron 3.872983
... xo3oo3ox&#q, longer variant of tetrahedral antiprism, vertex figure of scad 0.866025
... cyclo-hexagonally diminished ico, tegum sum of 2 bi-dual (x,q)-triddips 1
... tetra-augmented axially-octahedral ursachoron xoBo3ofox3xooo&#xt ...
... xofo3ofox5xoxx&#xt 3.077684
... tetra-augmented axially-tetrahedral ursachoron xofo3ooox3oxoo&#xt ...
... triaugmented trigonal mibdi-laced wedge ...
... xofxxFfooFxfo3xxxoFxxxFoxxx3ofxFoofFxxfox&#xt
... xoo3ofx5xox&#xt 3.077684
... xoofoox3ofxoxfo5xoxxxox&#xt
... xooFxxFfooFoofo3xxFooFxxxFooFxx3ofooFoofFxxFoox&#xt
... xoofxxFfooFxofo3xxFxoFxxxFoxFxx3ofoxFoofFxxfoox&#xt
... :xoqo:4:xxox:3:oooo:4:oxxx:&##x
... hexastratic ike-first cap of rectified hexacosachoron 3.077684
... xoxFoFxox3oxoooooxo5ooxofoxoo&#xt
... xoxFxFxox3oxfoxofxo5xxoxxxoxx&#xt
... ike atop id atop srid atop ti
... xoxxFxxox3oxoxoxoxo5ooxoooxoo&#xt
... decachoron-derived Gévay polychoron ...
... xxfoF3oxxFx3xFxxo3Fofxx&#zx
... magnaursachoron, cell-expanded tetrahedral ursachoron ...
xxo ooo3oxx&#xt line || trip || {3}, stack of tepe and triddip
... xxxFooAFxxAxxFx3oxFxxAxxxFooFxx3xfoxFoofFxxFoox&#xt
... xxxoooFFFAAA 2 FxfoFfxFofxo 2 xfFFfoFoxxof 2 fFxfoFoxFofx &#zx
... xxxoooFFFAAABxxxF FxfoFfxFofxooVoof xfFFfoFoxxofooVof FAoFxAxoAxFoxxxBF&#zx

Count of actually available polytopes: 1654



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---- 5D ----


Acronym Name Circumradius
... 2dah (?) 0.790569
... 2firx (?) 0.816497
... 2hehad (?) 0.707107
... 2howoh (?) 1.732051
... 2rhohid (?) 1
3,n-dippip triangle - n-gon duoprismatic prism sqrt[7/12+1/(4 sin2(π/n))]
..., {4} || perp {4} (degenerate) square atop fully orthogonal square, square disphenoid ∞   i.e. flat in euclidean space
5,n-dippip pentagon - n-gon duoprismatic prism sqrt[(15+2 sqrt(5))/20+1/(4 sin2(π/n))]
..., {5} || perp {5/2} (degenerate) pentagon atop fully perpendicular pentagram ∞   i.e. flat in euclidean space
..., {5} || gyro pedip (degenerate) pentagon atop gyrated pedip ∞   i.e. flat in euclidean space
bacox biprismatocellihexateron 1
bad biprismatododecateron 0.866025
bend biprismatointercepted dodecateron 0.866025
bidhin (alt.: octahex, tetalrap, tetaltet octtric) bidiminished hemipenteract, oct || hex, tet || inverted rap, (tet,dual tet,oct)-trigonic 0.790569
bidot bidodecateron, triangular duotegmatic icosateron, triangular duotegmatic alterprism, dodecateron dual 0.790569
bidrappy bidrap pyramid 0.790569
bittin bitruncated penteract 2.549510
bittit bitruncated triacontiditeron, Voronoi cell of lattice D5* 2.121320
bittix (old: dittox) bitruncated hexateron 1.554563
brinoh birectified penteractic pentacomb
cabbix cellibiprismatohexateron 0.866025
caddix cellidishexateron 0.866025
cappin celliprismated penteract, steritruncated pentacross 2.423081
cappix (old: happix) celliprismated hexateron, cellitruncated hexateron, hedratoprismated hexateron, steritruncated hexateron 1.632993
capt celliprismated triacontiditeron, steritruncated penteract 2.878460
captid (old: hiptid) celliprismatotruncated dodecateron, hedratoprismatotruncated dodecateron, steriruncitruncated hexateron 2.236068
captint celliprismatotruncated penteractitriacontiditeron, steriruncitruncated penteract, steriruncitruncated pentacross 3.701317
card (old: scard, shard) (small) cellirhombated dodecateron, small hedratorhombated dodecateron, stericantellated hexateron 1.658312
carnit (old: scarnit) (small) cellirhombated penteractitriacontiditeron, stericantellated penteract, stericantellated pentacross 2.660531
chad cellihemidodecateron 1
coa tutcup, co || tutcup co atop tuta 1.224745
coarit co atop rit 1.224745
coatope (alt.: cotoe totric) co atop tope, (co,toe,toe)-trigonic, co-first cap of sibrant at (rico,rico)-margin 2.236068
coatuttip co atop tuttip, co-first cap of sarx 1.290994
cogart (old: gocart) celligreatorhombated triacontiditeron, (great cellirhombated triacontiditeron), stericantitruncated pentacross 3.534493
cograx (old: gocrax, goharx) celligreatorhombated hexateron (great cellirhombated hexateron, great hedratorhombated hexateron), stericanitruncated hexateron 2.327373
cogrin (old: gocrin) celligreatorhombated penteract (great cellirhombated penteract), stericantitruncated penteract 3.988340
..., cont || grico (degenerate) cont atop grico ∞   i.e. flat in euclidean space
contip tetracontoctachoron prism, bitruncated-icositetrachoron prism 3.450631
copatoe (alt.: coco totric) cope atop toe, (co,co,toe)-trigonic 1.870829
copatope cope atop tope, coatoe prism, cope-first monostratic cap of ricope 1.802776
copatut cope atop tut 1.190238
copea tuttip cope atop tuttip, cope-first monostratic cap of srippip 1.284523
copeatope cope atop tope, coatoe-prism 1.802776
cotut totric (co,tut,toe)-trigonic 1.732051
cubaope cube atop octahedral-prism 0.895420
cubasc (degenerate) cubical scalene, line atop fully orthogonal cube ∞   i.e. flat in euclidean space
cubasquasc cube atop squasc 1
cubpyp cubpy prism 1.118034
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
dah dishexadecateron, vertex figure of kaje 0.790569
danbitot dispenteractibitruncated triacontaditeron 1.802776
danpit dispenteractiprismated triacontaditeron 2.5
deca agrip deca atop grip, deca-first cap of pirx 1.914854
deca aprip deca atop prip 1.620185
..., deca || gippid (degenerate) deca atop gippid ∞   i.e. flat in euclidean space
decap decachoron prism 1.5
dehad dodecahemidodecateron 1
dibhid dodecabiprismatohemidodecateron 1
dihin (alt.: penalrap) (vertex-)diminished hemipenteract, pentachoron atop alternate rectified pentachoron 0.790569
ditetaf (alt.: traltepe, penaltrip) diminished tetaf, triangle atop gyrated tepe, pen atop gyrated trip, (edge,perp triangle,gyro trip)-trigonic 0.790569
..., doe || ipe (degenerate) doe atop ipe ∞   i.e. flat in euclidean space
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
... point || hex || gyro hex, Dutour polyteron type A
ecypit elongated cyclopentachoric tetracomb, elongated pentachoric-dispentachoric tetracomb
editetaf edge-diminished tetaf, (top base) edge-diminishing of tet-first rotunda of hin 0.790569
exip hexacosachoron prism 1.693527
fawdint frustisphenary dispenteractitriacontaditeron, fastegiverted dispenteractitriacontaditeron 0.914214
fenandoh facetospinopenteractidishexadecateron 1.274755
fidoh facetoinverted decahexadecateron 1.274755
firx facetorectified hexateron 0.816497
..., fix || padohi (degenerate) fix atop padohi ∞   i.e. flat in euclidean space
gabdacan great biprismatodiscellipenteract 1.021221
gacnet great cellated penteractitriacontiditeron, omnitruncated penteract, omnitruncated pentacross 4.829189
gadencorn great dispinocellirhombated penteract 1.192297
gadinnert great dispenteractirhombated triacontaditeron 2.336045
gadtaxadiap grand ditetrahedronary hexacosadishecatonicosachoron atop alternate grand ditetrahedronary hexacosadishecatonicosachoron, grand ditetrahedronary hexacosadishecatonicosachoron alterprism 0.951057
gadtaxhiap grand ditetrahedrary hexacontahecatonicosachoron antiprism 0.951057
gafwan great facetosphenary penteract 0.792893
..., gaghi || gofix (degenerate) gaghi atop gofix, (degenerate) gaghi antiprism, (degenerate) gofix antiprism ∞   i.e. flat in euclidean space
gaghipy, pt || gaghi (degenerate) gaghi pyramid ∞   i.e. flat in euclidean space
gancpan great spinocelliprismated penteract 1.276197
gapcyxh great prismated cyclohexateric honeycomb, Voronoi complex of lattice A5*
gappip great-antiprism prism 1.693527
gapquinoh great prismated quarterpenteractic pentacomb
gaqrin great quasirhombated penteract 1.673396
gaquacint great quasicellated penteractitriacontiditeron 3.029675
gaquapan great quasiprismated penteract 2.527061
gaquidpothip great-quasidisprismatotesseractihexadecachoric prism, great-quasiprismated-tesseract prism 2.001839
garcornit great retrocellirhombated penteractitriacontaditeron 1.192297
gart great rhombated triacontiditeron, cantitruncated pentacross 2.645751
garx great rhombated hexateron, cantitruncated hexateron 2
gashia grand stellated hecatonicosachoron antiprism, grand stellated hecatonicosachoron alterprism, grand stellated hecatonicosachoron atop dual grand stellated hecatonicosachoron 0.680827
gatopin great pteroprismated penteract 0.914214
gektabcadont (old: giktabacadint) great skewtrigonary biprismatocellidispenteractitriacontiditeron 1.5
getitdin great tesseractitriacontidiadispenteract 1.276197
gibcotdin great biprismatocellitriacontadiadispenteract 2.001839
gibrant great birhombated penteractitriacontiditeron, bicantitruncated penteract 3.391165
gibrid (old: gadrid) great birhombated dodecateron, bicantitruncated hexateron 2.179449
gibtadin great biprismatotriacontadiadispenteract 1.488108
gidpithip great-disprismatotesseractihexadecachoric prism, great-prismated-tesseract prism, central segment of cogart 3.534493
gidpixhip great-disprismatohexacosihecatonicosachoron prism, omnitruncated-hexacosachoron prism 12.796423
gidtixhipy, pt || gidtixhi (degenerate) gidtixhi pyramid ∞   i.e. flat in euclidean space
ginnont great penteractipenteractitriacontiditeron 1.021221
gipbin great prismated biprismatopenteract 0.914214
giphin great prismated hemipenteract, steriruncicantic penteract 3.259601
gippiccup great-prismatotetracontoctachoron prism, omnitruncated-icositetrachoron prism 5.194028
gippiddip great-prismatodecachoron prism 2.291288
gippin great prismated penteract, runcicantitruncated penteract 4.371952
gippit great prismated triacontiditeron, omnitruncated hemipenteract 3.872983
gippix great prismated hexateron, runcicantitruncated hexateron 2.581989
gircaptint (old: grecaptint) great retrocelliprismatotruncated penteractitriacontaditeron 1.949424
girhin great rhombated hemipenteract, cantitruncated demipenteract, runcicantic penteract 2.761340
girn great rhombated penteract, cantitruncated penteract 3.563671
gittithip great-tesseractitesseractihexadecachoron prism 1.021221
gloptin great lapidoprismatotruncated penteract 1.416813
gocad (old: gohad) great cellated dodecateron (great hedrated dodecateron), omnitruncated hexateron, Voronoi cell of lattice A5* 2.958040
gocypapit bitruncated pentachoric tetracomb, great cycloprismated pentachoric tetrachomb, grand prismatodispentachoric tetracomb
..., gofix || quipdohi (degenerate) gofix atop quipdohi ∞   i.e. flat in euclidean space
gogishiagax great grand stellated hecatonicosachoron antiprism, grand hexacosachoron antiprism, taller great grand stellated hecatonicosachoron atop grand hexacosachoron 0.667731
gogishiragax great grand stellated hecatonicosachoron retroprism, grand hexacosachoron retroprism, narrower great grand stellated hecatonicosachoron atop grand hexacosachoron 0.636010
gohip great hexacosachoron prism 1.693527
gorcrin great retrocelligreat rhombated penteract 2.143163
grahip (old: grahipe) great-rhombated-hecatonicosachoron prism, cantitruncated-hecatonicosachoron prism 11.263210
..., grico || gippic (degenerate) grico atop gippic ∞   i.e. flat in euclidean space
gricoa (old: gricoalgrico) great-rhombated-icositetrachoron alterprism, great-rhombated-icositetrachoron atop alternate great-rhombated-icositetrachoron 4.311477
gricope (old: gripe) great-rhombated-icositetrachoron prism, cantitruncated-icositetrachoron prism 4.328427
gripagippid grip atop gippid, grip-first cap of cograx 2.327373
grippip great-rhombated-pentachoron prism 1.910497
gritta gidpith grit atop gidpith, grit-first segment of cogrin 3.988340
grittip truncated-tesseract prism, central segment of prin 3.047217
..., grix || prix (degenerate) grix atop prix ∞   i.e. flat in euclidean space
grixip great-rhombated-hexacosachoron prism 9.137791
groh great rhombihexahedron 0.736813
gyepcuro, J47 gyroelongated pentagonal cupolarotunda
haco (old: hicco) hexagon cuboctahedron duoprism 1.414214
hacube (old: hiccube) hexagon cube duoprism 1.322876
hadoe hexagon - dodecahedron duoprism 1.721489
hagirco (old: higgirco) hexagon great-rhombicuboctahedron duoprism 2.524147
hagrid hexagon - great-rhombicosidodecahedron duoprism 3.931692
hahip (old: hiddippip) hexagon hexagonal-prism duoprism, hexagon-hexagon duoprismatic prism 1.5
han hexadecapenteract, vertex figure of daj 0.790569
haquitco hexagon quasitruncated-cuboctahedron duoprism 1.459000
hasirco (old: hissirco) hexagon small-rhombicuboctahedron duoprism 1.719624
hasrid hexagon - small-rhombicosidodecahedron duoprism 2.446644
hatet (old: hittet, alt. hipdaw) hexagon-tetrahedron duoprism, hexagon duofastegium, hip disphenoid 1.172604
hati hexagon - truncated-icosahedron duoprism 2.672186
hatic (old: hittic) hexagon truncated-cube duoprism 2.040640
hatid hexagon - truncated-dodecahedron duoprism 3.133309
hatoe (old: hittoe) hexagon truncated-octahedron duoprism 1.870829
hatricu hexagon-tricu duoprism, trip-first half of haco 1.414214
hatut (old: hittut) hexagon truncatet-tetrahedron duoprism 1.541104
hehad hexadecahemidecateron, vertex figure of thox 0.707107
..., hex || sidpith (degenerate) hex atop sidpith ∞   i.e. flat in euclidean space
hexaco hexadecachoron atop cuboctahedron, 0.147584-luna of rectified triacontiditeron 1
hexaico, hex || ico hexadecachoron-first rotunda of rectified triacontiditeron, hexadecachoron atop icositetrachoron 1
hexalrit hex atop gyrated rit, hex-first cap of siphin 1.274755
hexarit (degenerate) hex atop rit ∞   i.e. flat in euclidean space
hexathex (degenerate) hex atop thex ∞   i.e. flat in euclidean space
hexip hexadecachoron prism, vertex figure of rag 0.866025
hexpy hexadecachoral pyramid, vertex-first rotunda of triacontiditeron 0.707107
hextum hex-based tutsatope, hex-based tutism, hex-first rotunda of tot 1.581139
hexu hexadecachoral-based ursateron ofx3xoo3ooo4ooo&#xt, hex-based ursulate 1.144123
hiarahi, hi || rahi (degenerate) hi atop rahi ∞   i.e. flat in euclidean space
hid hexagon icosidodecahedron duoprism 1.902113
hike hexagon icosahedron duoprism 1.380039
hin hemipenteract, demipenteract, hemitesseractic gyroprism, tetrahedral altersquarism, vertex figure of jak, Gosset polytope 12,1 0.790569
hinoh hemipenteractic pentacomb, Delone complex of lattice D5
hipe hecatonicosachoron prism 3.736068
hisquippy hexagon-squippy douprism, half of hoct 1.224745
hit hexadecateron 0.790569
hix hexateron, 5D simplex5), 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
hoct hexagon octahedron duoprism 1.224745
hosiap hollow stellated icosatetrachoric antiprism, pseudo stico atop pseudo stico 0.790569
howoh hexadecasphenohexadecateron, cantellated hexadecahemidecateron 1.732051
ica sidpith, ico || sidpith icositetrachoron atop small disprismatotesseractihexadecachoron 1.847759
ica tutcup, ico || tutcup icositetrachoron atop truncated-tetrahedral-cupoliprism 1.224745
icarico (degenerate) ico atop rico ∞   i.e. flat in euclidean space
icarit, ico || rit icositetrachoron atop rectified tesseract, ico-first half of nit 1.224745
icates, ico || tes icositetrachoron atop tesseract 1.050501
icathex ico atop thex, ico-first segment of sart 1.732051
..., ico || sadi ico atop sadi ∞   i.e. flat in euclidean space
..., ico || spic (degenerate) ico atop spic ∞   i.e. flat in euclidean space
..., ico || srit (degenerate) ico atop srit ∞   i.e. flat in euclidean space
icoap (alt.: icoalico) icositetrachoral antiprism, icositetrachoron atop dual icositetrachoron 1.050501
icope icositetrachoron prism 1.118034
icopy (degenerate) ico pyramid ∞   i.e. flat in euclidean space
icou icositetrachoral-based ursateron ofx3xoo4ooo3ooo&#xt, ico-based ursulate 1.738546
..., ike || dope (degenerate) ike atop dope ∞   i.e. flat in euclidean space
irl invertiretrolepidoteron 1.224745
irohlohn invertiretrohexadecalepidohemipenteract 1.224745
kafandoh spikifacetospinodishexadecateron 1.620185
lawx ???-sphenary hexateron 1.290994
mibdinit metabidiminished nit, rectified bidhin 1.224745
n,co-dip n-gon - cuboctahedron duoprism sqrt[1+1/(4 sin2(π/n))]
n,cube-dip n-gon - cube duoprism sqrt[3/4+1/(4 sin2(π/n))]
n,doe-dip n-gon - dodecahedron duoprism sqrt[(9+3 sqrt(5))/8+1/(4 sin2(π/n))]
n,girco-dip n-gon - great-rhombicuboctahedron duoprism sqrt[(13+6 sqrt(2))/4+1/(4 sin2(π/n))]
n,grid-dip n-gon - great-rhombicosidodecahedron duoprism sqrt[(31+12 sqrt(5))/4+1/(4 sin2(π/n))]
n,id-dip n-gon - icosidodecahedron duoprism sqrt[(3+sqrt(5))/2+1/(4 sin2(π/n))]
n,ike-dip n-gon - icosahedron duoprism sqrt[(5+sqrt(5))/8+1/(4 sin2(π/n))]
n,k-dippip n-gon - k-gon duoprismatic prism sqrt[1/4+1/(4 sin2(π/n))+1/(4 sin2(π/k))]
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)
n,n-dippip n-gon - n-gon duoprismatic prism sqrt[1/4+1/(2 sin2(π/n))]
n,oct-dip n-gon - octahedron duoprism sqrt[1/2+1/(4 sin2(π/n))]
n,sirco-dip n-gon small-rhombicuboctahedron duoprism sqrt[(5+2 sqrt(2))/4+1/(4 sin2(π/n))]
n,srid-dip n-gon - small-rhombicosidodecahedron duoprism sqrt[sqrt(5)+11/4+1/(4 sin2(π/n))]
n,tet-dip n-gon - tetrahedron duoprism, n-gonal duofastegium, n-gonal prism disphenoid sqrt[3/8+1/(4 sin2(π/n))]
n,ti-dip n-gon - truncated-icosahedron duoprism sqrt[(29+9 sqrt(5))/8+1/(4 sin2(π/n))]
n,tic-dip n-gon - truncated-cube duoprism sqrt[sqrt(2)+7/4+1/(4 sin2(π/n))]
n,tid-dip n-gon - truncated-dodecahedron duoprism sqrt[(37+15 sqrt(5))/8+1/(4 sin2(π/n))]
n,toe-dip n-gon truncated-octahedron duoprism sqrt[5/2+1/(4 sin2(π/n))]
n,tut-dip n-gon - truncated-tetrahedron duoprism sqrt[11/8+1/(4 sin2(π/n))]
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)])
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)
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
naquiptant penteractiquasiprismatotruncated penteractitriacontaditeron 1.621320
naquitant penteractiquasitruncated penteractitriacontaditeron 1.354911
narptint penteractiretroprismatotruncated penteractitriacontaditeron 2.621320
nat spinotriacontaditeron 1.224745
nippant penteractiprismated penteractitriacontaditeron 3.505073
niptant penteractiprismatotruncated penteractitriacontaditeron 2.621320
nit penteractitriacontiditeron, birectified penteract, birectified triacontiditeron, birectified pentacross, Gosset polytope 02,1,1 1.224745
noqrant penteractiquasirhombated penteractitriacontaditeron 1.849749
noqraptant penteractiquasiretroprismatotruncated penteractitriacontaditeron 1.621320
noquapant penteractiquasiprismated penteractitriacontaditeron 2.283521
nottant penteractitruncated penteractitriacontaditeron 2.159679
nurrant penteractirhombated penteractitriacontaditeron 3.013043
... hyperbolic order 3 icositetrachoric-tetracomb pentacomb 1 i
oco (old: occo) octagon cuboctahedron duoprism 1.645329
octa tutcup, oct || tutcup oct atop tuta 1.274755
octacope oct atop cope, oct-first cap of nit 1.224745
octasc octahedral scalene, octahedron-pyramid pyramid, line atop fully orthogonal octahedron, 1/4-lune of triacontiditeron 0.707107
octatepe (alt.: tettet octtric) oct atop tepe, diminished rix, (tet,tet,oct)-trigonic 0.816497
octatuttip (alt.: octtut tuttric) oct atop tuttip, (oct,tut,tut)-trigonic 1.414214
octco tuttric (oct,co,tut)-trigonic 1.224745
octhipdaw (alt.: traporhip) (oct,hip)-disphenoid, trigonal antiprism atop axis-orthogonal hexagonal prism 1.224745
octpy || octaco 1/4-lune of rectified triacontiditeron, octahedron-pyramid atop octhedron-first-rotunda-of-icositetrachoron 1
octpyp, line||ope octahedron-prismatic wedge, line atop ope, octahedral-pyramid prism, half of hexip 0.866025
ocube octagon - cube duoprism 1.567516
odnit octadiminished nit 1.224745
odoe octagon - dodecahedron duoprism 1.915889
..., ofx3xoo4ooo&#xt || o3o4x cube atop (oct,co)-ursachoron, (oct,co)-ursachoron based wedge 1.994779
ogirco octagon - great-rhombicuboctahedron duoprism 2.660531
ogrid octagon - great-rhombicosidodecahedron duoprism 4.020611
oid octagon-icosidodecahedron duoprism 2.079697
oike octagon-icosahedron duoprism 1.616049
opeaco octahedron-prism atop cuboctahedron, diminished 1/4-lune of rat 1
opeacope ope atop cope, octaco-prism, ope-first half of icope 1.118034
opeah ope atop hexagon, (trip,gyro trip,hexagon)-trigonic 1
opeatut (alt.: octoct tuttric) ope atop tut, (oct,oct,tut)-trigonic 1.190238
opeatuttip ope atop tuttip, octatut-prism, ope-first cap of srippip 1.284523
opepy octahedral-prismatic pyramid, vertex pyramid of rectified triacontiditeron 1
osirco octagon small-rhombicuboctahedron duoprism 1.914214
osrid octagon - small-rhombicosidodecahedron duoprism 2.587117
otet octagon-tetrahedron duoprism, octagon duofastegium 1.442951
oti octagon - truncated-icosahedron duoprism 2.801372
otic (old: ottic) octagon - truncated-cube duoprism 2.207107
otid octagon - truncated-dodecahedron duoprism 3.244185
otoe (old: otto) octagon truncated-octahedron duoprism 2.051123
otut octagon - truncated-tetrahedron duoprism 1.755593
owoct octagon octahedron duoprism 1.485633
pabex hix (alt.: thiddipcup) partially bi-expanded hexateron, thiddip cupoliprism 1.190238
..., padohi || rofix (degenerate) padohi atop rofix ∞   i.e. flat in euclidean space
pattin prismatotruncated penteract, runcitruncated penteract 3.239235
pattit prismatotruncated triacontiditeron, runcitruncated pentacross 2.738613
pattix prismatotruncated hexateron, runcitruncated hexateron 1.848423
peco pentagon-cuboctahedron duoprism 1.312862
pecube pentagon-cube duoprism 1.213922
pedoe pentagon-dodecahedron duoprism 1.639247
penalsrip, pen || inv srip (degenerate) pen atop inverted srip ∞   i.e. flat in euclidean space
penaspid pentachoron atop small prismated decachoron, pen-first rotunda of scad 1
penasrip pen atop srip 1.274755
penatrip pentachoron atop trigonal prism, (edge,perp triangle,trip)-trigonic 1
penit (old: pendpy) pentachoral (line-)tegum, pentachoral dipyramid
pennatip pen atop tip, pen-first cap of rin 1.414214
penp pentachoron prism, vertex figure of ril 0.806226
pent penteract, decateron, 5D measure-polytope5), geopet(id) 1.118034
penth (alt.: stenoh) penteractic pentacomb, 5D hypercubical honeycomb5), (alt.: small terated penteractic pentacomb)
penu pentachoral-based ursateron ofx3xoo3ooo3ooo&#xt, pen-based ursulate 1.029086
pepip pentagon duoprismatic prism 1.302772
petet pentagon-tetrahedron duoprism, pentagon duofastegium 1.048144
pexhin (old: tutas) partially expanded hemipenteract, truncated tetrahedron altersquarism, tuta alterprism, cyclodiminished siphin 1.274755
pexhix (alt.: triddipah, tripotricudaw) partially expanded hexateron, triangle-triangle duoprism atop hexagon, (trip, ortho tricu)-disphenoid 1
pid pentagon - icosidodecahedron duoprism 1.828016
pike pentagon-icosahedron duoprism 1.275976
pirghia prismatorhombated great hecatonicosachoron alterprism 4.923348
pirhin prismatorhombated hemipenteract, runcicantellated demipenteract, steriruncic penteract 2.150581
pirt prismatorhombated triacontiditeron, runcicantellated pentacross 3
pirx prismatorhombated hexateron, runcicantellated hexateron 1.914854
pithin prismatotruncated hemipenteract, runcitruncated demipenteract, stericantic penteract 2.371708
poct pentagon - octahedron duoprism 1.106168
..., prahi || grix (degenerate) prahi atop grix ∞   i.e. flat in euclidean space
prahip (old: prahipe) prismatorhombated-hexacosachoron prism, runcitruncated-hexacosachoron prism 8.294035
praquinoh prismatorhombated quarterpenteractic pentacomb
..., prico || gyro grico (degenerate) prico atop gyrated grico ∞   i.e. flat in euclidean space
pricoa (old: pricoalprico) prismatorhombated-icositetrachoron alterprism, prismatorhombated-icositetrachoron atop alternate prismatorhombated-icositetrachoron 3.522336
pricope (old: pripe) prismatorhombated-icositetrachoron prism, runcitruncated-icositetrachoron prism 3.534493
prin prismatorhombated penteract, runcicantellated penteract 3.047217
pripa (old: pripalprip) prip alterprism, prip atop inverted prip, medial segment of card 1.658312
pripa gippid prip atop gippid, prip-first cap of pattit 2.738613
pripagrip prip atop grip 1.870829
pripalgrip prip atop alternate grip 1.848423
prippip prismatorhombated-pentachoron prism 1.688194
pripro prip-first rotunda of captid 2.236068
..., prit || grit (degenerate) prit atop grit ∞   i.e. flat in euclidean space
prittip prismatorhombated-tesseract prism, prismatotruncated-hexadecachoron prism, runcitruncated-hexadecachoron prism, central segment of cappin 2.423081
prixip prismatorhombated-hexacosachoron prism, runcitruncated-hexacosachoron prism 9.757429
..., proh || gidpith (degenerate) proh atop gidpith ∞   i.e. flat in euclidean space
prohagrit proh atop grit, proh-first segment of pattin 3.239235
prohp prismatorhombated-hexadecachoron prism, prismatotruncated-tesseract prism, runcitruncated-tesseract prism, central segment of carnit 2.660531
pysnan pyritosnub penteract, edge-alternation of great cellated penteractitriacontiditeron ...
... q x3o3o3o, variation of pentachoron prism, vertex figure of rectified hexeract 0.948683
quacant quasicellated penteractitriacontiditeron 1.021221
quacgarn quasicelligreatorhombated penteract 2.143163
quacpot quasicelliprismated triacontiditeron 1.102028
quacrant quasicellirhombipenteractitriacontiditeron 1.192297
quicgrat (old: cogqrit) quasicelligreat rhombated triacontiditeron, (celligreat quasirhombated triacontiditeron) 2.001839
quicpatint quasicelliprismatotruncated penteractitriacontiditeron 1.949424
quiprin quasiprismatorhombated penteract 1.488108
quiptin quasiprismatotruncated penteract 1.416813
quititip quasitruncated-tesseract prism 0.792893
quittin quasitruncated penteract 0.649286
rabird retrobirhombidodecateron 1.414214
raccoth retrocellitriacontadiahexadecateron 1.224745
radah retrodishexadecateron 0.790569
..., ragaghi || tigaghi (degenerate) ragaghi atop tigaghi ∞   i.e. flat in euclidean space
ragashia rectified grand stellated hecatonicosachoron alterprism 1.248606
..., rahi || tex (degenerate) rahi atop tex ∞   i.e. flat in euclidean space
rahia sidpixhi (degenerate) rahi atop sidpixhi ∞   i.e. flat in euclidean space
rahipe rectified-hecatonicosachoron prism 4.562051
rapaco (alt.: tetoct cotric) rap atop co, 0.176208-luna of rat, (tet,oct,co)-trigonic 1
rapadeca rap atop deca, rap-first cap of sirhin 1.620185
rapalprip, rap || inv prip (degenerate) rap atop inverted prip ∞   i.e. flat in euclidean space
rapalsrip rap atop inverted srip, rap-first cap of spix 1.190238
rapaltip (degenerate) rap atop inverted tip ∞   i.e. flat in euclidean space
rapaspid rectified pentachoron atop small prismated decachoron, rap-first half of rat 1
rapasrip rectified pentachoron atop small rhombated pentachoron, rap-first cap of nit 1.224745
rapatip rap atop tip, rap-first cap of sarx 0.774597
rapatut (alt.: tetoct tuttric) rap atop tut, (tet,oct,tut)-trigonic 1.190238
rapirx retroprismatorhombated hexateron 1.914854
rappip rectified-pentachoron prism, vertex figure of rojak 0.921954
rappy rectified-pentachoric pyramid, vertex cap of hin 0.790569
rapt rectified-pentachoric (line-)tegum, rectified-pentachoric dipyramid ...
raptum rap-first bistratic cap of thin, rap-based tutsatope, rap-based tutism 1.903943
rapu rectified-pentachoral-based ursateron xoo3ofx3xoo3ooo&#xt, rap-based ursulate 1.258489
rasishia rasishi alterprism 2.829949
... rasishia + 2x 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
ratchet retrotriacontidicellihemitriacontaditeron 1
rawcax (old: rawvdipdopdix) retrosphenary cellihexateron, (retrosphenoverted disprismatoduoprismatodiakishexateron) 1.290994
rawcbinant (old: recarnit) retrosphenary cellibiprismatopenteractipenteractitriacontaditeron, retrocellirhombated penteractitriacontaditeron 2.660531
rawn (old: rawvanant) retrosphenary penteract 2.207107
rawx retrosphenary hexateron 1.290994
recaptid retrocelliprismatotruncated dodecateron 2.236068
repirt retroprismatorhombated triacontiditeron 3
rhohid rectified hexadecahemidecateron 1
ri rhombicosahedron 1.322876
ricasrit, rico || srit rectified-icositetrachoron atop small-rhombated-tesseract 1.847759
ricatah rico atop tah, rico-first cap of sibrant 2.236068
..., rico || gyro srico (degenerate) rico atop gyrated srico ∞   i.e. flat in euclidean space
..., rico || proh (degenerate) rico atop proh ∞   i.e. flat in euclidean space
..., rico || sadi rico atop sadi 1.738546
ricoa (old: ricoalrico), rico || gyro rico rectified icositetrachoron alterprism, rectified icositetrachoron atop gyrated rectified icositetrachoron 1.778824
ricoa ticotum rico-based tutsatope, rico-based tutism, rico-first bistratic cap of pattit 2.738613
ricoaspic rectified icositetrachoron atop small prismated icositetrachoron 1.847759
ricoatico (degenerate) rico atop tico ∞   i.e. flat in euclidean space
ricope rectified-icositetrachoron prism 1.802776
..., rigfix || quipdohi (degenerate) rigfix atop quipdohi ∞   i.e. flat in euclidean space
..., rigfix || sirgaghi (degenerate) rigfix atop sirgaghi ∞   i.e. flat in euclidean space
righia rectified great hecatonicosachoron alterprism 1.917564
rin rectified penteract 1.414214
rinah retropenteractihexadecateron 0.790569
rinoh rectified penteractic pentacomb
rippix retroprismated hexateron 1.190238
..., rit || tat (degenerate) rit atop tat ∞   i.e. flat in euclidean space
rita (old: ritag rit) rit atop gyro rit, medial segment of hex-first siphin 1.274755
rita sidpith, rit || sidpith rectified-tesseract atop small-disprismated-tesseractihexadecachoron 1.502958
ritag thex rit atop gyrated thex, rit-first cap of sirhin 1.620185
ritarico rectified-tesseract atop rectified-icositetrachoron, rectified-tesseract-first segment of small-prismated-triacontiditeron 1.870829
ritasrit, rit || srit rectified-tesseract atop small-rhombated-tesseract 2.632865
ritatah, rit || tah (degenerate) rit atop tah ∞   i.e. flat in euclidean space
ritathex (degenerate) rit atop thex ∞   i.e. flat in euclidean space
rittip rectified-tesseract prism 1.322876
rix rectified hexateron, vertex figure of hax, Gosset polytope 03,1 0.816497
rocgrax retrocelligreat rhombated hexateron 2.327373
rocrax (old: sircrax) (small) retrocellirhombated hexateron 1.658312
..., rofix || sirsashi (degenerate) rofix atop sirsashi ∞   i.e. flat in euclidean space
roxahi, rox || hi (degenerate) rox atop hi ∞   i.e. flat in euclidean space
roxip rectified-hexacosachoron prism 3.118034
... tetrahedral - n-prismantiprismoid ...
... tetrahedral - 2n-prismantiprismoid ...
... tetrahedral - square-prismantiprismoid ...
... triangular,tetrahedral duoantiprism ...
... tetrahedral - hexagon-prismantiprismoid ...
sadinnert small dispenteractirhombated triacontaditeron 2.010695
sadip snub-icositetrachoron prism, snub-disicositetrachoron prism, semistruncated-icositetrachoron prism 1.693527
sart small rhombated triacontiditeron, cantellated pentacross 1.732051
sarx small rhombated hexateron, cantellated hexateron 1.290994
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
scant small cellated penteractitriacontiditeron, stericated penteract, stericated pentacross 1.567516
setitdin small tesseractitriacontidiadispenteract 2.423081
shadow small heptagrammic disphenoid, small heptagramm atop fully orthogonal small heptagramm 0.674163
sibcotdin small biprismatocellitriacontadiadispenteract 3.534493
sibrant small birhombated penteractitriacontiditeron, bicantellated penteract, bicantellated pentacross 2.236068
sibrid (old: sadrid) small birhombated dodecateron, bicantellated hexateron 1.414214
sibtadin small biprismatotriacontadiadispenteract 3.047217
sid pippadiap small dipentary prismatodishecatonicosachoral antiprism 2.527959
siddy small dodekicosahedron 1.721489
... sid pippady + 240 2sissid (?) 2.527959
..., sidpith || prit (degenerate) sidpith atop prit ∞   i.e. flat in euclidean space
..., sidpith || tat (degenerate) sidpith atop tat ∞   i.e. flat in euclidean space
sidpithip small-disprismatotesseractihexadecachoron prism, runcinated-tesseract prism, small-prismated-tesseract prism, central segment of scant 1.567516
..., sidpixhi || srix (degenerate) sidpixhi atop srix ∞   i.e. flat in euclidean space
sidpixhip small-disprismatohexacosihecatonicosachoron prism, runcinated-hecatonicosachoron prism, runcinated-hexacosachoron prism 5.259887
sidtaxhiap small ditetrahedrary hexacontahecatonicosachoron antiprism 2.321762
sidtixhipy, pt || sidtixhi (degenerate) sidtixhi pyramid ∞   i.e. flat in euclidean space
sinnont small penteractipenteractitriacontiditeron 1.567516
siphin small prismated hemipenteract, runcinated demipenteract, steric penteract 1.274755
sircaptint (old: srecaptint) small retrocelliprismatotruncated penteractitriacontaditeron 3.701317
sird small rhombidodecahedron 2.232951
sirdtaxadiap small retroditetrahedronary hexacosidishecatonicosachoron atop alternate small retroditetrahedronary hexacosidishecatonicosachoron, small retroditetrahedronary hexacosidishecatonicosachoron alterprism 2.321762
sirgashia small rhombated grand stellated hecatonicosachoron alterprism 1.618034
sirghia small rhombated great hecatonicosachoron alterprism 3.404434
sirhin small rhombihemipenteract, cantellated demipenteract, runcic penteract 1.620185
sirn small rhombated penteract, cantellated penteract 2.207107
sirpin small retroprismated penteract 1.914214
..., sishi || fix (degenerate) sishi atop fix, (degenerate) sishi antiprism, (degenerate) fix antiprism ∞   i.e. flat in euclidean space
sishia small stellated hecatonicosachoron alterprism, narrower sishi atop sishi 1.074481
... sishia + 2x 2sishi (?) 1.074481
sishipy, pt || sishi (degenerate) sishi pyramid ∞   i.e. flat in euclidean space
sissidisc small-stellated-dodecahedral scalene, small-stellated-dodecahedral-pyramid pyramid, line atop fully orthogonal small stellated dodecahedron 0.636010
sitpodadia small (intersected) tripesic dodecahedronary dishecatonicosachoron alterprism 1.074481
skatbacadint small skewtrigonary biprismatocellidispenteractitriacontiditeron 1.5
snan snub penteract, alternation of great cellated penteractitriacontiditeron ...
snippit (old: spitac, alt.: snahin) snub prismatotriacontaditeron (snub demipenteract), alternation of great prismated triacontaditeron ...
snod (snix) snub dodecateron (snub hexateron), alternation of great cellated hexateron ...
span small prismated penteract, runcinated penteract 1.914214
spaquinoh small prismated quarterpenteractic pentacomb
spat small prismated triacontiditeron, runcinated pentacross 1.870829
sphiddixa small prismatohecatonicosadishexacosachoron alterprism 6.893126
..., spic || srico (degenerate) spic atop srico ∞   i.e. flat in euclidean space
spiccup small-prismatotetracontoctachoron prism, runcinated-icositetrachoron prism 1.914214
spidadeca, spid || deca (degenerate) spid atop deca ∞   i.e. flat in euclidean space
spidaprip spid atop prip, spid-first monostratic cap of spat 1.870829
spidasrip spid atop srip, spid-first cap of spix 1.190238
spidatip small-prismate-pentachoron atop alternate truncated-pentachoron 1.274755
spiddip small-prismatodecachoron prism 1.118034
spidpy (degenerate) spid pyramid ∞   i.e. flat in euclidean space
... vertex figure of spil 0.924211
spix small prismated hexateron, runcinated hexateron 1.190238
squaco square-cuboctahedron duoprism 1.224745
squadinit square-diminished nit 1.224745
squadoe square-dodecahedron duoprism 1.569562
squagirco square great-rhombicuboctahedron duoprism 2.423081
squagrid square - great-rhombicosidodecahedron duoprism 3.867584
... squap - square duoprism, {4}-wedge of tessap 1.050501
squascop squasc prism, square-scalene prism, square atop cube 0.866025
squasirco square - small-rhombicuboctahedron duoprism 1.567516
squasnic square - snub-cube duoprism 1.518409
squasnid square - snub-dodecahedron duoprism 2.268840
squasquasc {4} atop squasc 0.790569
squasquippy square-squippy duoprism, squippyp prism 1
squasrid square - small-rhombicosidodecahedron duoprism 2.342236
squatet square-tetrahedron duoprism, square duofastegium, 2,4-duoprism cupoliprism, vertex figure of brox 0.935414
squati square - truncated-icosahedron duoprism 2.576932
squatic square - truncated-cube duoprism 1.914214
squatid square - truncated-dodecahedron duoprism 3.052479
squatoe (old: squato) square - truncated-octahedron duoprism 1.732051
squatricu square-tricu duoprism 1.224745
squatut square - truncated-tetrahedron duoprism 1.369306
squete square-pyramidal pyramid pyramid, square-tettene, 1/8 of the triacontiditeron 0.707107
squicuffip squicuf prism, tes atop op 1.567516
squid square-icosidodecahedron duoprism 1.765796
squiddaf square duoantifastegium, digonal-square duoantiwedge, square prism atop bidual square prism 0.895420
squike square-icosahedron duoprism 1.185120
squippyippy square-pyramidal-prismatic pyramid, half of vertex pyramid of rectified triacontiditeron 1
squoct square-octahedron duoprism, vertex figure of brinoh 1
..., srahi || xhi (degenerate) srahi atop xhi ∞   i.e. flat in euclidean space
srahip (old: srahipe) small-rhombated-hecatonicosachoron prism 6.753568
..., srico || cont (degenerate) srico atop cont ∞   i.e. flat in euclidean space
..., srico || prico (degenerate) srico atop prico ∞   i.e. flat in euclidean space
sricoa (old: sricoalsrico), srico || gyro srico small-rhombated-icositetrachoron alterprism, small-rhombated-icositetrachoron atop gyrated small-rhombated-icositetrachoron 2.632865
sricope (old: sripe) small-rhombated-icositetrachoron prism, cantellated-icositetrachoron prism 2.660531
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
sripa gippidtum srip-first bistratic cap of pithin, (srip,gippid)-based tutsateron, (srip,gippid)-based tutism 2.371708
sripadeca srip atop deca, srip-first half of sibrid 1.414214
sripadecu (srip,deca)-based ursateron 1.514954
sripagrip srip atop grip, srip-first cap of sibrant 2.236068
sripal pripu (srip,inv.prip)-based ursateron 1.637956
sripalgrip, srip || inv grip (degenerate) srip atop inverted grip ∞   i.e. flat in euclidean space
sripalprip srip atop inverted prip, srip-first cap of sart 1.732051
sripaltip srip atop inverted tip 1.274755
sripaprip srip atop prip, srip-first cap of card 1.658312
sripatip srip atop tip, srip-first segment of sarx 1.290994
srippip small-rhombated-pentachoron prism 1.284523
..., srit || proh (degenerate) srit atop proh ∞   i.e. flat in euclidean space
srittip small-rhombated-tesseract prism 1.914214
srixasrahi (degenerate) srix atop srahi ∞   i.e. flat in euclidean space
srixip small-rhombated-hexacosachoron prism, cantellated-hexacosachoron prism 6.094140
srocgrin small retrocelligreat rhombated penteract 3.988340
sroh small rhombihexahedron 1.398966
stade stellated dodecateron, compound of 2 hix 0.645497
stadow pentagrammic disphenoid, pentagram atop fully orthogonal pentagram 0.623054
starpedippy, pt || starpedip (degenerate) starpedip pyramid ∞   i.e. flat in euclidean space
stethip small-tesseractitesseractihexadecachoron prism 1.567516
stoct pentagram - octahedron duoprism 0.881132
stotet octagram-tetrahedron duoprism, octagram duofastegium 0.817247
stotoe octagram truncated-octahedron duoprism, star-octagon truncated-octahedron duoprism 1.671195
stowoct octagram octahedron duoprism 0.890446
stut phiddixa small tritrigonal prismatohecatonicosidishexacosachoron alterprism 3.855219
tac triacontiditeron, pentacross5), aeropet(id), pentachoral antiprism, vertex figure of gee, Gosset polytopes 21,1, lattice C5 contact polytope (span of its small roots) 0.707107
..., tah || grit (degenerate) tah atop grit ∞   i.e. flat in euclidean space
taha (old: tahagtah), tah || gyro tah tah alterprism, tah atop gyro tah 2.150581
tahatico tah atop tico, tah-first segment of pirt 3
tahp tesseractihexadecachoron prism, bitruncated-tesseract prism, bitruncated-hexadecachoron prism 2.179449
tan truncated penteract 2.465447
tanoh truncated penteractic pentacomb
taope triangle atop octahedral-prism 0.866025
..., tat || grit (degenerate) tat atop grit ∞   i.e. flat in euclidean space
..., tat || prit (degenerate) tat atop prit ∞   i.e. flat in euclidean space
tattip truncated-tesseract prism 2.207107
tedhin tetradiminished hemipenteract, square || hex 0.790569
tedrix tridiminished rectified hexateron, square triorthowedge, lace simplex of 3 mutually orthogonal squares 0.816497
tepaco (alt.: tettet cotric) tepe atop co, 0.217953-luna of scad, (tet,tet,co)-trigonic, partial Stott expansion of hix 1
tepacube tepe || cube, bidrap prism, bi-edge-dimin. rappip, wedge-faceted rappip 0.921954
tepatut (alt.: tettet tuttric) tepe atop tut, tepe-first wedge of siphin, (tet,tet,tut)-trigonic 1.274755
tepeacope tepe atop cope, tepe-first half of spiddip 1.118034
tepeatuttip tepe atop tuttip, tetatut-prism 1.322876
tepepy tetrahedral-prismatic pyramid, vertex pyramid of rectified hexateron 0.816497
..., tes || sadi tes atop sadi ∞   i.e. flat in euclidean space
..., tes || srit (degenerate) tes atop srit ∞   i.e. flat in euclidean space
tespy (degenerate) tes pyramid ∞   i.e. flat in euclidean space
tessap tesseract antiprism, hexadecachoron antiprism 1.050501
tessarit tesseract atop rectified tesseract 1.227160
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
teta tuttip (alt.: tettut tuttric) tet atop tuttip, tet-first cap of sirhin, (tet,tut,tut)-trigonic 1.620185
tetacope tet atop cope, tet-first segment of spix 1.190238
tetaf (alt.: tetaltepe, tettet altettric) tetrahedral antifastegium, tet atop inverted tepe, tet-first rotunda of hin, (tet,tet,dual tet)-trigonic 0.790569
tetco tuttric (tet,co,tut)-trigonic 1.274755
tetcubedaw (alt.: daworsquip) (tet,cube)-disphenoid, 1/6-lune of dodecateron, digonal antiprism atop axis-orthogonal square prism 0.866025
tetcubedaw (alt.: daworsquip) (tet,cube)-disphenoid, dispenoid atop axis-orthogonal square prism 0.873214
..., tex || sidpixhi (degenerate) tex atop sidpixhi ∞   i.e. flat in euclidean space
texip truncated-hexacosachoron prism 4.749980
..., thex || prit (degenerate) thex atop prit ∞   i.e. flat in euclidean space
thexa (old: thexag thex), thex || gyro thex thex alterprism, thex atop gyro thex, equatorial segment of sirhin 1.620185
thexagtah thex atop gyrated tah 2.371708
thexatah (degenerate) thex atop tah ∞   i.e. flat in euclidean space
thexip truncated-hexadecachoron prism 1.658312
thin truncated hemipenteract, cantic penteract 1.903943
thinoh truncated hemipenteractic pentacomb
thipe truncated-hecatonicosachoron prism 8.233530
..., tico || gidpith (degenerate) tico atop gidpith ∞   i.e. flat in euclidean space
..., tico || gyro prico (degenerate) tico atop gyrated prico ∞   i.e. flat in euclidean space
..., tico || prissi tico atop prissi 2.647378
ticope truncated-icositetrachoron prism 2.692582
tin triacontadipenteract 1.414214
tipadeca tip atop deca, 2nd segment of rin in pen-first orientation 1.414214
tipagrip tip atop grip 2.150581
tipalprip tip atop inverted prip 1.632993
tipaprip, tip || prip (degenerate) tip atop prip ∞   i.e. flat in euclidean space
tippip truncated-pentachoron prism 1.360147
tisdipah tisdip atop hexagon 1
tisdippy triangle-square-duoprism pyramid, vertex pyramid of nit 1.224745
tisquippy triangle-squippy douprism, half of troct, (triangle,trip,trip)-trigonic 0.912871
titanoh tritruncated penteractic pentacomb, Voronoi complex of body-centered penteractic lattice (lattice D5*)
tix (alt.: pentum) truncated hexateron, pen-based tutism 1.322876
todin triacontadiadispenteract, compound of 2 hin 0.790569
topax pteroprismated hexateron 1.190238
tot truncated triacontiditeron, truncated pentacross 1.581139
traco (alt.: cocoe cotric) triangle - cuboctahedron duoprism, (co,co,co)-trigonic 1.154701
tracube triangle - cube duoprism 1.040833
tradoe triangle - dodecahedron duoprism 1.515539
traffip traf prism, trip atop inverted tisdip 0.921954
trafpy triangular antifastegium pyramid, (triangular prism, gyro triangular pyramid)-disphenoid 0.790569
tragirco triangle - great-rhombicuboctahedron duoprism 2.388442
tragocco triangle - great-cubicuboctahedron duoprism 0.936070
tragrid triangle - great-rhombicosidodecahedron duoprism 3.845977
trahip (old: thiddippip) triangle hexagonal-prism duoprism, triangle-hexagon duoprismatic prism 1.258306
traltisdip triangle atop gyrated tisdip 1
trapip (old: trapedippip) triangle pentagonal-prism duoprism, triangle-pentagon duoprismatic prism 1.143215
traquith triangle quasitruncated-cube duoprism 0.817997
trashiddip triangle atop shiddip 1.732051
trasirco triangle small-rhombicuboctahedron duoprism 1.513420
trasnic triangle - snub-cube duoprism 1.462497
trasnid triangle - snub-dodecahedron duoprism 2.231808
trasocco triangle - small-cubicuboctahedron duoprism 1.513420
trasrid triangle - small-rhombicosidodecahedron duoprism 2.306383
tratet (alt.: tettet tettric) triangle - tetrahedron duoprism, triangle duofastegium, vertex figure of bril, (tet,tet,tet)-trigonic 0.841625
trathiddip triangle atop thiddip, triangle-first cap of sarx 1.290994
trati triangle - truncated-icosahedron duoprism 2.544388
tratic triangle truncated-cube duoprism 1.870173
tratid triangle - truncated-dodecahedron duoprism 3.025056
tratoe (alt.: totoe totric) triangle truncated-octahedron duoprism, (toe,toe,toe)-trigonic 1.683251
tratrip (old: triddippip) triangle triangular-prism duoprism, triangle-triangle duoprismatic prism, vertex figure of ram 0.957427
tratut (alt.: tuttut tuttric) triangle truncated-tetrahedron duoprism, (tut,tut,tut)-trigonic 1.307032
trawp (alt.: opea hip) traw prism, ope atop hip, 1/6-lune of icope 1.118034
trial tricupe triangle atop gyrated tricupe, (triangle,gyro trip,hip)-trigonic 1.224745
trial triddip {3} atop gyrated triddip, {3}-first cap of rix 0.816497
tricufip tricuf prism 1.118034
trid triangle - icosidodecahedron duoprism 1.717954
tridafup (alt.: pabdidot) triangular duoantifastegiaprism, triangular duoantiwedge, triddip atop bidual triddip, central segment of vertex first dot, parabidiminished dot 0.866025
triddaf triangular duoantifastegium, digonal-triangular duoantiwedge, trip atop bidual trip 0.790569
triddip althiddip triddip atop gyrated thiddip 1.190238
triddipa hip triddip atop hip, (triangle,trip,hip)-trigonic 1.190238
triddippa hiddip triddip atop hiddip, triddip-first cap of card 1.658312
triddippy trigonal-duoprismatic pyramid, vertex pyramid of the dodecateron 0.866025
trike triangle - icosahedron duoprism 1.112583
tripa thiddip trip atop thiddip, (hexagon,trip,hip)-trigonic 1.190238
tripgytricudaw (trip, gyro tricu)-disphenoid 1
triphipdaw (alt.: tripalhip) (trip,hip)-disphenoid, trip atop lacing-orthogonal hip 1.274755
trippasc triangular-prismatic scalene, triangular-prismatic-pyramid pyramid, line atop fully orthogonal triangular-prism 0.790569
trippyp trigonal-prismatic pyramid prism, lacing edge cap of the rectified-pentachoron prism 0.921954
tripufip (alt.: tripa shiddip) tripuf prism, trip-first cap of srippip 1.284523
tritricu triangle-tricu duoprism, half of traco 1.154701
troct (alt.: octoct octtric) triangle-octahedron duoprism, vertex figure of brag, (oct,oct,oct)-trigonic 0.912871
tutaf (old: tutaltuttip) tut alterfastegium, tut atop inverted tuttip 1.274755
tutatope tut atop tope, tut-first cap of pattix 1.848423
tutcupa toe (alt.: tutaltut toetric) tuta atop toe, (tut,inv tut,toe)-trigonic 1.620185
tutcupip tuttip atop inverted tuttip, tuta-prism, medial segment of rittip 1.322876
tuttipa toe (alt.: tuttut totric) tuttip atop toe, (tut,tut,toe)-trigonic 1.632993
tuttipa tope tuttip atop tope, tutatoe-prism, tuttip-first cap of prippip 1.688194
twacube dodecagon - cube duoprism 2.117085
wacbinant sphenary cellibiprismatopenteractipenteractitriacontaditeron 1.192297
wavhiddixa sphenoverted hecatonicosadishexacosachoron alterprism 5.345177
wavinant sphenoverted penteractipenteractitriacontaditeron 0.792893
... hyperbolic order 3 triacontiditeric pentacomb 0 i
..., xhi || thi (degenerate) xhi atop thi ∞   i.e. flat in euclidean space
xhip hexacosihecatonicosachoron prism, bitruncated-hecatonicosachoron prism, bitruncated-hexacosachoron prism 7.596108
zucypit schmoozed cyclopentachoric tetracomb, schmoozed pentachoric-dispentachoric tetracomb

Count of actually available polytopes: 633



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---- 6D ----


Acronym Name Circumradius
... 2thox (?) 0.707107
4,n,m-tip square - n-gon - m-gon - triprism sqrt[1/2+1/(4 sin2(π/n))+1/(4 sin2(π/m))]
4,n,n-tip square - n-gon - n-gon - triprism sqrt[1/2+1/(2 sin2(π/n))]
ax (old: hexe) hexeract, dodecapeton, 6D measure-polytope6), geoex(id) 1.224745
axh hexeractic pentacomb, 6D hypercubical honeycomb6)
bapril biprismatorhombated heptapeton, biruncitruncated heptapeton 2.203893
barm (old: scram, bram, remak, kram) birectified pentacontitetrapeton, (small centrorhombated pentacontitetrapeton) 2.449490
batal bitruncated heptapeton 1.647509
bicotoe bi - (cuboctahedron, truncated octahedron)-duoprism 1.870829
bitem (old: gacram, botam, kobtam) bitruncated pentacontitetrapeton, (great centrorhombated pentacontitetrapeton, heptacontidia-bitruncated pentacontitetrapeton) 4.123106
bitettut (alt.: pabex gee) bi - (tetrahedron, truncated tetrahedron)-duoprism, partially bi-expanded hexacontitetrapeton 1.322876
bittixa (old: bittixalbittix) bitruncated-hexateron alterprism, bitruncated-hexateron atop inverted bitruncated-hexateron 1.581139
boprag biprismatorhombated hexacontitetrapeton, biruncitruncated hexeract 3.674235
boprax biprismatorhombated hexeract, biruncitruncated hexacross 3.464102
botag bitruncated hexacontitetrapeton, bitruncated hexacross 2.121320
botajik bitruncated icosiheptaheptacontidipeton 2.943920
botox bitruncated hexeract 2.915476
brag (old: dric) birectified hexacontitetrapeton, Voronoi cell of lattice D6* 1.224745
bril (old: driss) birectified heptapeton, vertex figure of lin, Gosset polytope 03,2 0.925820
brox (old: drax) birectified hexeract, Gosset polytope 03,1,1 1.414214
cagral (old: gacral) celligreatorhombated heptapeton, stericantitruncated heptapeton 2.618615
cakix celliskewed hexeract 1.581139
cappixa (old: cappixalcappix) cappix alterprism, cappix atop alternate cappix 1.658312
caprohax small celliprismatorhombated hemihexeract, steriruncicantellated demihexeract, pentisteriruncic hexeract 3.278719
captal celliprismatotruncated heptapeton, steriruncitruncated heptapeton 2.591194
captog celliprismatotruncated hexacontitetrapeton, steriruncitruncated hexacross 4.123106
cardip cellirhombated-dodecateron prism 1.732051
catal cellitruncated heptapeton, steritruncated heptapeton 1.851640
catax cellitruncated hexeract 3.456841
cathix cellitruncated hemihexeract, steritruncated demihexeract, penticantic hexeract 2.598076
catjak (old: detidjik) cellitruncated icosiheptapeton (disteridisicosiheptaheptacontidipeton) 2.581989
catog cellitruncated hexacontitetrapeton, steritruncated hexacross 2.828427
cocube cuboctahedron-cube duoprism 1.322876
codip cuboctahedron-cuboctahedron duoprism 1.414214
codoe cuboctahedron-dodecahedron duoprism 1.721489
cograxa (old: cograxalcograx) cograx alterprism, cograx atop alternate cograx 2.345208
coid cuboctahedron-icosidodecahedron duoprism 1.902113
coike cuboctahedron-icosahedron duoprism 1.380039
copal celliprismated heptapeton, steriruncinated heptapeton 1.963961
cophix small celliprismated hemihexeract, steriruncinated demihexeract, pentisteric hexeract 2.179449
copog celliprismated hexacontitetrapeton, steriruncinated hexacross 3.316625
copox celliprismated hexeract, steriruncinated hexeract 3.087966
copril celliprismatorhombated heptapeton, steriruncicantellated heptapeton 2.725541
cotoe cuboctahedron - truncated-octahedron duoprism 1.870829
crag (old: scrag) cellirhombated hexacontitetrapeton, stericantellated hexacross 3.082207
cral (old: scral) cellirhombated heptapeton, stericantellated heptapeton 1.927248
crax (old: scrax) (small) cellirhombated hexeract, stericantellated hexeract 3.277597
crohax (old: scrohax) (small) cellirhombated hemihexeract, pentiruncinated demihexeract, pentiruncic hexeract 2.397916
cubedoe cube-dodecahedron duoprism 1.647278
cubesirco cube-small-rhombicuboctahedron duoprism 1.645329
cubid cube-icosidodecahedron duoprism 1.835220
cubike cube-icosahedron duoprism 1.286277
cyloh cycloheptapetic honeycomb, Delone complex of lattice A6
dadjak decadiminishing of jak 0.816497
daj (old: dije) disicosiheptapeton, vertex figure of nal 0.816497
dijak (alt.: taccahin) (mono-)diminished icosiheptaheptacontidipeton, tac atop hin 0.816497
dodoe dodecahedron-dodecahedron duoprism (or simply: dodecahedral duoprism) 1.981679
dotet (line,)dodecateron-tegum, dodecateron dipyramid
dotip dodecateron prism 1
dotpy dodecateron pyramid, vertex pyramid of mo 1
dottascad dodecateron atop small cellated dodecateron 1
dottasibrid dot atop sibrid, dot-first cap of ram 1.732051
dottaspix dodecateron atop small prismated hexateron, dot-first cap of birectified hexacontitetrapeton 1.224745
dotum dot-first bistratic cap of tim, dot-based tutsatope, dot-based tutism 2.645751
endjak ennea-diminished jak 0.816497
fe tetradecapeton, tritruncated heptapeton, equatorial cross-section of (vertex first) q-hept 1.732051
gaborg great birhombihexacontitetrapeton, bicantitruncated hexacross 3.391165
gaborx great birhombated hexeract, bicantitruncated hexeract 4
gabril great birhombated heptapeton, bicantitruncated heptapeton 2.390457
gacal great cellated heptapeton, steriruncicantitruncated heptapeton 3.380617
gaje (old: gaj, older: gij) great icosiheptaheptacontidipeton 0.816497
gapil great prismated heptapeton, runcicantitruncated heptapeton 2.803060
gaqrox great quasirhombihexeract 1.906840
gaquitxog great quasiterated hexeractihexacontatetrapeton 4.288753
gee (old: xic) hexacontitetrapeton, hexacross6), 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
gibpof great biprismated tetradecapeton, biruncicantitruncated heptapeton 3
ginnontip ginnont prism 1.137055
gippitip great-prismated-triacontiditeron prism 3.905125
girhax great rhombated hemihexeract, cantitruncated demihexeract, runcicantic hexeract 3.278719
girjak great rhombated icosiheptaheptacontidipeton 3.605551
gocadip great-cellated-hexateron prism 3
gocog great cellated hexacontitetrapeton, steriruncicantitruncated hemihexeract, omnitruncated hemihexeract 5.244044
gopam (old: gakpam) great prismated pentacontitetrapeton, (great heptaheptacontidiprismated pentacontitetrapeton), omnitruncated pentacontitetrapeton, omnitruncated icosiheptaheptacontidipeton 6.244998
gopog great prismated hexacontitetrapeton, runcicantitruncated hexacross 3.872983
gotaf great terated tetradecapeton, omnitruncated heptapeton, Voronoi cell of lattice A6* 3.741657
gotaxog great terated hexeractihexacontatetrapeton 6.293378
goxaxog great hexeractihexeractihexacontitetrapeton 1.137055
gram (old: gakbram) great rhombated pentacontitetrapeton, (old: great heptacontiduo-birhombated pentacontitetrapeton), cantitruncated pentacontitetrapeton 5
gril great rhombated heptapeton, cantitruncated heptapeton 2.104417
grog great rhombihexacontitetrapeton, cantitruncated hexacross 2.645751
grox great rhombihexeract, cantitruncated hexeract 4.045239
hagippid hexagon - great-prismated-pentachoron duoprism 2.449490
haprojak demiprismatorhombated icosiheptapeton 3.559026
harjak (old: trojak) demirectified icosiheptaheptacontidipeton (trirectified icosiheptaheptacontidipeton) 2.160247
hatope hexagon - truncated-octahedron duoprismatic prism 1.936492
hax hemihexeract, vertex figure of laq, Gosset polytope 13,1 0.866025
haxh hemihexeractic pentacomb, Delone complex of lattice D6
hedjak heptadiminished jak, square || hin 0.816497
hejak demified icosiheptaheptacontidipeton 1.632993
hexaf, hex || gyro hexip hexadecachoral alterfastegium, hex atop gyrated hexip, hex-first rotunda of hax 0.866025
hexasc hexadecachoric scalene, hexadecachoron-pyramid pyramid, line atop fully orthogonal hexadecachoron, 1/4-lune of hexacontatetrapeton 0.707107
hexipaico hexip atop ico, diminished 1/4-lune of rag 1
hexippy hexip pyramid, vertex pyramid of rag 1
hinanit hin atop nit, hin-first cap of rojak 1.290994
hinarin demipenteract atop rectified penteract, demipenteract-first cap of demified icosiheptaheptacontidipeton 1.632993
hinasiphin hin atop siphin, hin-first cap of sochax 1.322876
hinnip hemipenteractic prism, vertex figure of ranq 0.935414
hinpy demipenteractic pyramid, vertex pyramid of jak 0.816497
hinro (alt.: hinarat) demipenteractic rotunda, hin-first half of mo, hin atop rat 1
hint demipenteractic (line-)tegum, demipenteractic dipyramid ...
hittip hexagon-hexagon-hexagon-triprism 1.732051
hixacube hix atop edge-parallel cube 0.866025
hixadot hexateron atop dodecateron, hix-first half of hax 0.866025
hixalrix hexateron atop inverted rectified hexateron, hix-first rotunda of jak 0.816497
hixascad hexateron atop small cellated decateron, hix-first rotunda of small terated tetradecapeton 1
hixip hexateron prism, vertex figure of roc 0.816497
hixu hexateral-based ursapeton ofx3xoo3ooo3ooo3ooo&#xt, hix-based ursulate 1.048383
hop (old: hep) heptapeton, 6D simplex6), pyroex(id), hexateral pyramid, vertex figure of oca, Gosset polytope 05 0.654654
hopitjak (old: hoptijak) demiprismatotruncated icosiheptaheptacontidipeton 3.109126
hotjak demitruncated icosiheptapeton 2.828427
icaf (alt.: icalicope) icositetrachoron antifastegium, icositetrachoron atop inverted icositetrachoral-prism 1.123033
iddoe icosidodecahedron-dodecahedron duoprism 2.140458
idodip icosidodecahedron-icosidodecahedron duoprism 2.288246
ikedip icosahedron-icosahedron duoprism 1.344997
ikedoe icosahedron-dodecahedron duoprism 1.693527
ikid icosahedron-icosidodecahedron duoprism 1.876844
jak icosiheptaheptacontidipeton, Gosset polypeton 22,1, vertex figure of naq, Delone cell of lattice E6 0.816497
jakoh icosiheptaheptacontidipetic hexacomb, Gosset hexacomb 22,2, Delone complex of lattice E6
kaje heptacontidiaicosiheptapeton, vertex figure of quil 0.816497
madek pentacontatetradisheptacontadipeton, compound of 2 jak 0.816497
medrojak (alt.: tritith) pentacontitetra-diminished rojak, tri - (triangle,triangle,hexagon)-trioprism 1.290994
mo pentacontitetrapeton, Gosset polypeton 12,2, vertex figure of jakoh, lattice E6 contact polytope (span of its roots) 1
n,co-dippip n-gon - cuboctahedron duoprismatic prism
n,doe-dippip n-gon - dodecahedron duoprismatic prism
n,ex-dip n-gon - hexacosachoron duoprism
n,hex-dip n-gon - hexadecachoron duoprism
n,hi-dip n-gon - hecatonicosachoron duoprism
n,ico-dip n-gon - icositetrachoron duoprism
n,id-dippip n-gon - icosidodecahedron duoprismatic prism
n,ike-dippip n-gon - icosahedron duoprismatic prism
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))]
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))]
n,n,k-tip n-gon - n-gon - k-gon - triprism sqrt[1/(2 sin2(π/n))+1/(4 sin2(π/k))]
n,n,n-tip n-gon - n-gon - n-gon - triprism sqrt[3/(4 sin2(π/n))]
n,oct-dippip n-gon - octahedron duoprismatic prism
n,pen-dip n-gon - pentachoron duoprism sqrt[1/(4 sin2(π d/n))+2/5]
n,rahi-dip n-gon - rectified-hecatonicosachoron duoprism
n,rap-dip n-gon - rectified-pentachoron duoprism
n,rico-dip n-gon - rectified-icositetrachoron duoprism
n,rit-dip n-gon - rectified-tesseract duoprism
n,rox-dip n-gon - rectified-hexacosachoron duoprism
n,tes-dip n-gon - tesseract duoprism
n,tet-dippip n-gon - tetrahedron duoprismatic prism
nitarin nit atop rin, nit-first rotunda of brox 1.414214
nitasiphin nit atop siphin, hin-first medial segment of rojak 1.290994
nitasirhin nit atop sirhin, nit-first cap of ram 1.732051
nitip penteractitriacontiditeron prism 1.322876
... tetradecapeton dual 0.774597
... pentacontitetrapeton dual, convex hull of madek 0.816497
octa tratet oct atop tratet, oct-first cap of ril 0.845154
octco octahedron-cuboctahedron duoprism 1.224745
octcube octahedron-cube duoprism 1.118034
octdip octahedron-octahedron duoprism, dual of Delone cell of lattice D6*, vertex figure of traxh 1
octdoe octahedron-dodecahedron duoprism 1.569562
octete octahedral tettene, octahedral-pyramid pyramid pyramid, triangle atop fully orthogonal octahedron 0.707107
octid octahedron-icosidodecahedron duoprism 1.765796
octike octahedron-icosahedron duoprism 1.185120
oddimo (alt.: bittip) octadeca-diminished mo, bitriangular trioprism, triangular trioalterprism 1
open octagon-pentachoron duoprism 1.614654
... (mono) tetal tratet augmented tetdip 0.866025
pabdimo, dot||scad||dot parabidiminished mo, dodecateron atop pseudo small cellated dodecateron atop dodecateron 1
pabex hax partially biexpanded hemihexeract 1.658312
patal prismatotruncated heptapeton, runcitruncated heptapeton 2
patom (old: kaprom) prismatotruncated pentacontitetrapeton, runcitruncated pentacontitetrapeton, (heptacontidiprismatorhombated pentacontitetrapeton) 3.872983
penaf (old: penalpenp) pentachoron antifastegium, pentachoron atop inverted pentachoral-prism, pen-first cap of jak 0.816497
penarappip pen-first cap of birectified heptapeton 0.925820
penppy penp pyramid, vertex-pyramid of ril 0.845154
pentanit pent atop nit 1.228783
pentarin tesseract atop rectified tesseract 1.418705
pettip pentagon-pentagon-pentagon-triprism 1.473370
pexhax partially expanded hemihexeract 1.322876
pithax prismatotruncated hemihexeract, runcitruncated demihexeract, stericantic hexeract 2.958040
potag prismatotruncated hexacontitetrapeton, runcitruncated hexacross 2.738613
potax prismatotruncated hexeract, runcitruncated hexeract 3.762560
pril prismatorhombated heptapeton, runcicantellated heptapeton 2.104417
prog prismatorhombated hexacontitetrapeton, runcicantellated hexacross 3
prohax prismatorhombated hemihexeract, runcicantellated demihexeract, steriruncic hexeract 2.783882
prom (old: kaptom) prismatorhombated pentacontitetrapeton, (heptacontidiprismatotruncated pentacontitetrapeton) 4.582576
prox prismatorhombated hexeract, runcicantellated hexeract 3.598576
quactix quasicellitruncated hexeract 1.431870
quitoxog quasiterated hexeractihexacontatetrapeton 1.137055
quoptax quasiprismatotruncated hexeract 1.686163
quotacog quasitericellated hexacontatetrapeton 1.121320
quotox quasitruncated hexeract 0.681517
rackix retrocelliskewed hexeract 1.581139
raddirag rhombidodecahedraly-diminished rectified hexacontatetrapeton 1
rag (old: ric) rectified hexacontitetrapeton, lattice B6 contact polytope (span of its small roots), lattice D6 contact polytope (span of its roots) 1
ram rectified pentacontitetrapeton, Gosset polypeton 02,2,1, Voronoi cell of lattice E6* 1.732051
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
rapalpenp rap atop inverted penp, pen-first medial subsegment of jak 0.816497
rapesc rectified-pentachoric scalene, rectified-pentachoron-pyramid pyramid, line atop fully orthogonal rectified pentachoron 0.816497
ratanit rectified triacontaditeron atop penteractitriacontiditeron, rat-first rotunda of brag 1.224745
ratasiphin rat atop siphin, rat-first cap of rojak 1.290994
ratip rectified-triacontiditeron prism 1.118034
rax rectified hexeract, rectified dodecapeton 1.581139
raxh rectified hexeractic pentacomb
redscox (alt.: trisoo) hecatonenenecontadia-diminished small cellihexeract, partially triexpanded xedrag, tri - (4,8,8)-trioprism 1.978437
ril (old: riss) rectified heptapeton, vertex figure of hesa, Gosset polytope 04,1 0.845154
rinathin rectified penteract atop truncated demipenteract, rectified demipenteract-first cap of demirectified icosiheptaheptacontidipeton 2.160247
rinnip rectified-penteract prism 1.5
ritas rit altersquarism, cyclotetra-diminished sochax, medial segment of siphina, partial Stott expansion of hax 1.322876
ritgyt rectified-tesseractic gyrotrigonism 1.290994
rixa (alt.: pabdihax, old: rixalrix) rectified hexateron alterprism, parabidiminished demihexeract, rectified hexateron atop inverted rectified hexateron 0.866025
rixalspix rectified hexateron atop small prismated hexateron, rix-first cap of scal 1.195229
rixasarx rectified hexateron atop small rhombated hexateron, rix-first cap of brox 1.414214
rixascad rectified hexateron atop small cellated dodecateron, half of rectified hexacontitetrapeton (its rix-first rotunda) 1
rixaspix rectified hexateron atop small prismated hexateron, rix-first cap of rojak 1.290994
rixip rectified-hexateron prism, vertex figure of rolaq 0.957427
rixpy rectified-hexateronal pyramid, vertex pyramid of demihexeract 0.866025
rojak rectified icosiheptaheptacontidipeton 1.290994
saborx small birhombated hexeract, bicantellated hexeract 2.645751
sabril small birhombated heptapeton, bicantellated heptapeton 1.558387
sabrim (old: pirm, sirmak, skorm) small birhombated pentacontitetrapeton, (prismatorectified pentacontitetrapeton, small rhombated pentacontitetraheptacontidipeton, small heptacontidirhombated pentacontitetrapeton) 3
sarxasibrid small rhombated hexateron atop small birhombated dodecateron, rix-first subsegment of brox 1.414214
scadaspix small cellated dodecateron atop small prismated hexateron, scad-first cap of scal 1.195229
scag small cellihexacontitetrapeton, stericated hexacross 2
scal small cellated heptapeton, stericated heptapeton 1.195229
scox small cellihexeract, stericated hexeract 1.978437
shopjak small demiprismated icosiheptaheptacontidipeton 1.914854
shorjak small demirhombated icosiheptaheptacontidipeton 3.265986
siborg small birhombated hexacontitetrapeton, bicantellated hexacross 2.236068
sibpof small biprismated tetradecapeton, biruncinated heptapeton 1.414214
sibridacard sibrid atop card, first subsegment of dot-first ram 1.732051
sinnontip sinnont prism 1.645329
siphina siphin alterprism, medial segment of sochax 1.322876
sirhax small rhombated hemihexeract, cantellated demihexeract, runcic hexeract 1.936492
sirhina sirhin alterprism, medial segment of sophax 1.658312
sirhinasart sirhin atop sart, nit-first subsegment of ram 1.732051
sirjak small rhombated icosiheptaheptacontidipeton 2.380476
sobpoxog small biprismated hexeractihexacontatetrapeton, biruncinated hexeract, biruncinated hexacross 2.345208
sochax small cellated hemihexeract, stericated demihexeract, pentic hexaract 1.322876
sophax small prismated hemihexeract, runcinated demihexeract, steric hexeract 1.658312
soxaxog small hexeractihexeractihexacontitetrapeton 1.645329
spam (old: skopam) small prismated pentacontitetrapeton, (small hebdomecontadiaprismated pentacontitetrapeton) 2.236068
spida rappip spid || rappip, (rap,rap,spid)-trigonic 1
spidapenp spid atop penp, wedge of staf 1
spil small prismated heptapeton, runcinated heptapeton 1.309307
spixa (old: spixalspix) small prismated hexateron alterprism, small prismated hexateron atop inverted small prismated hexateron, medial segment of dot-first birectified hexacontitetrapeton 1.224745
spixalsarx spix atop inverted sarx 1.290994
spixip small-prismated-hexateron prism 1.290994
spog small prismatohexacontitetrapeton, runcinated hexacross 1.870829
spojak small prismated icosiheptapeton 2.768875
spox small prismated hexeract, runcinated hexeract 2.263033
squahex square-hexadecachoron duoprism 1
squahi square-hecatonicosachoron duoprism 3.769377
squapen square-pentachoron duoprism, vertex figure of bersa 0.948683
squarahi square - rectified-hecatonicosachoron duoprism 4.589369
squarap square - rectified-pentachoron duoprism 1.048809
squarico square - rectified-icositetrachoron duoprism 1.870829
squarit square - rectified-tesseract duoprism 1.414214
squarox square - rectified-hexacosachoron duoprism 3.157869
squepe square pennene 0.707107
squex square-hexacosachoron duoprism 1.765796
squico square-icositetrachoron duoprism 1.224745
sram (old: skobram, skabram) small rhombated pentacontitetrapeton, (small hebdomecontadiabirhombated pentacontitetrapeton) 3.316625
sril small rhombated heptapeton, cantellated heptapeton 1.362770
srog small rhombihexacontitetrapeton, cantellated hexacross 1.732051
srox small rhombated hexeract, cantellated hexeract 2.515637
staf (interim: stef) small terated tetradecapeton, pentellated heptapeton, expanded heptapeton, lattice A6 contact polytope (span of its roots) 1
stasissiddow (pentagramm,sissid)-disphenoid, pentagram atop fully orthogonal small stellated doedcahedron 0.639240
stef stellated tetradecapeton, compound of 2 hop 0.654654
stopen octagram-pentachoron duoprism 1.092197
stoxog small terated hexeractihexacontatetrapeton, pentellated hexeract, pentellated hexacross 1.645329
taccarat triacontaditeron atop rectified triacontaditeron, tac-first rotunda of rectified hexacontitetrapeton 1
taccup triacontiditeron prism, vertex figure of rez 0.866025
tacog tericellated hexacontitetrapeton, pentitruncated hexeract 3.121320
tacogral (old: gatocral) tericelligreatorhombated heptapeton, pentistericantitruncated heptapeton 2.976095
tacox tericellated hexeract, pentitruncated hexacross 2.474130
tacpy triacontaditeric pyramid, vertex-first rotunda of gee 0.707107
tactaf tericellitruncated tetradecapeton, pentisteritruncated heptapeton 2.236068
tag truncated hexacontitetrapeton 1.581139
tagopal (old: gatopal) terigreatoprismated heptapeton, pentiruncicantitruncated heptapeton 3.116775
tahgyt tesseractihexadecachoric gyrotrigonism 2.160247
taporf (old: staporf) teriprismatorhombitetradecapeton, pentiruncicantellated heptapeton 2.449490
tapox (old: stapox) teriprismated hexeract, penticantellated hexacross 2.707107
tedjak (alt.: hexgyt, hexalhin) tridiminished icosiheptaheptacontidipeton, tridiminished 22,1, hexadecachoral gyrotrigonism 0.816497
tepasc tetrahedral-prismatic scalene, tetrahedron-prism-pyramid pyramid, line atop fully orthogonal tetrahedron prism 0.866025
tepepyp tetrahedral-prismatic pyramid prism, prism of tepepy 0.957427
tetafip prism of tetrahedral antifastegium, tetaf prism, tepe atop inverted squatet, half of hinnip 0.935414
tetal tratet tetrahedron atop alternate triangle,tetrahedron-duoprism 0.866025
tetco tetrahedron-cuboctahedron duoprism 1.172604
tetcube tetrahedron - cube duoprism 1.060660
tetdip tetrahedron-tetrahedron duoprism, vertex figure of he 0.866025
tetdoe tetrahedron-dodecahedron duoprism 1.529224
tetgocco (tet,gocco)-duoprism 0.958067
tetid tetrahedron-icosidodecahedron duoprism 1.730039
tetike tetrahedron-icosahedron duoprism 1.131154
tetoct tetrahedron-octahedron duoprism, vertex figure of sez 0.935414
tetsocco (tet,socco)-duoprism 1.527124
tettut (tetrahedron,truncated-tetrahedron)-duoprism 1.322876
thax truncated hemihexeract, cantic hexeract 2.179449
thexgyt (alt.: pex tedjak) truncated-hexadecachoral gyrotrigonism, partially expanded tridiminished icosiheptaheptacontidipeton, partially expanded tridiminished 21,2 1.632993
thox triacontidiahemihexeract, cytohemiectid, vertex figure of guhsa 0.707107
til truncated heptapeton 1.362771
tim truncated pentacontitetrapeton 2.645751
titajak (old: totajik, oldest: hibtajak) tritruncated icosiheptaheptacontidipeton, (demibitruncated icosiheptaheptacontidipeton) 3.829708
titam (old: cacram, totam, tomak, katom) tritruncated pentacontitetrapeton, (centrocellirhombated pentacontitetrapeton, trunkated pentacontitetraheptacontidipeton, heptacontiditruncated pentacontitetrapeton) 3.741657
tithtip triangle-triangle-hexagon triprism 1.290994
titstip triangle-triangle-square triprism 1.080123
tixip truncated-hexateron prism 1.414214
tocal teracellated heptapeton, pentitruncated heptapeton 1.647509
tocral (old: stocral) tericellirhombated heptapeton, pentiruncitruncated heptapeton 2.329929
toedip truncated-octahedron - truncated-octahedron duoprism 2.236068
togral (old: gotral) terigreatorhombated heptapeton, penticantitruncated heptapeton 2.390457
tojak truncated icosiheptaheptacontidipeton 2
topag (old: stopag) teriprismated hexacontitetrapeton, penticantellated hexeract 2.921564
topal (old: stopal) teriprismated heptapeton, penticantellated heptapeton 1.690309
tox truncated hexeract 2.745093
tracope triangle-cuboctahedron duoprismatic prism 1.258306
tradope triangle-dodecahedron duoprismatic prism 1.595888
tragittith (triangle,gittith)-duoprism 1.061238
tragrip triangle - great-rhombated-pentachoron duoprism 2.645751
trahex triangle - hexadecachoron duoprism, vertex figure of barz 0.912871
trahi triangle - hecatonicosachoron duoprism 3.747204
trapen triangle - pentachoron duoprism, vertex figure of broc 0.856349
trarahi triangle - rectified-hecatonicosachoron duoprism 4.571175
trarap triangle - rectified-pentachoron duoprism, vertex figure of branq 0.966092
trarico triangle - rectified-icositetrachoron duoprism 1.825742
trarit triangle - rectified-tesseract duoprism 1.354006
trarox triangle - rectified-hexacosachoron duoprism 3.131369
traspid triangle - small-prismated-pentachoron duoprism 1.154701
trasteth (triangle,steth)-duoprism 1.593876
tratah triangle - tesseractihexadecachoron duoprism 2.198484
tratepe triangle-tetrahedron-duoprism prism, vertex figure of rolin 0.978945
tratess triangle - tesseract duoprism 1.154701
tratet altroct triangle-tetrahedron duoprism atop gyrated triangle-octahedron duoprism, vertex-first medial segment of birectified heptapeton 0.925820
tratetdafup triangular-tetrahedral duoantifastegiaprism, tratet atop bidual tratet 0.866025
tratetpy (triangle,tetrahedron)-duoprism pyramid, vertex-pyramid of bril 0.925820
tratriddipdit (triangle,triangular duoprism)-duotegum, tegum product of triangle and triangular duoprism
traxh tri-rectified hexeractic pentacomb, Voronoi complex of body-centered hexeractic lattice (lattice D6*)
trex triangle - hexacosachoron duoprism 1.717954
trial tratet triangle atop dual tratet, triangle-first cap of ril 0.845154
trico triangle - icositetrachoron duoprism 1.154701
triddipabl tratrip triddip atop bidual tratrip 1
tridep triangle-icosidodecahedron duoprismatic prism 1.789237
trikep triangle-icosahedron duoprismatic prism 1.219771
trim (old: cacam, tram, mak) trirectified pentacontitetrapeton, (centrocellated pentacontitetrapeton, pentacontitetraheptacontidipeton) 1.414214
tripal triddip trip atop gyro-perp triddip 0.816497
trippete trip tettene, {3}-first cap of jak 0.816497
trittip triangle-triangle-triangle-triprism, vertex figure of ramoh 1
trope (old: troctip) triangle-octahedron duoprismatic prism 1.040833
tutdip truncated-tetrahedron duoprism 1.658312
xedrag hexeractidiminished rectified hexacontatetrapeton, square cuboctahedroltriate, scaliform dodecadiminished rectified hexacontatetrapeton 1
xog hexeractihexacontatetrapeton, tritruncated hexeract, tritruncated hexacross 2.549510

Count of actually available polytopes: 355



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---- 7D ----


Acronym Name Circumradius
... 2guhsa (?) 0.707107
barz (old: drhio) birectified hecatonicosoctaexon 1.224745
berlin (old: shabrilq) birhombated pentacontihexahecatonicosihexaexon (small demibirhombated pentacontihexapentacosiheptacontihexaexon) 3.570714
bersa (old: dars) birectified hepteract, Gosset polytope 04,1,1 1.581139
bittoc bitruncated octaexon 1.713914
bragabrox brag atop brox, brag-first rotunda of sez 1.414214
bragasochax brag atop sochax, 2nd subsegment of lin in hax-first orientation 1.322876
branq (old: dranq) birectified hecatonicosihexapentacosiheptacontihexaexon 1.936492
brilalspil bril atop inverted spil 1.322876
brilastaf bril atop staf, hop-first subsegment of laq 1
brillip birectified - heptapeton prism 1.052209
brilpy birectified-heptapetonal pyramid, vertex pyramid of pentacontihexahecatonicosihexaexon 1.322876
broc (old: droc) birectified octaexon, duorectified octaexon, vertex figure of bif, Gosset polytope 04,2 0.968246
broxa sophax brox atop sophax, hax-first subsegment of rolaq 1.732051
copen cuboctahedron - pentachoron duoprism 1.183216
cubhex cube-hexadecachoron duoprism 1.118034
cubpen cube-pentachoron duoprism 1.072381
... point || pseudo hax || gee, Dutour polyexon type A
gabach great bicellihexadecaexon 3.872983
gahax gee atop hax, gee-first segment of naq 0.866025
garag gee atop rag, gee-first rotunda of rez 1
geep hexacontitetrapeton prism, hexacross prism, vertex figure of rek 0.866025
geepy hexacontitetrapeton pyramid, vertex-first rotunda of gee 0.707107
goccopen (gocco,pen)-duoprism 0.971027
gososaz great hepteractihepteractihecatonicosoctaexon 1.242133
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
goxaxogip goxaxog prism 1.242133
grohp great-rhombihexahedron prism 0.890446
guhsa hexacontitetrahemihepteract 0.707107
guph great petated hexadecaexon, hexipentisteriruncicantitruncated octaexon, omnitruncated octaexon 4.582576
guposaz great petated hepteractihecatonicosoctaexon 1.242133
haxabrag hax-first monostratic cap of lin, hax atop brag 1.322876
haxabrox hax atop brox, hax-first cap of rolaq 1.732051
haxarag hemihexeract atop rectified hexacontitetrapeton, vertex-first subsegment of pentacontihexapentacosiheptacontihexaexon 1
haxip hemihexeractic prism, vertex figure of rinquoh 1.060660
haxpy hemihexeractic pyramid, vertex pyramid of laq 1
haxt demihexeractic (line-)tegum, demihexeractic bipyramid ...
he (old: ache) hexadecaexon, trirectified octaexon, equatorial cross-section of (vertex first) 1/q-octo, Gosset polytope 03,3 1
hejaka hejak alterprism, hejak atop alternate hejak 1.658312
hept hepteract, tetradecaexon, 7D measure-polytope7), geozett(id) 1.322876
hesa (old: hiss) hemihepteract, vertex figure of bay, Gosset polytope 14,1 0.935414
hexal trahex hex atop gyrated trahex, hex-first cap of hesa 0.935414
hexalhax hex atop alternate hax 0.866025
hexete hexadecachoric tettene, hexadecachoron-pyramid pyramid-pyramid, triangle atop fully orthogonal hexadecachoron 0.707107
hidlin hexadeca-diminished pentacontihexahecatonicosihexaexon 1.322876
hinaf, hin || alt. hinnip hemipenteractic alterfastegium, hin atop alternate hinnip, hin-first rotunda of hesa 0.935414
hinsc demipenteractic scalene, demipenteractic-pyramid pyramid, line atop fully orthogonal demipenteract 0.866025
hixaf hexateron antifastegium, hix atop inverted hixip, hix-first cap of naq 0.866025
hopabril heptapeton atop birectified heptapeton, hop-first monostratic cap of hesa 0.935414
hopalbril hop atop inverted bril, hop-first cap of laq 1
hopalril hop atop inverted ril, hop-first cap of naq 0.866025
hopastaf hop atop staf, half of suph (its hop-first rotunda), partial Stott expansion of oca 1
hopip heptapeton prism, vertex figure of rene 0.823754
idinaq (alt.: trahixdap) icosa-diminished naq, triangular-hexateric duoalterprism 0.866025
jaka (alt.: pabdinaq, old: jakaljak) jak alterprism, jak atop inverted jak, vertex-first medial segment of naq, parabidiminished naq 0.866025
jakamo jak atop mo, jak-first half of parabidiminished laq 1
jakatrim jak atop trim, jak-first cap of stanq 1.658312
jakip icosihepta-heptacontidi-peton prism, vertex figure of riffy 0.957427
jakpy icosihepta-heptacontidi-peton pyramid, vertex-first cap of naq 0.866025
laq pentacontihexapentacosiheptacontihexaexon, Gosset polyexon 21,3, vertex figure of naquoh, lattice E7 contact polytope (span of its roots) 1
lin pentacontihexahecatonicosihexaexon, Gosset polyexon 12,3, Voronoi cell of lattice E7* 1.322876
linoh pentacontihexahecatonicosihexaexic heptacomb, Gosset heptacomb 13,3, Voronoi complex of lattice E7*
moarojak mo-first monostratic cap of lin, mo atop rojak 1.322876
n,hix-dip n-gon - hexateron duoprism sqrt[5/12 + 1/(2 sin(π/n))2]
n,n,n-tippip n-gon - n-gon - n-gon - triprismatic prism sqrt[1/4+3/(4 sin2(π/n))]
nal hecatonicosihexa-pentacontihexa-exon, vertex figure of fib 0.866025
naq (alt: rocalroc) hecatonicosihexapentacosiheptacontihexaexon, Gosset polyexon 32,1, 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
naquoh hecatonicosihexapentacosiheptacontihexaexic heptacomb, Gosset heptacomb 33,1, Delone complex of lattice E7
oca (old: oc) octaexon, 7D simplex7), pyrozett(id), heptapetal pyramid, vertex figure of ene, (one of the) Delone cell(s) of lattice E7, Gosset polytope 06 0.661438
octatetdip oct atop tetdip, oct-first half of roc 0.866025
octepe octahedral pennene 0.707107
octhex octahedron - hexadecachoron duoprism, vertex figure of troch 1
octico octahedron - icositetrachoron duoprism 1.224745
octpen octahedron - pentachoron duoprism, vertex figure of tro 0.948683
octrap octahedron - rectified-pentachoron duoprism 1.048809
odinaq octa-diminished naq 0.866025
ohix octagon - hexateron duoprism 1.457317
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papaid, pap || id, K-4.142 pentagonal-antiprism atop icosidodecahedron 3.077684
penpasc pentachoron-prismatic scalene, pentachoron-prism-pyramid pyramid, line atop fully orthogonal pentachoron prism 0.935414
puph petaprismated hexadecaexon 1.732051
quil pentacosiheptacontihexa-pentacontihexa-exon, vertex figure of yab 0.866025
quiposaz quasipetated hepteractihecatonicosoctaexon 1.242133
ragabrag rag atop brag, rag-first rotunda of barz 1.224745
ranq rectified hecatonicosihexapentacosiheptacontihexaexon 1.414214
rapete rap tettene 0.866025
rasa (old: ras) rectified hepteract 1.732051
ratkus retroteriskewed hepteract 1.658312
rez (old: rhio) rectified hecatonicosoctaexon, lattice B7 contact polytope (span of its small roots), lattice D7 contact polytope (span of its roots) 1
rila (old: rilalril) rectified heptapeton alterprism, rectified heptapeton atop inverted rectified heptapeton, hop-first medial segment of naq 0.866025
rilalbril rectified heptapeton atop inverted birectified heptapeton, equatorial monostratic segment of demihepteract 0.935414
rilastaf ril atop staf, ril-first rotunda of rez 1
rillip rectified-heptapeton prism, vertex figure of robay 0.981981
rilpy rectified-heptapetonal pyramid, vertex pyramid of demihepteract 0.935414
rixasc rectified-hexateronal scalene, rectified-hexateronal-pyramid pyramid, line atop fully orthogonal rectified-hexateron 1
roc rectified octaexon, vertex figure of hocto, Gosset polytope 05,1 0.866025
rojaka (alt.: pabdilin, old: rojakalrojak) rojak alterprism, parabidiminished lin, rojak atop alternate rojak 1.322876
rojaka hejak rojak atop hejak, rojak-first cap of rolaq 1.732051
rolaq rectified pentacontihexapentacosiheptacontihexaexon 1.732051
rolin (old: lanq) rectified pentacontihexahecatonicosihexaexon, pentacontihexahecatonicosihexapentacosiheptacontihexaexon, Gosset polytope 03,2,1 2.449490
rolinoh rectified pentacontihexahecatonicosihexaexic heptacomb, Gosset heptacomb 03,3,1
sabach small bicellated hexadecaexon, bistericated octaexon 1.414214
sabro small birhombated octaexon, bicantellated octaexon 1.658312
saro small rhombated octaexon, cantellated octaexon 1.414214
sarz small rhombated hecatonicosoctaexon, cantellated heptacross 1.732051
scala (old: scalal scal) small cellated heptapeton alterprism, small cellated heptapeton atop inverted small cellated heptapeton, medial segment of barz 1.224745
scala spil scal atop spil 1.322876
sco small cellated octaexon, stericated octaexon 1.322876
sersa small rhombated hepteract, cantellated hepteract 2.790257
seto small terated octaexon, pentellated octaexon 1.198958
sez (old: shio) hepteractihecatonicosoctaexon 1.414214
shanq small demified hecatonicosihexapentacosiheptacontihexaexon 2
shilq small demified pentacontihexapentacosiheptacontihexaexon 2.179449
sibpo small biprismated octaexon, biruncinated octaexon 1.561250
sirhesa small rhombated hemihepteract, cantellated demihepteract 2.207940
sissiddow sissidic disphenoid, sissid atop fully orthogonal sissid 0.831254
soccopen (socco,pen)-duoprism 1.535287
sososaz small hepteractihepteractihecatonicosoctaexon 1.719624
soxaxogip soxaxog prism 1.719624
spaz small prismated hecatonicosoctaexon, runcinated heptacross 1.870829
spila (old: spilal spil) small prismated heptapeton atop inverted small prismated heptapeton 1.322876
spo small prismated octaexon, runcinated octaexon 1.391941
squahix square - hexateron duoprism, hixip prism, vertex figure of bro 0.957427
squarat square rectified-triacontiditeron duoprism 1
squix square hixene, square atop fully orthogonal pentachoron 0.707107
stanq small terated hecatonicosihexapentacosiheptacontihexaexon 1.658312
stiroh small trirhombihexadecaexon, tricantellated octaexon 1.732051
stohix octagram - hexateron duoprism 0.842354
suph small petated hexadecaexon, hexicated octaexon, expanded octaexon, lattice A7 contact polytope (span of its roots) 1
suposaz small petated hepteractihecatonicosoctaexon, hexicated hepteract 1.719624
suthesa small terated demihepteract, hexic hepteract 1.369306
taccasc triacontiditeron scalene 0.707107
taccuppy triancontaditeron-prism pyramid, vertex pyramid of rectified hecatonicosoctaexon 1
takus teriskewed hepteract 1.658312
talq truncated pentacontihexapentacosiheptacontihexaexon 2.645751
tanq truncated hecatonicosihexapentacosiheptacontihexaexon 2.179449
tasa truncated hepteract 2.998773
tattoc tritruncated octaexon 1.854050
taz truncated hecatonicosoctaexon, truncated heptacross 1.581139
tetal tetdip tet atop dual tetdip 0.935414
tetdippy tetdip pyramid, vertex pyramid of he 1
tetgittith (tet,gittith)-duoprism 1.080691
tethex tetrahedron - hexadecachoron duoprism, vertex figure of tark 0.935414
tetpen tetrahedron-pentachoron duoprism, vertex figure of trene 0.880341
tetrap tetrahedron - rectified-pentachoron duoprism, vertex figure of torfy 0.987421
tetsteth (tet,steth)-duoprism 1.606894
tettepe tetrahedron-tetrahedron duoprismatic prism, vertex figure of 03,3,1 1
tettes tetrahedron-tesseract duoprism 1.172604
thesa truncated demihepteract, cantic hepteract 2.423840
toc truncated octaexon 1.391941
tolin truncated pentacontihexahecatonicosihexaexon 3.708099
traginnont (triangle,ginnont)-duoprism 1.173127
trahex aico trahex atop ico 1
trahexpy trahex pyramid, vertex pyramid of barz 1.224745
trahin triangle - hemipenteract duoprism, vertex figure of borfy 0.978945
trahix triangle - hexateron duoprism, vertex figure of brene 0.866025
trapendafup triangular-pentachoron duoantifastegiaprism, trapen atop bidual trapen 0.866025
trapent triangle-penteract duoprism 1.258306
trarix triangle-rix duoprism 1
trarixdit (triangle,rix)-duotegum, tegum product of triangle and rectified hexateron
trasinnont (triangle,sinnont)-duoprism 1.670461
tratac triangle - triacontiditeron duoprism, vertex figure of bark 1.154701
tratratrip triangle - triangle - triangle - triprismatic prism 1.118034
trial trahex triangle atop inverted trahex 1
trippen triangle - pentachoron duoprism-prism, vertex figure of buffy 0.991632
zee (old: hio) hecatonicosoctaexon, heptacross7), aerozett(id), heptapetal antiprism, vertex figure of ek, Gosset polytope 41,1, lattice C7 contact polytope (span of its small roots) 0.707107

Count of actually available polytopes: 166



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---- 8D ----


Acronym Name Circumradius
bark birectified diacosipentacontahexazetton 1.224745
bay diacositetraconta-myriaheptachiliadiacosioctaconta-zetton, Gosset polyzetton 24,1 1.414214
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
bif diacositetracont-dischiliahectohexaconta-zetton, Gosset polyzetton 14,2 2
bifoh diacositetracont-dischiliahectohexaconta-zettic octacomb, Gosset octacomb 15,2
borfy birectified dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton, t2(41,2) 2.449490
brene birectified enneazetton, Gosset polytope 05,2 1
bro birectified octeract, birectified hexadecazetton, Gosset polytopes 05,1,1 1.732051
broca (old: brocalbroc) broc alterprism, broc atop inverted broc, central segment of hocto 1
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
codify (alt.: trihexdip) tetracontaocta-diminished dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton, tegum sum of 3 pairwise bigyrated hexadecachoron duoprisms, tri-hexadecachoron-duoprism 1
... point || pseudo hesa || zee, Dutour polyzetton type A
ek diacosipentacontahexazetton, octacross8), 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
ene enneazetton, 8D simplex8), pyroyott(id), octaexal pyramid, vertex figure of day, (one of the) Delone cell(s) of lattice E8, Gosset polytope 07 0.666667
fib dischiliahectohexaconta-diacositetraconta-zetton 1
fy dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton, Gosset polyzetton 41,2, Witting polytope, vertex figure of goh, lattice E8 contact polytope (span of its roots) 1
goh Gosset octacomb 52,1, Delone complex of lattice E8
gook great octeractiocteractidiacosipentacontahexazetton 1.338990
hauhocto hexadeca-augmented hemiocteract ...
haxesc (degenerate) demihexaractic scalene, line atop fully orthogonal demihexaract ∞   i.e. flat in euclidean space
hesapy hemihepteractic pyramid, vertex pyramid of bay 1.414214
hexal hesa hex atop alternated hesa, hex-first cap of codify 1
hexdip hexadecachoron duoprism 1
hextes hexadecachoron-tesseract duoprism 1.224745
hocto (alt.: gecdify) hemiocteract, 64(=g)+48(=c)-diminished fy, Gosset polytope 15,1 1
icodip icositetrachoron duoprism 1.414214
idirek icositetra-diminished rectified diacosipentacontahexazetton 1
jakaf (old: jakaljakip) icosiheptaheptacontidipeton alterfastegium, icosiheptaheptacontidipeton atop inverted icosiheptaheptacontidipeton-prism 1
kadify heptacontadia-diminished dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton, tegum sum of two mutually inverted birectified enneazetta, bidiambooctadecazetton 1
laqalin pentacontihexapentacosiheptacontihexaexon atop pentacontihexahecatonicosihexaexon, 21,3 atop 12,3 , laq-first cap of bay, 21,3 -first cap of 21,4 1.414214
laqpe pentacontihexapentacosiheptacontihexaexon prism 1.118034
linaranq pentacontihexahecatonicosihexaexon atop rectified pentacontihexapentacosiheptacontihexaexon, laq-first subsegment of bay 1.414214
n,n,n,n-quip n-gon - n-gon - n-gon - n-gon - tetraprism (or: -quadprism) sqrt[1/sin2(π/n)]
naqpe naq prism, prism of Gosset polyexon 32,1 1
ocalroc oca atop inverted roc, oca-first cap of fy 1
ocpe octaexon prism, vertex figure of reday 0.829156
octa tethex oct atop tethex 1
octo octeract, hexadecazetton, 8D measure-polytope8), geoyott(id) 1.414214
pendip pentachoron duoprism, vertex figure of icoy 0.894427
penrap (pentachoron, rectified pentachoron)-duoprism 1
penrapdit (pen,rap)-duotegum, tegum product of pentachoron and rectified pentachoron
puko petiskewed octeract 1.732051
quaxoke quasi-exiocteracti-diacosipentacontahexazetton 1.338990
recto rectified octeract, rectified hexadecazetton 1.870829
rek rectified diacosipentacontahexazetton, lattice B8 contact polytope (span of its small roots), lattice D8 contact polytope (span of its roots) 1
rene rectified enneazetton, vertex figure of henne, Gosset polytope 06,1 0.881917
repuko retropetiskewed octeract 1.732051
ribfoh rectified diacositetracont-dischiliahectohexaconta-zettic octacomb, Gosset heptacomb 05,2,1
riffy rectified dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton, t1(41,2) 1.732051
robay rectified diacositetracont-myriaheptachiliadiacosioctaconta-zetton, t1(21,4) 2.645751
rocalbroc roc atop inverted broc, oca-first subsegment of fy 1
rocpy rectified-octaexonal pyramid, vertex pyramid of demiocteract 1
satpeb small triprismated bi-enneazetton, triruncinated enneazetton 1.732051
saxoke small exiocteracti-diacosipentacontahexazetton, heptellated octeract 1.790840
sobteb small biterated bi-enneazetton, bipentellated enneazetton 1.414214
soro small rhombated octeract, cantellated octeract 3.040171
sotho small terated hemiocteract, hexic octeract 1.732051