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 both a global alphabetical sorted order as well as in dimensionally alphabetical sorted order. (Those ones also contain further entries where no explicit face vector is given.) Parts of this index - as far as circumradii are explicitly given - are also available in an (accordingly) numerically sorted order.


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 3D
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Acronym Name Circumradius Face vector
... f v5o, variation of pentagonal prism, vertex figure of righi 0.964832 10, 15, 7
... f x5/2o, variation of 5/2-prism, vertex figure of raghi 0.964832 10, 15, 7
... f x5o, variation of pentagonal prism 1.173932 10, 15, 7
pip pentagonal prism, 5-p, vertex figure of rox 0.986715 10, 15, 7
... q x5o, variation of pentagonal prism 1.106168 10, 15, 7
starpglass pentagrammic retroprismatic hourglass 0.707107 10, 15, 7
stip stellated pentagonal prism, 5/2-prism, 5-prism with winding number 2, vertex figure of raggix 0.725530 10, 15, 7
... u x5o, variation of pentagonal prism 1.312862 10, 15, 7
... v f5/2o, variation of 5/2-prism, vertex figure of ragashi 0.905040 10, 15, 7
... v x5o, variation of pentagonal prism, vertex figure of ragishi 0.905040 10, 15, 7
... x f5/2o, variation of 5/2-prism, vertex figure of rofix 0.986715 10, 15, 7
... x v5o, variation of pentagonal prism, vertex figure of rigfix 0.725530 10, 15, 7
ebot elongated bowtie tegum 1 10, 16, 8
auteddi, J64 augmented tridiminished icosahedron 10, 18, 10
trippescu tripod pentagonized semicupola, edge faceting sidtid-0-3-3-3 0.866025 10, 18, 9
rapescu retrograde pentagonal cuploid, retrograde pentagonal semicupola 0.866025 10, 20, 11
stiscu pentagrammic cuploid, star semicupola 0.866025 10, 20, 11
esquidpy, J15 elongated square dipyramid 10, 20, 12
mibdi, J62 metabidiminished icosahedron 0.951057 10, 20, 12
pap pentagonal antiprism, para-bidiminished icosahedron 0.951057 10, 20, 12
stap bistrophic pentagrammic antiprism, stellar antiprism, 5/2-antiprism 0.656431 10, 20, 12
starp (old: restap) tristrophic pentagrammic antiprism, stellar retroprism (retrograde stellar antiprism), 5/3-antiprism 0.587785 10, 20, 12
waco, J86 sphenocorona 10, 22, 14
gyesqidpy, J17 gyroelongated square dipyramid 10, 24, 16
aupip, J52 augmented pentagonal prism 11, 19, 10
degpy, 10/3-pyr decagrammic pyramid 0.636010 11, 20, 11
epeppy, J9 elongated pentagonal pyramid 11, 20, 11
gyepip, J11 gyroelongated pentagonal pyramid, diminished icosahedron 11, 25, 16
auwaco, J87 augmented sphenocorona 11, 26, 17
... t60-r60-p12, Stott contraction of t80-s60-r60-d12 ... 110, 240, 132
ditra ditriangular trapezoprism sqrt[(a+b)2+c2]/2 12, 18, 8
hip hexagonal prism, Voronoi cell of unit-stacked hexagonal lattice 1.118034 12, 18, 8
pacop partially Stott contracted octagonal prism 12, 18, 8
... q x6o, variation of hexagonal prism 1.224745 12, 18, 8
... q3x3o, variation of truncated tetrahedron, triangle-snub small rhombicuboctahedron 1.398966 12, 18, 8
tut truncated tetrahedron, cantic cube, Waterman polyhedron number 2 wrt. face-centered cubic lattice A3 centered at a shallow hole 1.172604 12, 18, 8
... u x6o, variation of hexagonal prism 1.414214 12, 18, 8
... u3x3o, variation of truncated tetrahedron 1.732051 12, 18, 8
... v3x3o, variation of truncated tetrahedron, vertex figure of sidtaxhi 0.975835 12, 18, 8
... w3x3o, variation of truncated tetrahedron 1.973010 12, 18, 8
... x3q3o, variation of truncated tetrahedron 1.442951 12, 18, 8
... x3u3o, variation of truncated tetrahedron 1.837117 12, 18, 8
... x3v3o, variation of truncated tetrahedron, vertex figure of dattady 0.935414 12, 18, 8
... x3w3o, variation of truncated tetrahedron 2.120453 12, 18, 8
mibkid metabikis dodecahedron, (subsymmetrically) metabistellated-dodecahedron, dual of mibdi 12, 20, 10
... pentagonal antidipyramid, pentagonal antitegum, pentagonal kiteohedron, dual of pap, axial bi-kis-doe, deca-truncated sissid 12, 20, 10
pabextet partially bi-expanded tetrahedron 12, 20, 10
rasquacu retrograde square cupola, crossed square cupola, 4/3-cupola 0.736813 12, 20, 10
squacu, J4 square cupola 1.398966 12, 20, 10
... axially trigonal variant of pentagonal rotunda ... 12, 21, 11
baupip, J53 biaugmented pentagonal prism 12, 23, 13
cho cubohemioctahedron, rhomballelohedron 1 12, 24, 10
toif toroidal icosahedron faceting, edge faceting ike-6-6-a 0.951057 12, 24, 12
oho octahemioctahedron, facetorectified cube, allelotetratetrahedron 1 12, 24, 12
... toroidal tiler 12, 24, 12
co   (alt.: ratet – old: ratit, rotet) cuboctahedron, (small) rhombitetratetrahedron, rectified cube, rectified octahedron, cantellated tetrahedron, expanded tetrahedron, trigonal gyrobicupola, vertex figure of octet, lattice A3 contact polytope (span of its roots), lattice B3 contact polytope (span of its small roots) 1 12, 24, 14
... d3o3x, variation of cuboctahedron 2.661453 12, 24, 14
... f3o3x, variation of cuboctahedron 1.327129 12, 24, 14
hap, 6-ap hexagonal antiprism 1.087664 12, 24, 14
... q3o3x, variation of cuboctahedron 1.215958 12, 24, 14
tobcu, J27 triangular orthobicupola, vertex figure of gytoh 1 12, 24, 14
... u3o3x, variation of cuboctahedron, Waterman polyhedron number 3 wrt. face-centered cubic lattice A3 centered at a shallow hole 1.541104 12, 24, 14
... v3o3x, variation of cuboctahedron, vertex figure of gadtaxady 0.820211 12, 24, 14
epedpy, J16 elongated pentagonal dipyramid 12, 25, 15
... blend of 2 pentagonal antiprisms, pair of pentagonal butterfly wedges 0.951057 12, 26, 16
wamco, J88 sphenomegacorona 12, 28, 18
gad great dodecahedron, faceted icosahedron, vertex figure of fix 0.951057 12, 30, 12
sissid small stellated dodecahedron, penta-stellahedron, vertex figure of gofix 0.587785 12, 30, 12
... x3β3o (?) ... 12, 30, 14
... cubically-diminished dodecahedron, bi-tetrahedrally-diminished dodecahedron 1.401259 12, 30, 20
snit pyritohedron, pyritosnub tetrahedron, o2o2o symmetric ike variant, vertex figure of hyperbolic cube + n-prism honeycomb sqrt[a2+c2] 12, 30, 20
gike great icosahedron, retrosnub tetrahedron, retrosnub tetratetrahedron, edgified penta-stellahedron, vertex figure of gax 0.587785 12, 30, 20
ike   (alt.: snit) icosahedron, snub tetrahedron, snub tetratetrahedron, snub triangle antiprism, hydrohedron, gyroelongated pentagonal bipyramid, vertex figure of ex 0.951057 12, 30, 20
snit pyritohedron, pyritosnub tetrahedron, vertex alternated toe 1.581139 12, 30, 20
... o3β4o (?) ... 12, 36, 20
... β3/2o3β (?) ... 12, 36, 20
... 24 face equihedral toroid 12, 36, 24
... Shephard's 4-generalised octahedron, complex polyhedron x2-3-o2-4-o4 , β4 3 0.707107 12, 48, 64
idtid icosidodecatruncated icosidodecahedron, icositruncated dodecadodecahedron 2 120, 180, 44
quitdid quasitruncated dodecadodecahedron, stellatruncated dodecadodecahedron 1.658312 120, 180, 54
... a3b5c, general variation of great rhombicosidodecahedron sqrt[(f+2)a2+4(f+1)ab+2(2f+1)ac+4(f+1)b2+4(2f+1)bc+3(f+1)c2]/2 120, 180, 62
... f3v5v, variation of grid, hull of idtid 3.236068 120, 180, 62
... f3x5x, variation of great rhombicosidodecahedron, hull of quitdid 4.341518 120, 180, 62
gaquatid great quasitruncated icosidodecahedron, stellatruncated icosidodecahedron 1.020684 120, 180, 62
grid great (convex) rhombicosidodecahedron (i.e. not qrid), truncated icosidodecahedron, omnitruncated icosahedron, omnitruncated dodecahedron 3.802395 120, 180, 62
... v3x5f, variation of grid, hull of gaquatid 4.323687 120, 180, 62
... x3(-x)5f, variation of grid 1.618034 120, 180, 62
resrid (alt.: amsrid) rectified/ambified small-rhombated-icosidodecahedron 4.352502 120, 240, 122
exrhote expanded rhombic triacontahedron 120, 240, 122
... β5/2x5β (?) ... 120, 240, 84
... β3x5β (?) ... 120, 240, 92
... Leonardo polyhedron of type {5,4;13} 120, 240, 96
... Shephard's 5-generalised cube, complex polyhedron x5-4-o2-3-o2 , γ5 3 1.473370 125, 75, 15
auhip, J54 augmented hexagonal prism 13, 22, 11
... icosa-expanded rhombic enneacontahedron 132, 240, 110
giship tristrophic heptagrammic prism, heptagrammic prism of winding number 3, great heptagrammic prism, great stellated heptagonal prism 0.716257 14, 21, 9
hep heptagonal prism 1.256179 14, 21, 9
ship bistrophic heptagrammic prism, heptagrammic prism of winding number 2, small heptagrammic prism, small stellated heptagonal prism 0.811783 14, 21, 9
... cell of gap dual, adjacent bikis doe 14, 22, 10
bauco bi-augmented cuboctahedron, 4fold rhombohedron ... 14, 24, 12
rad (old: rhode) rhombic dodecahedron, Voronoi cell of face-centered cubic (fcc) lattice, terminally chamfered cube, terminally chamfered octahedron, surtegmated cube, surtegmated octahedron, Waterman polyhedron number 4 wrt. primitive cubic lattice C3 centered at a lattice point, Waterman polyhedron number 2 (and 6) wrt. body-centered cubic lattice C3* centered at a lattice point 14, 24, 12
bilbiro, J91 bilunabirotunda 14, 26, 14
gibil biro great bilunabirotunda 14, 26, 14
mabauhip, J56 metabiaugmented hexagonal prism 14, 26, 14
pabauhip, J55 parabiaugmented hexagonal prism 14, 26, 14
... elongated hexagonal dipyramid 14, 30, 18
hawmco, J89 hebesphenomegacorona 14, 33, 21
tekah tetrakis hexahedron, apiculated cube 14, 36, 24
tikko triakis octahedron, apiculated octahedron 14, 36, 24
... xfo3foo5oxf&#zx 140, 270, 132
... Leonardo polyhedron of type {4,5;19} 144, 360, 180
... mono lowered small rhombicuboctahedron ... 15, 24 ,11
dritit (old: sipstar) disrhombitritrihedron, "square-pentagon-pentagram(star)-thingy", vertex figure of retroantiprismatosnub disicositetrachoron, edge faceting sidtid-3-0-6-3-b 0.866025 15, 24, 12
pecu, J5 pentagonal cupola 2.232951 15, 25, 12
rastacu retrograde pentagrammic cupola, 5/3-cupola 0.716891 15, 25, 12
stacu pentagrammic cupola, star cupola 0.866025 15, 25, 12
autut, J65 augmented truncated tetrahedron 15, 27, 14
etcu, J18 elongated triangular cupola 15, 27, 14
repip (alt. ampip) rectified/ambified pip, o2o5o symmetric co relative 1.203002 15, 30, 17
tauhip, J57 triaugmented hexagonal prism 15, 30, 17
tepdid tripentadiminished icosidodecahedron 1.618034 15, 30, 17
gyetcu, J22 gyroelongated triangular cupola 15, 33, 20
... toroidal pentagrammic bicuploid, star semicupolaic diabolo 15, 35, 20
mesdi-verf vertex figure of medial snub disicositetrachoron 0.866025 15, 42, 21
... Shephard's 5-generalised octahedron, complex polyhedron x2-3-o2-4-o5 , β5 3 0.707107 15, 75, 125
... truncated Shephard's 5-generalised octahedron, complex polyhedron x2-3-x2-4-o5 150, 450, 140
... p60-r60, 41st stellation of ti 152, 270, 120
... squippy-teddi-G3 toroid ... 158, 408, 230
odsnic octadiminished snub cube, chiral 4fold dodecahedron-like barrel, vertex figure of octsnich 1.343713 16, 24, 10
op octagonal prism, bidiminished small rhombicuboctahedron 1.398966 16, 24, 10
... q x8o, variation of octagonal prism 1.485633 16, 24, 10
stop (old: sop) (tristrophic) octagrammic prism, stellated octagonal prism, 8/3-prism, 8-prism with winding number 3 0.736813 16, 24, 10
chat (alt.: patex cube) chamfered tetrahedron, partially tetrahedrally-expanded cube, tetrahedrally truncated cube, partially tri-expanded tetrahedron 16, 24, 10
... w x8o, variation of octagonal prism, hull of 8/3-prism 1.778824 16, 24, 10
tupip orthogonal blend of pentagonal prisms, vertex figure of sadsadox 0.986715 16, 26, 12
tustip orthogonal blend of pentagagramic prisms, vertex figure of gadsadox 0.725530 16, 26, 12
tuhip orthogonal blend of hexagonal prisms 1.118034 16, 28, 12
pexco partially (mono-)expanded cuboctahedron, 4fold elongated cuboctahedron ... 16, 28, 14
... Dohány synagoge polyhedron, Tabakgasse polyhedron 1.080123 16, 28, 14
... Waterman polyhedron number 4 wrt. body-centered cubic lattice C3* centered at a hole 16, 28, 14
teddoe tetrahedrally diminished dodecahedron, vertex figure of pd{3,5,3} 1.401259 16, 30, 16
oap, 8-ap octagonal antiprism 1.375549 16, 32, 18
... Qo oq4xx&#zh, variation of squobcu 16, 32, 18
squigybcu, J29 square gyrobicupola 16, 32, 18
squobcu, J28 square orthobicupola 16, 32, 18
quistet quadratisnub tetratetrahedron, chiral edge faceting sidtid-0-8-12-0-b 0.866025 16, 36, 20
dawci, J90 disphenocingulum 16, 38, 24
... complex polyhedron x3-3-o3 || o3-3-x3 , vertex figure of x3-3-o3-3-o3-3-x3 0.790569 16, 40, 18
snisquap, J85 snub square antiprism 16, 40, 26
hiktut hexakis truncated tetrahedron 1.172604 16, 42, 28
... Waterman polyhedron number 4 wrt. face-centered cubic lattice A3 centered at a shallow hole 1.837117 16, 42, 28
... 32 face equihedral toroid 16, 48, 32
disdi-verf vertex figure of disnub disicositetrachoron 0.866025 17, 51, 24
titrip truncated triangular prism, expanded ambified trip sqrt[(7y2+16y+16)/12] 18, 27, 11
ebauco elongated bi-augmented cuboctahedron, 4fold elongated rhombohedron, bi-augmented pexco ... 18, 28, 12
tutut two tut cupolaic blend, gyrated blend of 2 truncated tetrahedra 1.172604 18, 30, 14
hicu hexagonal cupola ∞   i.e. flat in euclidean space 18, 30, 14
retut (alt.: amtut) rectified/ambified truncated tetrahedron 2.121320 18, 36, 20
etigybcu, J36 elongated triangular gyrobicupola 18, 36, 20
etobcu, J35 elongated triangular orthobicupola 18, 36, 20
githawro great triangular hebesphenorotunda 18, 36, 20
thawro, J92 triangular hebesphenorotunda 18, 36, 20
gyetibcu, J44 gyroelongated triangular bicupola 18, 42, 26
... truncated 4-generalised Shephard cube, complex polyhedron x4-4-x2-3-o2 192, 240, 76
... vertex figure of getut 0.866025 20, 108, 64
... vertex figure of setut 0.866025 20, 108, 64
dip (old: dep) decagonal prism 1.693527 20, 30, 12
doe dodecahedron, cosmohedron, Goldberg polyhedron GP(1,0) 1.401259 20, 30, 12
... f v10o, variation of decagonal prism, hull of 10/3-prism 1.286277 20, 30, 12
gissid great stellated dodecahedron, tri-stellahedron 0.535233 20, 30, 12
stiddip (tristrophic) decagrammic prism, stellated decagonal prism, 10/3-prism, 10-prism with winding number 3 0.794963 20, 30, 12
pactic partially (mono-)contracted truncated cube ... 20, 32, 14
pextut partially (edge-)expanded truncated tetrahedron 20, 34, 16
pero, J6 pentagonal rotunda, half of icosidodecahedron 1.618034 20, 35, 17
escu, J19 elongated square cupola, diminished small rhombicuboctahedron 1.398966 20, 36, 18
dap, 10-ap decagonal antiprism 1.674505 20, 40, 22
pegybcu, J31 pentagonal gyrobicupola 20, 40, 22
pobcu, J30 pentagonal orthobicupola 20, 40, 22
... pentagonal rhombic barrel 20, 40, 22
gyescu, J23 gyroelongated square cupola 20, 44, 26
... triangle triacontahexahedron 20, 54, 36
ditti ditrigonal icosahedron, vertex figure of idhi 1.401259 20, 60, 20
ditdid ditrigonal dodecadodecahedron, vertex figure of dittady 0.866025 20, 60, 24
gidtid great ditrigonary icosidodecahedron, vertex figure of gidtixhi 0.866025 20, 60, 32
gifodib sidtid faceting sidtid-2-10-20-0 (i.e. with 10(=d) {3}, 20(=i) {4}, and 2(=b) {5/2}) 0.866025 20, 60, 32
sidtid small ditrigonary icosidodecahedron, holosnub dodecahedron, vertex figure of sidtixhi 0.866025 20, 60, 32
sifodib sidtid faceting sidtid-0-10-20-2 (i.e. with 10(=d) {3}, 20(=i) {4}, and 2(=b) {5}) 0.866025 20, 60, 32
dudsi small noble triangular hexecontahedron, dual of D-stellation of icosahedron, D-faceting of dodecahedron, vertex figure of paphicki 0.866025 20, 90, 60
hudsi great noble triangular hexecontahedron, dual of H-stellation of icosahedron, H-faceting of dodecahedron, vertex figure of paphacki, huitzilopochtli 0.866025 20, 90, 60
... s60-r60-p12-h30 200, 360, 162
aud, J58 augmented dodecahedron 21, 35, 16
... t80-s60-r60-d12, Stott expansion of t60-r60-p12 ... 210, 420, 212
... truncated Hessian polyhedron, complex polyhedron x3-3-x3-3-o3 216, 288, 54
... complex polyhedron o3-3-x3-4-o2 , complex polyhedron x3-3-o3-3-x3 216, 432, 126
mabaud, J60 metabiaugmented dodecahedron 22, 40, 20
pabaud, J59 parabiaugmented dodecahedron 22, 40, 20
... t16-r12, Stott contraction of t16-s12-r12-h4 ... 22, 48, 28
taud, J61 triaugmented dodecahedron 23, 45, 24
... complex polyhedron x3   x3-3-o3 0.912871 24, 32, 11
tithah truncated tetrahemihexahedron 1.581139 24, 36, 13
... a3b3c, general variation of truncated octahedron sqrt[(3a2+4b2+3c2+4ab+2ac+4bc)/8] 24, 36, 14
... mono lowered truncated cube ... 24, 36, 14
... o3q4x, variation of truncated cube 2.179449 24, 36, 14
... o3x4q, variation of truncated cube, hull of sno 2.121320 24, 36, 14
... o3x4u, variation of truncated cube 2.613126 24, 36, 14
pabditoe parabidiminished truncated octahedron 1.581139 24, 36, 14
... para bi lowered truncated cube ... 24, 36, 14
quith quasitruncated hexahedron, stellated truncated hexahedron, stellatruncated cube 0.579471 24, 36, 14
tic truncated cube, truncated hexahedron 1.778824 24, 36, 14
toe (alt.: gratet) truncated octahedron, omnitruncated tetrahedron, great rhombitetratetrahedron, Voronoi cell of body-centered cubic (bcc) lattice, Kelvin's tetrakaidecahedron, Waterman polyhedron number 10 wrt. face-centered cubic lattice A3 centered at a lattice point, permutohedron of 4 elements 1.581139 24, 36, 14
twip dodecagonal prism 1.995508 24, 36, 14
... u3x4o, variation of truncated octahedron, Waterman polyhedron number 5 wrt. face-centered cubic lattice A3 centered at a lattice point 2.236068 24, 36, 14
... x3f4o, variation of truncated octahedron, hull of siddo, hull of passipsido 2.176251 24, 36, 14
... x3u4o, variation of truncated octahedron 2.549510 24, 36, 14
... x3w4o, variation of truncated octahedron, hull of rah, hull of snu 2.956796 24, 36, 14
... x3x3u, variation of truncated octahedron, Waterman polyhedron number 5 wrt. face-centered cubic lattice A3 centered at a shallow hole 2.091650 24, 36, 14
topfu two-op-fusion 1.398966 24, 40, 16
tepcus tetrapod-cut-sirco 1.398966 24, 40, 18
phexik partially hexa-expanded icosahedron 24, 42, 20
groh great rhombihexahedron 0.736813 24, 48, 18
sroh small rhombihexahedron 1.398966 24, 48, 18
gocco great cubicuboctahedron 0.736813 24, 48, 20
socco small cubicuboctahedron 1.398966 24, 48, 20
... x3β4o (?) ... 24, 48, 20
esquigybcu, J37 (alt.: pirco) elongated square gyrobicupola, pseudorhombicuboctahedron, Miller's solid 1.398966 24, 48, 26
... f3o4x, variation of small rhombicuboctahedron 1.789732 24, 48, 26
gyquerco (alt.: rers quigybcu) inverto-elongated retrograde square gyrobicupola, gyrated quasirhombicuboctahedron, pseudo great rhombicuboctahedron, retroelongated retrosquare gyrobicupola 0.736813 24, 48, 26
... q3o4x, variation of small rhombicuboctahedron, hull of tisso 1.658312 24, 48, 26
querco quasirhombicuboctahedron, great rhombicuboctahedron (but not girco) 0.736813 24, 48, 26
sirco (alt.: esquobcu) small rhombicuboctahedron, expanded octahedron, expanded cube, elongated square-orthobicupola 1.398966 24, 48, 26
... u3o4x, variation of small rhombicuboctahedron 2.040640 24, 48, 26
reco rectified cuboctahedron, variation of small rhombicuboctahedron, Waterman polyhedron number 6 wrt. primitive cubic lattice C3 centered at a lattice point, Waterman polyhedron number 3 wrt. face-centered cubic lattice A3 centered at a lattice point 1.732051 24, 48, 26
pysnic pyritosnub cube, pyritohedral sirco variant, hexadiminished id 1.618034 24, 48, 26
pysnic pyritosnub cube, pyritohedral sirco variant, faceted tigid 1.876844 24, 48, 26
pysnic pyritosnub cube, pyritohedral sirco variant, edge-alternated girco 2.317611 24, 48, 26
gyesquibcu, J45 gyroelongated square bicupola 24, 56, 34
... β3/2β3x3*a (?) ... 24, 60, 28
... o3β4x (?) ... 24, 60, 32
... β3o4β (?) ... 24, 60, 32
snic snub cube, snub cuboctahedron 1.343713 24, 60, 38
... Leonardo polyhedron of type {4,5;31} 240, 600, 300
... 20 thawroes toroid 240, 600, 340
epcu, J20 elongated pentagonal cupola 25, 45, 22
pegycuro, J33 pentagonal gyrocupolarotunda 25, 50, 27
pocuro, J32 pentagonal orthocupolarotunda 25, 50, 27
gyepcu, J24 gyroelongated pentagonal cupola 25, 55, 32
sladid (old: sit) small lanceal disdodecahedron, strombic icositetrahedron, deltoidal icositetrahedron, tetragonal icosikaitetrahedron 26, 48, 24
... octagonal Leonardo style "polyhedron of renaissance", vertex figure of lamina-trunc(o8o4xb3x) 1.847759 26, 56, 32
siddykid small didyakis dodecahedron 26, 72, 48
... expansion of 41th stellation of truncated icosahedron 260, 420, 162
... xfoE3fooo5xuFx&#zxt 260, 420, 162
... external blend of 12 raded-1-10-5-5 edge facetings 260, 480, 192
... Shephard's 3-generalised cube, complex polyhedron x3-4-o2-3-o2 , γ3 3 1 27, 27, 9
... Hessian polyhedron, complex polyhedron x3-3-o3-3-o3 0.816497 27, 72, 27
... Shephard's 3-generalised cuboctahedron, complex polyhedron o3-4-x2-3-o2 27, 81, 36
... p12-h4 28, 42, 16
autic, J66 augmented truncated cube 28, 48, 22
pabextut partially bi-expanded truncated tetrahedron 28, 48, 22
n-p n-gonal prism sqrt[1/4+1/(4 sin2(π/n))] 2n, 3n, n+2
n/d-p n/d-prism, n-prism with winding number d sqrt[1/4+1/(4 sin2(π d/n))] 2n, 3n, n+2
n-ap n-gonal antiprism sqrt[(3-2 cos(π/n))/(8-8 cos(π/n))] 2n, 4n, 2n+2
n/2-ap n/2 antiprism sqrt[(3-2 cos(2π/n))/(8-8 cos(2π/n))] 2n, 4n, 2n+2
n/d-ap n/d-antiprism, n-antiprism with winding number d (for d>n/2 also: n/(n-d)-retroprism, retrograde n/(n-d)-antiprism) sqrt[(3-2 cos(π d/n))/(8-8 cos(π d/n))] 2n, 4n, 2n+2
... o5/2β5o (?) ... 30, 120, 54
... icosidodecahedron faceting 1.618034 30, 120, 62
... o3β5o (?) ... 30, 120, 62
choct chamfered octahedron, cubically truncated rhombic dodecahedron 30, 48, 20
... edge faceting raded-1-10-5-5 1.322876 30, 50, 21
epro, J21 elongated pentagonal rotunda 30, 55, 27
gidhid great dodecahemidodecahedron 0.618034 30, 60, 18
sidhid small dodecahemidodecahedron 1.618034 30, 60, 18
gidhei great dodecahemicosahedron, small dodecahemiicosahedron (but not sidhei) 1 30, 60, 22
sidhei small dodecahemicosahedron, great dodecahemiicosahedron (but not gidhei) 1 30, 60, 22
did dodecadodecahedron, great dodecadodecahedron 1 30, 60, 24
geihid great icosihemidodecahedron 0.618034 30, 60, 26
seihid small icosihemidodecahedron 1.618034 30, 60, 26
epigybcu, J39 elongated pentagonal gyrobicupola 30, 60, 32
epobcu, J38 elongated pentagonal orthobicupola 30, 60, 32
gid great icosidodecahedron 0.618034 30, 60, 32
id icosidodecahedron, rectified icosahedron, rectified dodecahedron 1.618034 30, 60, 32
pobro, J34 pentagonal orthobirotunda 1.618034 30, 60, 32
... rhombical hexa-augmented snub-cubical variant, rhombi-propello-octahedron 30, 60, 32
gyepro, J25 gyroelongated pentagonal rotunda 30, 65, 37
gyepibcu, J46 gyroelongated pentagonal bicupola 30, 70, 42
... Waterman polyhedron number 8 wrt. primitive cubic lattice C3 centered at a lattice point, Waterman polyhedron number 4 wrt. face-centered cubic lattice A3 centered at a deep hole 2.121320 30, 84, 56
... Waterman polyhedron number 7 wrt. body-centered cubic lattice C3* centered at a lattice point 30, 84, 56
chic chamfered cube, octahedrally truncated rhombic dodecahedron 32, 48, 18
... Waterman polyhedron number 5 wrt. body-centered cubic lattice C3* centered at a lattice point, slightly chamfered cube, octahedrally shallow truncated rhombic dodecahedron 32, 48, 18
pextoe partially (mono-)expanded truncated octahedron ... 32, 48, 18
... Waterman polyhedron number 4 wrt. primitive cubic lattice C3 centered at a hole, cubically expanded rhombic dodecahedron 2.598076 32, 48, 18
tuquith blend of 2 quasitruncated cubes 0.579471 32, 56, 24
tutic blend of 2 truncated cubes 1.778824 32, 56, 24
stai small triambic icosahedron, first stellation of the icosahedron 32, 60, 20
bautic, J67 biaugmented truncated cube 32, 60, 30
rhote (old: rattic) rhombic triacontahedron, terminally chamfered dodecahedron, terminally chamfered icosahedron, surtegmated dodecahedron, surtegmated icosahedron 32, 60, 30
... rhombical octa-augmented truncated-octehedral variant 32, 72, 42
... Waterman polyhedron number 6 wrt. face-centered cubic lattice A3 centered at a lattice point 32, 72, 42
pakid pentakis dodecahedron, apiculated dodecahedron 32, 90, 60
epgycuro, J41 elongated pentagonal gyrocupolarotunda 35, 70, 37
epocuro, J40 elongated pentagonal orthocupolarotunda 35, 70, 37
dittet ditruncated tetrahedron, truncated truncated tetrahedron, expanded ambified tut sqrt[(11y2+36y+36)/8] 36, 54, 20
patex sirco partially tetrahedrally-expanded small rhombicuboctahedron, tetrahedrally lowered small rhombicuboctahedron, partially tri-expanded truncated tetrahedron ... 36, 60, 26
... dodeca-augmented rhombicuboctahedron 36, 72, 38
retic (alt.: amtic) rectified/ambified truncated cube 3.414214 36, 72, 38
retoe (alt.: amtoe) rectified/ambified truncated octahedron 2.121320 36, 72, 38
... Waterman polyhedron number 9 wrt. face-centered cubic lattice A3 centered at a lattice point 3 36, 72, 38
... truncated 5-generalised Shephard cube, complex polyhedron x5-4-x2-3-o2 375, 450, 140
pystid pyritohedrally stellated icosidodecahedron 38, 60, 24
n/d-cu n/d-gonal cupola sqrt[(7+4 cos(π d/n)-4 cos2(π d/n))/(12-16 cos2(π d/n))] 3n, 5n, 2n+2
... rectified/ambified n/d-prism, o o-n/d-o symmetric co relative 1/[sqrt(2) sin(π d/n)] 3n, 6n, 3n+2
... complex polyhedron xp   x2-3-o2 3p, 3(p+1), p+3
... Shephard's p-generalised octahedron, complex polyhedron x2-3-o2-4-op , βp 3 0.707107 3p, 3p2, p3
... Shephard's p-generalised cuboctahedron, complex polyhedron op-4-x2-3-o2 3p2, 3p3, p3+3p
... truncated p-generalised Shephard cube, complex polyhedron xp-4-x2-3-o2 3p3, 3p2(p+1), (p2+3)p
... complex polyhedron xp-4-o2-3-x2 3p3, 3p2(p+2), p(p2+3p+3)
... ho oh&#q, narrower variant of digonal antiprism 1.767767 4, 6, 4
... qo oq&#h, longer variant of digonal antiprism, vertex figure of batch 1 4, 6, 4
... qo ou&#h disphenoid 1.224745 4, 6, 4
... qo3oo&#h, taller variant of trigonal pyramid, vertex figure of tico 0.981981 4, 6, 4
... qo3oo&#x, shallower variant of trigonal pyramid, vertex pyramid of cube 0.866025 4, 6, 4
tet tetrahedron, 3D simplex (α3), pyrochor(id), regular trigonal pyramid, digonal antiprism, regular (di)sphenoid, hemicube, smaller Delone cell of face-centered cubic (fcc) lattice, regular line-scalene, regular (point-)tettene, vertex figure of pen, Gosset polytope 02, Waterman polyhedron number 1 wrt. face-centered cubic lattice A3 centered at a shallow hole 0.612372 4, 6, 4
... uo ou&#h, shorter variant of digonal antiprism 1.118034 4, 6, 4
... xo oq&#q, tetrahedron with one shorter edge, vertex figure of tisdip 0.836660 4, 6, 4
... xo ox&#h, longer variant of digonal antiprism, vertex figure of deca 0.935414 4, 6, 4
... xo ox&#k, longer variant of digonal antiprism, vertex figure of cont 0.989219 4, 6, 4
... xo ox&#q, longer variant of digonal antiprism, vertex figure of triddip 0.790569 4, 6, 4
... xo3oo&#q, longer variant of trigonal pyramid, vertex figure of tepe 0.774597 4, 6, 4
pac girco partially (mono-)contracted great rhombicuboctahedron ... 40, 60, 22
... triform blend of 6 pentagonal prisms 0.986715 40, 70, 32
epgybro, J43 elongated pentagonal gyrobirotunda 40, 80, 42
epobro, J42 elongated pentagonal orthobirotunda 40, 80, 42
gyepabro, J48 gyroelongated pentagonal birotunda 40, 90, 52
... t16-s12-r12-h4, Stott expansion of t16-r12 ... 42, 84, 44
... complex polyhedron x3-3-o3-4-x2 432, 1080, 342
... complex polyhedron x2-4-x3-3-o3 432, 648, 126
... t24-s6-24r, Stott contraction of t32-s24-r24-o6 ... 44, 96, 54
tedrid, J83 tridiminished rhombicosidodecahedron, magnaursahedron 2.232951 45, 75, 32
... Shephard's 4-generalised cuboctahedron, complex polyhedron o4-4-x2-3-o2 48, 192, 76
cotco cuboctatruncated cuboctahedron, cubitruncated cuboctahedron 1.322876 48, 72, 20
... a3b4c, general variation of great rhombicuboctahedron sqrt[2a2+4b2+3c2+4ab+(2ac+4bc)sqrt(2)]/2 48, 72, 26
girco great rhombicuboctahedron (but not querco), truncated cuboctahedron, omnitruncated octahedron, omnitruncated cube 2.317611 48, 72, 26
... q3q4x, Waterman polyhedron number 5 wrt. primitive cubic lattice C3 centered at a hole, variation of girco 2.958040 48, 72, 26
... q3x4x, variation of girco, hull of quitco 2.564844 48, 72, 26
quitco quasitruncated cuboctahedron, great truncated cuboctahedron, stellatruncated cuboctahedron 1.062393 48, 72, 26
... w3x4x, variation of girco, hull of cotco 3.193704 48, 72, 26
... x3x4q, variation of great rhombicuboctahedron, Waterman polyhedron number 7 wrt. face-centered cubic lattice A3 centered at a lattice point 2.645751 48, 72, 26
... t24-s6-n8 2.431352 48, 84, 38
padex snic partially dodeca-expanded snub cube 48, 84, 38
phexdo partially hexa-expanded dodecahedron 48, 90, 44
... 12S-24R-6O polyhedron within quitco's army 1.062393 48, 96, 42
... β3x4β (?) ... 48, 96, 44
resirco (alt.: amsirco) rectified/ambified small-rhombated-cuboctahedron 2.613126 48, 96, 50
pox snic partially octa-expanded snub cube 48, 96, 50
... Waterman polyhedron number 8 wrt. body-centered cubic lattice C3* centered at a lattice point 48, 96, 50
... expanded octa-augmented truncated-octehedral variant 48, 96, 50
exrad expanded rhombic dodecahedron 48, 96, 50
2n-p 2n-gonal prism sqrt[1/4+1/(4 sin2(π/2n))] 4n, 6n, 2n+2
2n/2-p 2n-gonal prism of winding number 2 sqrt[1/4+1/(4 sin2(π/n))] 4n, 6n, 2n+2
2n/d-p 2n/d-prism, 2n-prism with winding number d sqrt[1/4+1/(4 sin2(π d/2n))] 4n, 6n, 2n+2
... complex polygon x2-4-or prism, complex polyhedron x2   x2-4-or 4r, 2r(r+1), r2+2
... oq ou&#h squippy variant 1.224745 5, 8, 5
... oq4oo&#h squippy variant 1.060660 5, 8, 5
... vertex figure of thex 0.948683 5, 8, 5
... vertex figure of ope 0.816497 5, 8, 5
squippy, 4pyr, J1 tetragonal pyramid, half of oct 0.707107 5, 8, 5
... vertex figure of cope 0.894427 5, 8, 5
... (ico derived) tridpy variant, o3m4o3o cell 5, 9, 6
... (tes derived) tridpy variant, o4m3o3o cell 5, 9, 6
... (hi derived) tridpy variant, o5m3o3o cell 5, 9, 6
... dual of uniform triangular prism, triangular dipyramid (but not tridpy), o3m3o3o cell 5, 9, 6
tridpy (alt.: trit), J12 trigonal dipyramid, (line-)triangle-tegum 5, 9, 6
gybadrid, J82 gyrate(d) bidiminished rhombicosidodecahedron 2.232951 50, 90, 42
mabidrid, J81 metabidiminished rhombicosidodecahedron 2.232951 50, 90, 42
pabidrid, J80 parabidiminished rhombicosidodecahedron 2.232951 50, 90, 42
... truncated Shephard's 3-generalised octahedron, complex polyhedron x2-3-x2-4-o3 54, 108, 36
... Waterman polyhedron number 8 wrt. face-centered cubic lattice A3 centered at a lattice point 54, 120, 68
... complex polyhedron x2-4-o3-3-o3 1 54, 216, 72
phexid partially hexa-expanded icosidodecahedron 54, 96, 44
bagydrid, J79 bigyrate diminished rhombicosidodecahedron 2.232951 55, 105, 52
dirid, J76 diminished rhombicosidodecahedron 2.232951 55, 105, 52
magydrid, J78 metagyrate diminished rhombicosidodecahedron 2.232951 55, 105, 52
pagydrid, J77 paragyrate diminished rhombicosidodecahedron 2.232951 55, 105, 52
bitdi chiral Weimholt hexahedron, bitrigonally diminished icosahedron, vertex figure of bidex 0.951057 6, 10, 6
bobipyr bowtie bipyramid, crossed-square bipyramid, bowtie (line-)tegum 0.707107 6, 10, 6
peppy, 5pyr, J2 pentagonal pyramid 0.951057 6, 10, 6
stappy, 5/2-pyr pentagrammic pyramid, stellated pentagonal pyramid 0.587785 6, 10, 6
... diagonal square wedge, line atop dual square 1.069045 6, 11, 7
thah tetrahemihexahedron, vertex figure of tho, triangular crossed cuploid 0.707107 6, 12, 7
... ho3oh&#q, narrower variant of trigonal antiprism, hemiation of hip 1.118034 6, 12, 8
oct (alt.: trap, tatet) octahedron, rectified tetrahedron, tricross (β3), tetratetrahedron, aerochor(id), trigonal antiprism, snubbed triangular dihedron, larger Delone cell of face-centered cubic (fcc) lattice, equatorial cross-section of (vertex first) 1/q-tes, vertex figure of hex, Gosset polytope 01,1, lattice C3 contact polytope (span of its small roots) 0.707107 6, 12, 8
... qo3oq&#x, shallower variant of trigonal antiprism, medial segment of cube 0.866025 6, 12, 8
squit (line) square tegum, Waterman polyhedron number 2 wrt. body-centered cubic lattice C3* centered at a hole 6, 12, 8
trirp (degenerate) trigonal retroprism, retrograde trigonal antiprism ∞   i.e. flat in euclidean space 6, 12, 8
trirp (variant) vertex figure of faceted rectified pentachoron, taller trigonal retroprism (3/2 antiprism) variant 0.763763 6, 12, 8
... xo3ox&#h, longer variant of trigonal antiprism, cyclo-hexadiminished co, vertex figure of batatoh 1 6, 12, 8
... xo3ox&#q, longer variant of trigonal antiprism, vertex figure of spid 0.866025 6, 12, 8
... f v3o, variation of triangular prism, vertex figure of rectified great grand hecatonicosachoron 0.884212 6, 9, 5
... f x3o, variation of triangular prism, vertex figure of rectified hecatonicosachoron 0.993902 6, 9, 5
... q x3o, variation of triangular prism, vertex figure of rectified tesseract 0.912871 6, 9, 5
trip, 3-p triangular prism, digonal cupola, Delone cell of unit-stacked hexagonal lattice, vertex figure of rap 0.763763 6, 9, 5
... u q3o, variation of triangular prism 1.290994 6, 9, 5
... u x3o, variation of triangular prism, vertex figure of rectified hecatonicosachoron 1.154701 6, 9, 5
... v f3o, variation of triangular prism, vertex figure of rasishi 0.983956 6, 9, 5
... v x3o, variation of triangular prism, vertex figure of rectified great grand stellated hecatonicosachoron 0.654847 6, 9, 5
... x f3o, variation of triangular prism 1.059565 6, 9, 5
... x h3o, variation of triangular prism 1.118034 6, 9, 5
... x q3o, variation of triangular prism, vertex figure of rectified icositetrachoron 0.957427 6, 9, 5
... x u3o, variation of triangular prism 1.258306 6, 9, 5
... q-laced digonal cupola, vertex figure of srip 0.906327 6, 9, 5
giddy great dodekicosahedron 1.134229 60, 120, 32
gird great rhombidodecahedron 0.716891 60, 120, 42
sird small rhombidodecahedron 2.232951 60, 120, 42
gaddid great dodekicosidodecahedron 0.716891 60, 120, 44
gidditdid great ditrigonary dodekicosidodecahedron, great dodekified icosidodecahedron 1.134229 60, 120, 44
ided icosidodecadodecahedron 1.322876 60, 120, 44
saddid small dodekicosidodecahedron 2.232951 60, 120, 44
sidditdid small ditrigonary dodekicosidodecahedron, small dodekified icosidodecahedron 1.721489 60, 120, 44
ri rhombicosahedron 1.322876 60, 120, 50
giid great icosicosidodecahedron 1.134229 60, 120, 52
siid small icosicosidodecahedron 1.721489 60, 120, 52
raded rhombidodecadodecahedron 1.322876 60, 120, 54
... f3o5x, variation of srid, hull of siid, hull of quit gissid 2.785428 60, 120, 62
gicdatrid great complex (ditrigonary) rhombicosidodecahedron 0.866025 60, 120, 62
gyrid, J72 gyrated rhombicosidodecahedron 2.232951 60, 120, 62
mabgyrid, J74 metabigyrated rhombicosidodecahedron 2.232951 60, 120, 62
pabgyrid, J73 parabigyrated rhombicosidodecahedron 2.232951 60, 120, 62
... q3o5x, variation of srid 2.601518 60, 120, 62
qrid quasi rhombicosidodecahedron, great (non-convex) rhombicosidodecahedron (i.e. not grid) 0.716891 60, 120, 62
sicdatrid small complex (ditrigonary) rhombicosidodecahedron 0.866025 60, 120, 62
srid small rhombicosidodecahedron, expanded icosahedron, expanded dodecahedron 2.232951 60, 120, 62
tagyrid, J74 trigyrated rhombicosidodecahedron 2.232951 60, 120, 62
... v3o5f, variation of srid, hull of tiggy 2.757554 60, 120, 62
rid rectified icosidodecahedron, variation of small rhombicosidodecahedron 3.077684 60, 120, 62
... o5/2β5x (?) ... 60, 150, 54
... o3β5x (?) ... 60, 150, 62
... x3β5o (?) ... 60, 150, 62
isdid inverted snub dodecadodecahedron, vertisnub dodecadodecahedron, nyarlathotep 60, 150, 84
siddid (old: siided) snub dodecadodecahedron, chaugnar faugn 60, 150, 84
girsid great (inverted) retrosnub icosidodecahedron, azathoth 60, 150, 92
gisid great inverted snub icosidodecahedron, great vertisnub icosidodecahedron, cthulhu 60, 150, 92
gosid great snub icosidodecahedron, tsathoggua 60, 150, 92
snid snub dodecahedron, snub icosidodecahedron 2.155837 60, 150, 92
gisdid great snub dodekicosidodecahedron, shub-niggurath 0.707107 60, 180, 104
sided snub icosidodecadodecahedron, dagon 1.126898 60, 180, 104
seside small snub icosicosidodecahedron, snub disicosidodecahedron, holosnub icosahedron, hastur 1.458190 60, 180, 112
sirsid small (inverted) retrosnub icosicosidodecahedron, retrosnub disicosidodecahedron, yog sothoth 0.580695 60, 180, 112
... β5/2o5β (?) ... 60, 180, 84
... β3o5β (?) ... 60, 180, 92
gidrid (subsym.: gidrikid) great dirhombicosidodecahedron, great snub disicosidisdodecahedron, Miller's monster, (subsym.: great dirhombichiricosadodecahedron) 0.707107 60, 240, 124
gidisdrid great disnub dirhombicosidodecahedron, Skilling's figure 0.707107 60, 360, 204
... noble {9,3} modwrap within srid, Crennell number 4 stellation of the icosahedron 2.232951 60, 90, 20
... o5/2f5x variation of truncated great dodecahedron 2.478019 60, 90, 24
quit sissid quasitruncated small stellated dodecahedron, small stellated truncated dodecahedron, small stellatruncated dodecahedron 0.852911 60, 90, 24
tigid truncated great dodecahedron 1.876844 60, 90, 24
... f3x5o, variation of ti, hull of tigid, hull of gaddid 3.036797 60, 90, 32
quit gissid quasitruncated great stellated dodecahedron, great stellated truncated dodecahedron, great stellatruncated dodecahedron 0.657550 60, 90, 32
ti truncated icosahedron, buckyball, Goldberg polyhedron GP(1,1) 2.478019 60, 90, 32
tid truncated dodecahedron 2.969449 60, 90, 32
tiggy truncated great icosahedron, great truncated icosahedron 1.053292 60, 90, 32
... x3f5o, variation of ti, hull of raded, hull of kri 3.463334 60, 90, 32
sladit small lanceal ditriacontahedron, strombic hexecontahedron, deltoidal hexecontahedron, tetragonal hexecontahedron 62, 120, 60
... triangle hecatonicosahedron 62, 180, 120
... Shephard's 4-generalised cube, complex polyhedron x4-4-o2-3-o2 , γ4 3 1.224745 64, 48, 12
... complex polyhedron x3-3-x3-4-o2 , complex polyhedron x3-3-x3-3-x3 648, 648, 126
autid, J68 augmented truncated dodecahedron 65, 105, 42
... truncated Shephard's p-generalised octahedron, complex polyhedron x2-3-x2-4-op 6p2, 3p2(p+1), (p2+3)p
etripy, J7 elongated triangular pyramid 7, 12, 7
hippy, 6pyr (degenerate) hexagonal pyramid ∞   i.e. flat in euclidean space 7, 12, 7
... oqo3ooq&#xt, cubera (cube chimera), (fully) mono-truncated cube 0.866025 7, 12, 7
autip, J49 augmented triangular prism 7, 13, 8
... dual of pentagonal prism, (ex derived) pedpy variant, o3m3o5o cell 7, 15, 10
pedpy (alt.: pet), J13 pentagonal dipyramid, (line-)pentagon-tegum 7, 15, 10
mabautid, J70 metabiaugmented truncated dodecahedron 70, 120, 52
pabautid, J69 parabiaugmented truncated dodecahedron 70, 120, 52
... expanded dodeca-augmented great rhombicuboctahedron ... 72, 108, 38
dittec ditruncated cube, truncated truncated cube, expanded ambified tic sqrt[(7+4 sqrt(2))y2+(24+16 sqrt(2))y+(24+16 sqrt(2))]/2 72, 108, 38
dittoe ditruncated octahedron, truncated truncated octahedron, expanded ambified toe sqrt[(5y2+9y sqrt(2)+9)/2] 72, 108, 38
chike chamfered icosahedron, dodecahedrically truncated rhombic triacontahedron 72, 120, 50
... rhombical dodeca-augmented snub-dodecahedral variant, rhombi-propello-icosahedron 72, 150, 80
... complex polyhedron x3-3-o3-4-o2 1 72, 216, 54
tautid, J71 triaugmented truncated dodecahedron 75, 135, 62
... Shephard's 5-generalised cuboctahedron, complex polyhedron o5-4-x2-3-o2 75, 375, 140
cube (alt: squip) cube, hexahedron, 3D measure-polytope (γ3), geochor(id), square prism, cantellated square dihedron, triangular antitegum, Voronoi cell of primitive cubical lattice, Delone cell of primitive cubical lattice, terminally chamfered tetrahedron, surtegmated tetrahedron 0.866025 8, 12, 6
... f x4o, variation of cube 1.074481 8, 12, 6
... q x4o, variation of cube, vertex figure of rectified cubic honeycomb 1 8, 12, 6
recta rectangular alterprism, rectangular trapezoprism sqrt[c2+(a+b)2/2]/2 8, 12, 6
... u x4o, variation of cube 1.224745 8, 12, 6
... w x4o, variation of cube 1.398966 8, 12, 6
... x q4o, variation of cube 1.118034 8, 12, 6
tutrip two trip cupolaic blend, gyrated blend of 2 digonal cupola, Phillips head 0.763763 8, 14, 8
gybef, J26 gyrobifastegium 8, 14, 8
hog dhidicup verf vertex figure of hog dhidicup 0.730749 8, 14, 8
ifbah, ike-6-2 2-fold faceted icosahedron ike-6-2, pentagonal butterfly wedge, blend of 2 pentagonal pyramids, half of blend of 2 pentagonal antiprisms 0.951057 8, 14, 8
pextet partially (edge-)expanded tetrahedron 8, 14, 8
shappy, 7/2-pyr small heptagrammic pyramid 0.650389 8, 14, 8
etidpy, J14 elongated trigonal dipyramid 8, 15, 9
titdi tri-trigonally diminished icosahedron, (subsymmetrically) tristellated-dodecahedron, tri-kis-dodecahedron, dual of teddi, vertex figure of tridex 8, 15, 9
squap square antiprism 0.822664 8, 16, 10
... vertex figure of small prismated icositetrachoron 0.541196 8, 16, 10
bautip, J50 biaugmented triangular prism 8, 17, 11
... dual of hexagonal prism, hexgonal dipyramid 8, 18, 12
tikit triakis tetrahedron, apiculated tetrahedron 8, 18, 12
snadow, J84 snub disphenoid, snub digonal antiprism 8, 18, 12
... hexagonal dipyramid 8, 18, 12
chado chamfered dodecahedron, icosahedrally truncated rhombic triacontahedron, Goldberg polyhedron GP(2,0) 80, 120, 42
... truncated 3-generalised Shephard cube, complex polyhedron x3-4-x2-3-o2 81, 108, 36
... t32-s24-r24-o6, Stott expansion of t24-s6-24r ... 84, 168, 86
... complex polyhedron xp   x3-3-o3 sqrt[2+1/sin2(π/p)] 8p, 8(p+1), p+8
ratricu retrograde trigonal cupola, 3/2-cupola 0.707107 9, 15, 8
targi trireplenished great icosahedron 0.587785 9, 15, 8
teddi, J63 tridiminished icosahedron, ursahedron, vertex figure of sadi 0.951057 9, 15, 8
tricu, J3 triangular cupola, half of cuboctahedron 1 9, 15, 8
esquipy, J8 elongated square pyramid 9, 16, 9
ogpy, 8/3-pyr octagrammic pyramid 0.594604 9, 16, 9
scuffi, ike-7-3 semicupolaically faceted icosahedron 0.951057 9, 18, 10
scufgi, sissid-3-7 semicupolaically faceted great icosahedron 0.587785 9, 18, 10
... (hi derived) truncated tridpy variant, o2o3o symmetric co relative ... 9, 18, 11
... (ico derived) truncated tridpy variant, o2o3o symmetric co relative ... 9, 18, 11
... (tes derived) truncated tridpy variant, o2o3o symmetric co relative ... 9, 18, 11
retrip (alt.: amtrip) rectified/ambified trip, kernel of trip and m m3o, o2o3o symmetric co relative 0.816497 9, 18, 11
gyesp, J10 gyroelongated square pyramid 9, 20, 13
tautip, J51 triaugmented trigonal prism 9, 21, 14
... Shephard's 3-generalised octahedron, complex polyhedron x2-3-o2-4-o3 , β3 3 0.707107 9, 27, 27
... triaconta-augmented rhombicosidodeahedron ... 90, 180, 92
retid (alt.: amtid) rectified/ambified truncated dodecahedron 5.854102 90, 180, 92
reti (alt.: amti) rectified/ambified truncated icosahedron 4.854102 90, 180, 92
... rhombic enneacontahedron 92, 180, 90
... external blend of 20 trippescus 92, 240, 120
... truncated Shephard's 4-generalised octahedron, complex polyhedron x2-3-x2-4-o4 96, 240, 76
n/d-py n/d-gonal pyramid 1/sqrt[4-1/sin2(πd/n)] n+1, 2n, n+1
... dual of uniform n-gonal prism, n-gonal dipyramid n+2, 3n, 2n
... complex polyhedron sp-4-o2-3-o2 , (γp 3)/p sqrt(3/8) / sin(π/p) p2, 3p2, p(p+3)
... Shephard's p-generalised cube, complex polyhedron xp-4-o2-3-o2 , γp 3 sqrt(3)/(2 sin(π/p)) p3, 3p2, 3p
... complex polyhedron xp   xr-4-o2 , complex polyhedron xp   xr   xr pr2, 2(p+r)r, p+2r
... complex polyhedron xp   xr   xt prt, pr+pt+rt, p+r+t
... complex polyhedron xp   xr || op   xr r(p+1), pr+p+r+1, p+r+1

Count of actually available polytopes: 536


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 4D
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Acronym Name Circumradius Face vector
... vertex figure of hexadecasphenohexadecateron 0.957427 10, 21, 18, 7
squippyp, K-4.12 square-pyramidal prism, J1 prism, line || cube, digonal magnabicupolaic ring 0.866025 10, 21, 18, 7
tritep (alt: dycufbil) (line-)triangle-tegum prism, triangular-bipyramidal prism, dyadic cupofastegia biluna 10, 23, 21, 8
tridpyp triangular-bipyramid prism, tetrahedral prism bicupola, external blend of 2 tetrahedral prisms 10, 23, 21, 8
teddipy, K-4.88 tridiminished-icosahedral pyramid 1.618034 10, 24, 23, 9
etedpy elongated tetrahedral bipyramid 10, 24, 26, 12
cute (old: cubdipy) cubical (line-)tegum, cubical bipyramid ... 10, 28, 30, 12
tibbid (alt.: durap) triangular-bipyramidal decachoron, rectified-pentachoron dual, surtegmated pentachoron, joined pentachoron 10, 30, 30, 10
... qo3oq3oo&#x, shallower variant of rap, segment of tes 1 10, 30, 30, 10
rap (old: rip, alt.: tetaoct), tet || oct, K-4.5 rectified pentachoron, pyrorectichoron, tetrahedral cupola, vertex figure of hin, tetrahedron atop octahedron, Gosset polytope 02,1 0.774597 10, 30, 30, 10
firp faceted rectified pentachoron, retropyrohemiperichoron, vertex figure of dah, tetrahedral cuploid 0.774597 10, 30, 35, 15
dutip truncated-pentachoron dual, apiculated pentachoron, tetrakis pentachoron 10, 30, 40, 20
pinnip prismatointercepted pentachoron, retropyroinvertirectichoron, vertex figure of han 0.774597 10, 30, 45, 15
squapt (line-)square-antiprismatic tegum, square-antiprismatic bipyramid, square-pyramidal antiprism 10, 32, 42, 20
... vertex figure of facetospinopenteractidishexadecateron 0.919866 10, 33, 34, 11
stapedit ({5/2},{5})-duotegum, tegum product of a pentagon and a pentagram 10, 35, 50, 25
bideca (old: dudeca) bidecachoron, decachoron dual, bi-apiculated pentachoron 0.816497 10, 40, 60, 30
... vertex figure of facetoinverted decahexadecateron 0.919866 10, 45, 45, 10
... vertex figure of hexadecateron 0.774597 10, 45, 45, 10
... vertex figure of retrodishexadecateron 0.774597 10, 45, 50, 15
... vertex figure of retropenteractihexadecateron 0.774597 10, 45, 60, 15
dedip (old: dadip) decagon-decagon duoprism 2.288246 100, 200, 120, 20
distadedip decagon-decagram duoprism 1.732051 100, 200, 120, 20
stadidip decagram-decagram duoprism 0.874032 100, 200, 120, 20
... axially pyritohedral octa-diminishing of telex, hexa-diminishing of oofoo3oxoxo5xooox&#xt 100, 348, 340, 92
idimex spid-diminished ex, icosidiminished ex 1.618034 100, 480, 600, 220
dexdap dodecahedral extended double antiprism 1.618034 100, 500, 720, 220
gap great antiprism, grand antiprism, pentagonal double antiprismoid (but not: great duoantiprism), bicyclical decadiminishing of ex 1.618034 100, 500, 720, 320
padiap prismatic double inverted antiprism, pentagrammic double antiprismoid 0.618034 100, 500, 720, 320
biscrox bistratic icosahedron-first cap of rectified hexacosachoron 3.077684 102, 390, 372, 84
... terminally edge-beveled hexadecachoron 104, 256, 192, 40
pabex thex partially biexpanded truncated hexadecachoron, partially bicontracted prismatorhombated tesseract ... 104, 260, 200, 44
... Waterman polychoron number 5 wrt. alternated tessic lattice D4 centered at a hole 2.121320 104, 384, 408, 128
hexdex hexadecadiminished hexacosachoron 1.618034 104, 528, 716, 296
... xxxoooFFFAAA 2 FxfoFfxFofxo 2 xfFFfoFoxxof 2 fFxfoFoxFofx &#zx 108, 384, 404, 128
10,n-dip decagon - n-gon duoprism sqrt[(3+sqrt(5))/2+1/(4 sin2(π/n))] 10n, 20n, 11n+10, n+10
pippy, K-4.141 pentagonal-prismatic pyramid, vertex pyramid of the rectified hexacosachoron 3.077684 11, 25, 22, 8
stippy stellated-pentagonal prismatic pyramid, vertex pyramid of the rectified grand hexacosachoron 0.726543 11, 25, 22, 8
xxo ooo3oxx&#xt line || trip || {3}, stack of tepe and triddip 11, 25, 24, 10
mibdipy, K-4.87 metabidiminished-icosahedral pyramid 1.618034 11, 30, 32, 13
pappy pentagon-antiprismatical pyramid 1.618034 11, 30, 32, 13
stapepy pentagram-antiprismatical pyramid 0.662791 11, 30, 32, 13
..., {3} || gybef {3} || gyrobifastegium ... 11, 31, 32, 12
aurap augmented rectified pentachoron 11, 36, 42, 17
biscrahi bistratic icosidodecahedron-first cap of rectified hecatonicosachoron 4.534568 110, 270, 214, 54
... omni-pippy-augmented (5,20)-duoprism 110, 300, 255, 65
doasridaid doe atop srid atop id 110, 390, 406, 126
bicypdex (alt.: bicypaugap) bi-cyclopentadiminished hexacosachoron, bi-cyclopentaaugmented great antiprism 1.618034 110, 600, 900, 410
cydadex cyclical decadiminishing of ex 1.618034 110, 610, 960, 460
... medial tetrastratic segment of telex 112, 450, 484, 146
coqroc tetracontoctiquasirhombated tetracontoctachoron 1.325654 1152, 2304, 1104, 96
croc tetracontoctirhombated tetracontoctachoron 3.200413 1152, 2304, 1104, 96
iquatpic icositetraquasitruncated prismatotetracontoctachoron 2.828427 1152, 2304, 1248, 168
doc distetracontoctachoron 2.449490 1152, 2304, 1248, 96
gaquapac great quasiprismatotetracontoctachoron 1.127864 1152, 2304, 1392, 240
gippic great prismatotetracontoctachoron, omnitruncated icositetrachoron 5.169905 1152, 2304, 1392, 240
ticont truncated tetracontoctachoron sqrt[(6+4 sqrt(2))y2+(23+16 sqrt(2))y+(23+16 sqrt(2))] 1152, 2304, 1488, 336
... β3x4x3β (?) ... 1152, 2880, 1968, 384
tispic truncated small prismated tetracontoctachoron sqrt[(2+sqrt(2))y2+(7+4 sqrt(2))y+(7+4 sqrt(2))] 1152, 2880, 2112, 384
... β3x4β3x (?) ... 1152, 3456, 2688, 528
... x3β4β3x (?) ... 1152, 3456, 2688, 528
sobcotic small bicuntitruncated tetracontoctachoron, general variant of expanded tetracontoctachoron, general variant of expanded bicont sqrt[a2+3ab+3b2+2ac sqrt(2)+4bc sqrt(2)+3c2] 1152, 3456, 3552, 1248
... β3β4β3x (?) ... 1152, 4032, 3744, 936
... β3β4x3β (?) ... 1152, 4032, 3744, 936
... BxxFxfofx3oooxxxFFF3xBxfFxxof *b3xxBxfFfxo&#zx 1152, 4176, 3984, 960
tisdip, K-4.18 triangle - square duoprism, square - cube wedge, vertex figure of nit 0.912871 12, 24, 19, 7
peppyp, K-4.38 pentagon-pyramidal prism, J2 prism, line || pip 1.074481 12, 26, 22, 8
stappyp pentagram-pyramidal prism, line || stip 0.771681 12, 26, 22, 8
tricuf, K-4.25 trigonal cupofastegium, hexagon - triangle-prismatic wedge, triangle orthobicupolaic ring, {6} || trip, {3} || tricu, 0.209785-luna of small prismatodecachoron 1 12, 27, 24, 9
thahp tetrahemihexahedral prism, vertex figure of rhohid 0.866025 12, 30, 26, 9
traw, K-4.27 trigonal antitriwedge, hexagon - octahedral wedge, triangular gyrobicupolaic ring, {6} || oct, {3} || gyrated tricu, 1/6-luna of ico 1 12, 30, 27, 9
starpglassit pentagrammic-retroprismatic-hourglass tegum, pentagrammic-retroprismatic-hourglass bipyramid 0.707107 12, 30, 27, 9
ope, K-4.11 (alt: dytpuf) octahedron prism, vertex figure of rat, dyadic tegmipucofastegium 0.866025 12, 30, 28, 10
dygytpuf, K-4.13 dyadic gyrotegmipucofastegium, 3-prism atop reflected ortho 3-prism 0.866025 12, 30, 30, 12
... 4D corner hypercubera 1 12, 31, 31, 12
esquippidpy elongated square-pyramidal bipyramid, esquidpy-wedge, half of partially (mono-)expanded hex 12, 31, 32, 13
squaf, K-4.14 square antifastegium, square - squap wedge, {4} || gyro cube, bidiminished octahedral antiprism 0.879465 12, 32, 31, 11
trateddi, {3} || teddi, K-4.33 {3} atop teddi, teddi based wedge 1 12, 33, 33, 12
... vertex figure of spinotriacontaditeron 0.912871 12, 36, 36, 12
tidtes tetra-diminished tesseract 1 12, 36, 36, 12
... vertex figure of invertiretrolepidoteron 0.912871 12, 42, 42, 14
ditdap digon-triangle duoantiprism, hemiated shiddip sqrt[A2/2+B2] 12, 42, 52, 22
... vertex figure of retrocellitriacontadiahexadecateron 0.912871 12, 48, 64, 22
... Shephard's 3-generalised hexadecachoron, complex polychoron x2-3-o2-3-o2-4-o3 , β3 4 12, 54, 108, 81
... vertex figure of invertiretrohexadecalepidohemipenteract 0.912871 12, 54, 58, 18
... vertex figure of retrotriacontidicellihemitriacontaditeron 0.866025 12, 54, 82, 28
idhi invertidodecahedronary hecatonicosachoron 1 120, 1200, 1440, 120
dittady ditrigonary dishecatonicosachoron 1 120, 1200, 2400, 240
gidtixhi great ditrigonary hexacosihecatonicosachoron 1 120, 1200, 2400, 720
sidtixhi small ditrigonary hexacosihecatonicosachoron 1 120, 1200, 2400, 720
paphacki pentagon-prismatic heptacosicosachoron, great prismasaurus (also: great prismosaurus) 1 120, 1200, 2520, 720
paphicki pentagram-prismatic heptacosicosachoron, small prismasaurus (also: small prismosaurus) 1 120, 1200, 2520, 720
gifdahihox great fissary dodecahedronary hecatonicosihemihexacosachoron 1 120, 1200, 3000, 420
sifdahihox small fissary dodecahedronary hecatonicosihemihexacosachoron 1 120, 1200, 3000, 420
didhi dodecahedronary dishecatonicosachoron 1 120, 1200, 3120, 240
ofiddady omnifacetododecahedronary dishecatonicosachoron 1 120, 1200, 3120, 240
gridixhi great retroinverted dodecahedronary hexacosahecatonicosachoron 1 120, 1200, 3120, 720
sridixhi small retroinverted dodecahedronary hexacosahecatonicosachoron 1 120, 1200, 3120, 720
getut great tristetracosioctacontachoron 1 120, 1200, 3840, 1440
setut small tristetracosioctacontachoron 1 120, 1200, 3840, 1440
gridaphi great retroinverted dodecahedronary prismatohecatonicosachoron 1 120, 1200, 4200, 1320
sridaphi small retroinverted dodecahedronary prismatohecatonicosachoron 1 120, 1200, 4200, 1320
gaghi, gapD great grand hecatonicosachoron, greatened aggrandized polydodecahedron 1 120, 1200, 720, 120
sishi, spD small stellated hecatonicosachoron, stellated polydodecahedron 1 120, 1200, 720, 120
quit sissiddip quasitruncated-small-stellated-dodecahedron prism, small-stellated-truncated-dodecahedron prism 0.988665 120, 240, 138, 26
tigiddip truncated-great-dodecahedron prism 1.942303 120, 240, 138, 26
quit gissiddip quasitruncated-great-stellated-dodecahedron prism 0.826058 120, 240, 144, 34
gippid great prismatodecachoron, omnitruncated pentachoron, Voronoi cell of lattice A4*, permutochoron of 5 elements 2.236068 120, 240, 150, 30
pextah partially (mono-)expanded tesseractihexadecachoron 120, 240, 152, 32
tiddip, K-4.130 truncated-dodecahedron prism 3.011250 120, 240, 154, 34
tiggipe truncated-great-icosahedron prism 1.165943 120, 240, 154, 34
tipe, K-4.127 truncated-icosahedron prism 2.527959 120, 240, 154, 34
tadeca truncated decachoron sqrt(2y2+7y+7) 120, 240, 160, 40
girdip great-rhombidodecahedron prism 0.874032 120, 300, 204, 44
gaddiddip great-dodekicosidodecahedron prism 0.874032 120, 300, 208, 46
gidditdiddip great-ditrigonary-dodekicosidodecahedron prism 1.239546 120, 300, 208, 46
ididdip icosidodecadodecahedron prism 1.414214 120, 300, 208, 46
saddiddip small-dodekicosidodecahedron prism 2.288246 120, 300, 208, 46
sidditdiddip small-ditrigonary-dodekicosidodecahedron prism 1.792631 120, 300, 208, 46
... β3x3x3β (?) ... 120, 300, 220, 50
giidip great-icosicosidodecahedron prism 1.239546 120, 300, 224, 54
siidip small-icosicosidodecahedron prism 1.792631 120, 300, 224, 54
radiddip (old: radedip) rhombidodecadodecahedron prism 1.414214 120, 300, 228, 56
tispid truncated small prismated decachoron sqrt(y2+3y+3) 120, 300, 230, 50
... proh-cap augmented bistratic prit-cap ... 120, 300, 240, 60
qriddip quasi-rhombicosidodecahedron prism 0.874032 120, 300, 244, 64
sriddip, K-4.111 small-rhombicosidodecahedron prism 2.288246 120, 300, 244, 64
tiatid, ti || tid, K-4.151 truncated icosahedron atop truncated dodecahedron 3.835128 120, 300, 244, 64
hagy gircope hexa-gyro-augmented gircope 120, 312, 250, 58
hau gircope hexa-augmented gircope 120, 312, 274, 82
raded adoe raded atop 3doe 1.432173 120, 330, 258, 56
radeda tigid, raded || tigid rhombidodecadodecahedron atop truncated great dodecahedron 2.363565 120, 330, 258, 56
sridati, srid || ti, K-4.126 small-rhombicosidodecahedron atop truncated-icosahedron 2.485450 120, 330, 274, 64
sridatid, K-4.159 small rhombicosidodecahedron atop truncated dodecahedron, small-rhombicosidodecahedral cap of small rhombated hecatonicosachoron 6.735034 120, 330, 274, 64
pexrico partially (mono-)expanded rico 120, 336, 272, 56
... β3x3β3x (?) ... 120, 360, 270, 50
siida (alt.: siidcup) small icosicosidodecahedral alterprism, small icosicosidodecahedral cupoliprism, closer siid atop siid 1.765796 120, 360, 284, 54
... x3β3β3x (?) ... 120, 360, 290, 60
isdiddip inverted-snub-dodecadodecahedron prism 120, 360, 318, 86
siddiddip snub-dodecadodecahedron prism 120, 360, 318, 86
girsiddip great-(inverted)-retrosnub-icosidodecahedron prism 120, 360, 334, 94
gisiddip great-inverted-snub-icosidodecahedron prism 120, 360, 334, 94
gosiddip great-snub-icosidodecahedron prism 120, 360, 334, 94
sniddip, K-4.110 snub-dodecahedron prism, snub-icosidodecahedron prism 2.213060 120, 360, 334, 94
sobcated small bicuntitruncated decachoron, general variant of expanded decachoron, general variant of expanded bideca sqrt[(2a2+3ab+3b2+2ac+4bc+3c2)/5] 120, 360, 380, 140
gitpodady great (intersected) tripesic dodecahedronary dishecatonicosachoron 1 120, 3600, 3120, 240
sitpodady small (intersected) tripesic dodecahedronary dishecatonicosachoron 1 120, 3600, 3120, 240
... β3β3x3β (?) ... 120, 420, 380, 100
gisdiddip great-snub-dodekicosidodecahedron prism 120, 420, 388, 106
sididdip snub-icosidodecadodecahedron prism 120, 420, 388, 106
... β3β3β3x (?) ... 120, 420, 400, 105
sesidip small-snub-icosicosidodecahedron prism 1.541531 120, 420, 404, 114
sirsiddip small-(inverted)-retrosnub-icosicosidodecahedron prism 0.766294 120, 420, 404, 114
... (1,4)-expanded bited ... 120, 420, 440, 140
cyted spic cyclotetradiminished small prismatotetracontoctachoron 1.847759 120, 432, 468, 156
regikaike rectified gikaike 1.732051 120, 480, 424, 76
sniddap s2s3s5s, snub-dodecahedral antiprism, non-uniform alternation of griddip ... 120, 480, 544, 184
gidriddip great-dirhombicosidodecahedron prism, great-snub-disicosidisdodecahedron prism, prism of Miller's monster 0.866025 120, 540, 488, 126
gypasp great pyramidic swirlprism 0.618034 120, 600, 720, 240
spysp small pyramidic swirlprism 1.618034 120, 600, 720, 240
fix, pI icosahedral hecatonicosachoron, faceted hexacosichoron, polyicosahedron 1.618034 120, 720, 1200, 120
gofix, gpI great icosahedral hecatonicosachoron, great faceted hexacosichoron, greatened polyicosahedron 0.618034 120, 720, 1200, 120
ex, pT hexacosachoron, 600-cell, hydrochoron, tetraplex, polytetrahedron 1.618034 120, 720, 1200, 600
gax, apT grand hexacosachoron, aggrandized polytetrahedron 0.618034 120, 720, 1200, 600
gahi, apD grand hecatonicosachoron, aggrandized polydodecahedron 1.618034 120, 720, 720, 120
gashi, aspD grand stellated hecatonicosachoron, aggrandized stellated polydodecahedron 0.618034 120, 720, 720, 120
gishi, gspD great stellated hecatonicosachoron, greatened stellated polydodecahedron 0.618034 120, 720, 720, 120
gisp great swirlprism 0.618034 120, 720, 720, 120
gohi, gpD great hecatonicosachoron, greatened polydodecahedron 1.618034 120, 720, 720, 120
sisp small swirlprism 1.618034 120, 720, 720, 120
... o3o3β5o (?) ... 1200, 10800, 9120, 1920
ragaghi rectified great grand hecatonicosachoron 1.070466 1200, 3600, 2160, 240
rasishi rectified small stellated hecatonicosachoron 2.802517 1200, 3600, 2160, 240
firgaghi faceted rectified great grand hecatonicosachoron 1.070466 1200, 3600, 2640, 240
firsashi faceted rectified small stellated hecatonicosachoron 2.802517 1200, 3600, 2640, 240
firgogishi facetorectified great grand stellated hecatonicosachoron 0.661585 1200, 3600, 3120, 720
fry facetorectified hecatonicosachoron 4.534568 1200, 3600, 3120, 720
rahi rectified hecatonicosachoron 4.534568 1200, 3600, 3120, 720
rigogishi rectified great grand stellated hecatonicosachoron 0.661585 1200, 3600, 3120, 720
bhidtex bi-hecatonicosidiminished truncated hexacosichoron 4.643523 1200, 3600, 3240, 840
hinhi hecatonicosintercepted hecatonicosachoron 2.802517 1200, 3600, 3360, 240
mohiny medial hecatonicosintercepted hecatonicosachoron 1.070466 1200, 3600, 3360, 240
gohiny great hecatonicosintercepted hecatonicosachoron 0.661585 1200, 3600, 3840, 240
shinhi small hecatonicosintercepted hecatonicosachoron 4.534568 1200, 3600, 3840, 240
gaddit thix grand ditrigonal trishecatonicosihexacosachoron 1.732051 1200, 7200, 10440, 960
middit thix medial ditrigonal trishecatonicosihexacosachoron 1.732051 1200, 7200, 10440, 960
gidditdy great ditrigonary dishecatonicosachoron 1.732051 1200, 7200, 4560, 240
sidditdy small ditrigonary dishecatonicosachoron 1.732051 1200, 7200, 4560, 240
ridditdy retroditrigonary dishecatonicosachoron 1.732051 1200, 7200, 4680, 240
ridtidohi rectified ditrigonary dishecatonicosachoron 1.732051 1200, 7200, 5280, 360
gotdatixhi great toroidoditrigonary hexacosihecatonicosachoron 1.732051 1200, 7200, 5520, 720
stodatixhi small toroidoditrigonary hexacosihecatonicosachoron 1.732051 1200, 7200, 5520, 720
rissidtixhi rectified small ditrigonary hexacosihecatonicosachoron 1.732051 1200, 7200, 6240, 840
riggidtixhi rectified great ditrigonary hexacosihecatonicosachoron 1.732051 1200, 7200, 6420, 840
todtixhi toroidal ditrigonal hexacosihecatonicosachoron 1.732051 1200, 7200, 6600, 720
dithix ditrigonary hecatonicosihexacosichoron 1.732051 1200, 7200, 7440, 720
todithix toroidoditrigonary hecatonicosihexacosichoron 1.732051 1200, 7200, 7440, 720
gidthidy hi great ditrigonal hecatonicosadishecatonicosihecatonicosachoron 1.732051 1200, 7200, 8400, 480
sidthidy hi small ditrigonal hecatonicosadishecatonicosihecatonicosachoron 1.732051 1200, 7200, 8400, 480
gidditpix great ditrigonary prismatohexacosichoron 1.732051 1200, 7200, 8520, 1320
gotditpix great toroidoditrigonary prismatohexacosichoron 1.732051 1200, 7200, 8520, 1320
sidditpix small ditrigonary prismatohexacosichoron 1.732051 1200, 7200, 8520, 1320
stoditpix small toroidoditrigonary prismatohexacosichoron 1.732051 1200, 7200, 8520, 1320
giddit thix great ditrigonal trishecatonicosihexacosachoron 1.732051 1200, 7200, 9360, 960
siddit thix small ditrigonal trishecatonicosihexacosachoron 1.732051 1200, 7200, 9360, 960
... DCBAVFfxoo xxxFofxFVo3xoxxFxooxo5ofxooxFfoV&#zx 1220, 3900, 3460, 780
oditico octadiminished truncated icositetrachoron, Waterman polychoron number 4 wrt. alternated tessic lattice D4 centered at a hole 2.645751 128, 320, 240, 48
pahtex sidpith partially demitesseractic-expanded sidpith, partially demitesseractic-contracted proh 128, 336, 288, 80
otbaquitit octagonnally tetrablended quasitruncated tesseract 0.615370 128, 384, 320, 80
otbott octagonnally tetrablended truncated tesseract 2.149726 128, 384, 320, 80
... Waterman polychoron number 4 wrt. primitive tesseractic lattice C4 centered at a hole 2.645751 128, 416, 400, 112
gondip great octagonal spinoduoprism 0.890446 128, 512, 640, 256
ondip octagonal spinoduoprism 1.485633 128, 512, 640, 256
12,n-dip dodecagon - n-gon duoprism sqrt[2+sqrt(3)+1/(4 sin2(π/n))] 12n, 24n, 13n+12, n+12
... n-fold dissected great-dodecahedral polytwister, n-fold dissected gaditer, great-dodecaswirlic 12n-choron ... 12n, 72n, 72n, 12n
... n-fold dissected icosahedral polytwister, n-fold dissected ikter, icosaswirlic 20n-choron ... 12n, 72n, 80n, 20n
... truncated generalized Shephard hexadecachoron, complex polychoron op-4-o2-3-x2-3-x2 12p2, 6p2(2p+1), 4p3(p+1), p(p3+4)
... (small) rhombated generalized Shephard hexadecachoron, complex polychoron x2-3-o2-3-x2-4-op 12p3, 12p3(p+1), 2p2(5p2+2p+6), p(p3+6p+4)
... bitruncated generalized Shephard tesseract, bitruncated generalized Shephard hexadecachoron, complex polychoron op-4-x2-3-x2-3-o2 12p3, 6p3(p+2), 2p2(2p2+2p+3), p(p3+4)
tetatricu, tet || tricu, K-4.24 tetrahedron atop trigonal cupola, 0.290215-luna of small prismatodecachoron 1 13, 30, 27, 10
etrippy elongated trigonal-prismatic pyramid ... 13, 30, 28, 11
chopy, pt || cho (degenerate) cubohemioctahedron pyramid ∞   i.e. flat in euclidean space 13, 36, 34, 11
ohopy, pt || oho (degenerate) octahemioctahedron pyramid ∞   i.e. flat in euclidean space 13, 36, 36, 13
copy, pt || co (degenerate) cuboctahedron pyramid ∞   i.e. flat in euclidean space 13, 36, 38, 15
eoctpy elongated octahedral pyramid, diminished pex hex 13, 36, 40, 17
squippyal cube, K-4.16 squippy atop gyro cube 0.879465 13, 40, 47, 20
gadpy great-dodecahedral pyramid, vertex cap of fix 1.618034 13, 42, 42, 13
sissidpy small-stellated-dodecahedral pyramid, vertex cap of unit gofix, vertex cap of v-scaled gohi 0.618034 13, 42, 42, 13
gikepy great-icosahedral pyramid, vertex cap of gax 0.618034 13, 42, 50, 21
ikepy, K-4.84 icosahedral pyramid, vertex cap of hexacosachoron 1.618034 13, 42, 50, 21
... magnaursachoron, cell-expanded tetrahedral ursachoron ... 132, 342, 272, 62
twau tipe twelve-augmented truncated-icosahedral prism 132, 360, 334, 106
twau sriddip twelve-augmented sriddip 132, 420, 424, 136
twau sridati twelve-augmented sridati 132, 450, 514, 196
twausniddip twelve-augmented sniddip 132, 480, 514, 166
... hi dimpled in by 120 ikadoes ... 1320, 8400, 13200, 6120
... AxoFFxxo3oFFxofxx xofofxFo3oxofxfoF&#zx 135, 531, 555, 159
... thawro pyrite, octa-diminishing of id - srid - F-ike - ti tower ... 138, 438, 418, 118
... AxoFFxoox3oFFxofoxo xofofxFof3oxofxfoFf&#zx 138, 549, 576, 165
telex vertex first tele-elongated hexacosachoron 138, 654, 800, 284
... octa-diminished thawro-wedged 2/6-luna of hexacosachoron ... 14, 177, 193, 64
etepe elongated tetrahedral-prism, elongated-triangular-pyramid prism, external blend of tetrahedral prism and (triangle,square)-duoprism 14, 31, 26, 9
hippyp hexagon-pyramidal prism, line || hip ∞   i.e. flat in euclidean space 14, 31, 26, 9
autipip augmented-triangular-prism prism ... 14, 33, 29, 10
gyautisdip gyro-augmented 3-4-duoprism ... 14, 33, 31, 12
tetu axially-tetrahedral ursachoron ofx3xoo3ooo&#xt, tet-based ursulate, vertex figure of sadit 1 14, 34, 30, 10
etripdapy elongated trigonal-prismatic bipyramid ... 14, 36, 37, 15
squippiatricu, K-4.32 square-pyramid atop triangular-cupola 1 14, 37, 35, 12
..., trip || gybef triangular prism || gyrobifastegium ... 14, 37, 38, 15
pex hex partially (mono-)expanded hex, partially contracted quawros 14, 42, 52, 24
octacube (alt.: octap), oct || cube, K-4.15 octahedron atop cube, octahedral antiprism, cubical antiprism, vertex figure of icoap 0.879465 14, 48, 62, 28
ite (old: it, older: ikedpy) (line-)ikosahedron-tegum, icosahedral bipyramid 14, 54, 80, 40
... FAxoFFxxo3foFFxofxx oxofofxFo3ooxofxfoF&#zx 141, 585, 609, 183
... β3o4o3β (?) ... 144, 1728, 1824, 384
twaddip dodecagonal-dodecagonal duoprism 2.732051 144, 288, 168, 24
pabextah partially bi-expanded tesseractihexadecachoron, partially bi-contracted great rhombated tesseract 144, 288, 184, 40
pabdiproh parabidiminished prismatorhombated hexadecachoron, tristratic tic-first central segment of proh 2.613126 144, 312, 212, 44
pahtex srit partially demitesseractic-expanded srit, partially demitesseractic-contracted grit 144, 336, 248, 56
pacprit partially (mono-)contracted prit ... 144, 360, 276, 60
... wx ox3xx4xx&#zx 144, 360, 296, 80
pabexrico partially bi-expanded rico, partially bi-contracted proh 144, 384, 304, 64
quidex quatro-icositetradiminished hexacosachoron, tristellatododecahedral enneacontahexachoron, dual of sadi 144, 480, 432, 96
... xxxoooFFFAAAxxF FxfoFfxFofxoVof xfFFfoFoxxofoVf FAoFxAxoAxFoxxF&#zx 144, 496, 476, 124
girc great retrotetracontoctachoron 0.765367 144, 576, 432, 48
sirc small retrotetracontoctachoron 1.847759 144, 576, 432, 48
giddic great distetracontoctachoron 0.765367 144, 576, 528, 96
siddic small distetracontoctachoron 1.847759 144, 576, 528, 96
... q3o4o3x, variant of spic 2.236068 144, 576, 672, 240
quippic quasiprismatotetracontoctachoron 0.765367 144, 576, 672, 240
spic small prismatotetracontoctachoron, runcinated icositetrachoron, expanded icositetrachoron 1.847759 144, 576, 672, 240
inpac icositetraintercepted prismatotetracontaoctachoron 1.847759 144, 576, 744, 168
... FAxoFFxoox3foFFxofoxo oxofofxFof3ooxofxfoFf&#zx 144, 603, 648, 189
shi snub hecatonicosachoron (but not snahi) 2.739576 1440, 10800, 11040, 1560
... x3β3o5o (?) ... 1440, 11520, 8640, 1440
... shi+120x 2sissid(?) ... 1440, 14400, 12480, 1680
bidsid pixhi bi-icositetra-diminished small disprismatohexacosihecatonicosachoron 5.236068 1440, 3240, 2256, 456
quit gashi quasitruncated grand stellated hecatonicosachoron 0.953850 1440, 4320, 2160, 240
tighi truncated great hecatonicosachoron 3.477092 1440, 4320, 2160, 240
tiffix truncated faceted hexacosichoron 4.643523 1440, 4320, 2640, 240
tigfix truncated great faceted hexacosichoron 1.199039 1440, 4320, 2640, 240
quit gishi quasitruncated great stellated hecatonicosachoron 0.953850 1440, 4320, 3120, 240
taghi truncated grand hecatonicosachoron 3.477092 1440, 4320, 3120, 240
taggix truncated grand hexacosachoron 1.199039 1440, 4320, 3600, 720
tex truncated hexacosachoron 4.643523 1440, 4320, 3600, 720
gidipthi great dipental trishecatonicosachoron 1.328131 1440, 7200, 4560, 360
gisdipthi great stellated dipental trishecatonicosachoron 1.328131 1440, 7200, 4560, 360
sidipthi small dipental trishecatonicosachoron 2.497212 1440, 7200, 4560, 360
sisdipthi small stellated dipental trishecatonicosachoron 2.497212 1440, 7200, 4560, 360
gidpixathi great dipentagonal hexacositrihecatonicosachoron 1.328131 1440, 7200, 6240, 960
sidpixathi small dipentagonal hexacositrihecatonicosachoron 2.497212 1440, 7200, 6240, 960
sid pippady small dipentary prismatodishecatonicosachoron 2.497212 1440, 7200, 6480, 960
gad phiddix great dipentary hecatonicosadishexacosachoron 1.328131 1440, 7200, 7200, 1320
sad phiddix small dipentary hecatonicosadishexacosachoron 2.497212 1440, 7200, 7200, 1320
padohi prismatodishecatonicosachoron 2.497212 1440, 7200, 7440, 2160
quipdohi quasiprismatodishecatonicosachoron 1.328131 1440, 7200, 7440, 2160
gacdupthix small capped dipentary tetrishecatonicosahexacosichoron 1.328131 1440, 7200, 9600, 1080
scadupthix small capped dipentary tetrishecatonicosahexacosichoron 2.497212 1440, 7200, 9600, 1080
gidhiquit paddy great dishecatonicosaquasitruncated prismatodishecatonicosachoron 2.140933 14400, 28800, 13920, 1080
sidhiquit paddy small dishecatonicosaquasitruncated prismatodishecatonicosachoron 5.605034 14400, 28800, 13920, 1080
dohitipady dishecatonicositruncated prismatodishecatonicosachoron 4.472136 14400, 28800, 14880, 1560
hixquitphix hecatonicosihexacosiquasitruncated prismatohecatonicosihexacosachoron 2.483382 14400, 28800, 14880, 1560
hixtaphix hecatonicosihexacositruncated prismatohecatonicosihexacosachoron 7.735167 14400, 28800, 14880, 1560
xithi hexacositriakishecatonicosachoron 3.872983 14400, 28800, 14880, 960
gaquidphihi great quasidisprismatohecatonicosihecatonicosachoron 4.242641 14400, 28800, 16080, 1680
gaquidipdy grand quasidisprismatodishecatonicosachoron 1.695697 14400, 28800, 16080, 2160
goquidipdy great quasidisprismatodishecatonicosachoron 6.566933 14400, 28800, 16080, 2160
gaquidapixhi great quasidisprismatohexacosihecatonicosachoron 1.581630 14400, 28800, 17040, 2640
gidpixhi great disprismatohexacosihecatonicosachoron, omnitruncated hecatonicosachoron, omnitruncated hexacosachoron 12.786651 14400, 28800, 17040, 2640
... β3x3x5β (?) ... 14400, 36000, 25440, 5040
... β3x3β5x (?) ... 14400, 43200, 31440, 6240
... x3β3x5β (?) ... 14400, 43200, 31440, 6240
... x3β3β5x (?) ... 14400, 50400, 33840, 6240
... β3x3β5β (?) ... 14400, 50400, 43680, 10560
... β3β3x5β (?) ... 14400, 50400, 44640, 11040
... x3β3β5β (?) ... 14400, 50400, 46080, 10680
... β3β3β5x (?) ... 14400, 50400, 47040, 11640
tistadip triangle - pentagram duoprism, pentagram - stip wedge 0.780850 15, 30, 23, 8
trapedip, K-4.34 triangle - pentagon duoprism, pentagon - pip wedge 1.028076 15, 30, 23, 8
tripuf, K-4.51 trigonal pucofastegium, triangle - hexagon-prismatic wedge, trigonal magnabicupolaic ring, {3} || hip, {6} || tricu, {3}-first cap of srip 1.183216 15, 33, 27, 9
... augmented axially-tetrahedral ursachoron ofxo3xooo3oooo&#xt ... 15, 38, 36, 13
tracufbil triangular-cupofastegia biluna, {3} || tricu || {3}, 0.419569-luna of gyspid 1 15, 39, 40, 16
stafe stellar (pentagrammal) antifastegium, pentagram - stap wedge, {5/2} || gyro stip 0.535857 15, 40, 38, 13
paf, K-4.22 pentagonal antifastegium, pentagon - pap wedge, {5} || gyro pip 1 15, 40, 38, 13
stisaw reduced pentagrammic gyrobicupolaic ring, star semiantiwedge, pseudo {10/2} || stap 0.870153 15, 45, 42, 13
octatricu, oct || tricu, K-4.30 octahedron atop trigonal cupola, 2/6-luna of icositetrachoron 1 15, 45, 43, 13
tautisdip triaugmented 3,4-duoprism ... 15, 48, 55, 22
... xoo3ofx5xox&#xt 3.077684 150, 390, 304, 64
... omni-pecu-augmented (10,10)-duoprism 150, 450, 420, 120
... omni-pecu-gyroaugmented (10,10)-duoprism 150, 450, 420, 120
idasridati id atop srid atop ti 150, 510, 486, 126
... xxxoooFFFAAABxxxF FxfoFfxFofxooVoof xfFFfoFoxxofooVof FAoFxAxoAxFoxxxBF&#zx 152, 564, 572, 160
... tetracontadisdiminished sidpixhi 5.236068 1560, 3720, 2856, 696
... FAxoFFxxox3foFFxofxxo oxofofxFof3ooxofxfoFf&#zx 159, 729, 849, 279
squaw, K-4.64, {8} || squap antitetrawedge, octagon - square-antiprismatic wedge, square gyrobicupolaic ring, {8} || squap, {4} || gyrated squacu 1.447009 16, 30, 35, 11
tes (alt.: squadip), K-4.20 tesseract, octachoron, "hypercube", 4D measure-polytope (γ4), 8-cell, geoter(id), square duoprism, vertex figure of icot 1 16, 32, 24, 8
gybeffip gybef prism 16, 36, 30, 10
tetatut, K-4.56 tetrahedron atop truncated tetrahedron, tetrahedral cap of rectified tesseract 1.224745 16, 36, 30, 10
squicuf, K-4.73 square cupofastegium, octagon - cube wedge of sidpith, square orthobicupolaic ring, {8} || cube, {4} || squacu, 1/4-luna of quawros 1.485634 16, 36, 31, 11
squappip, K-4.19 square-antiprism prism 0.962692 16, 40, 36, 12
dispap dyad-square prismantiprismoid, s2s2s4x, edge-alternated sodip ... 16, 40, 40, 16
bautipip biaugmented-triangular-prism prism 16, 42, 39, 13
tetaco, tet || co, K-4.23 tetrahedron atop cuboctahedron, tetrahedral rotunda of small prismatodecachoron 1 16, 42, 42, 16
... bilbiro wedge ... 16, 43, 42, 15
bidoctaco, {4} || co, K-4.28 square atop cuboctahedron, bidiminished octaco, square first rotunda of cytau tes 1 16, 44, 43, 15
retepe (alt.: amtepe) rectified/ambified tepe 1.224745 16, 48, 46, 14
... ox3/2ox3xo&#x 0.707107 16, 48, 48, 16
tetaltut, tet || inv. tut (degenerate) tetrahedron atop inverted truncated tetrahedron, (degenerate) tetrahedron atop alternate truncated tetrahedron ∞   i.e. flat in euclidean space 16, 48, 48, 16
bauautipip biaugmented augmented-triangular-prism prism ... 16, 49, 53, 20
tau ope tetra-augmented ope 16, 54, 64, 26
... Shephard's 4-generalised hexadecachoron, complex polychoron x2-3-o2-3-o2-4-o4 , β4 4 16, 96, 256, 256
pox rico partially octa-expanded rectified icositetrachoron 160, 384, 272, 48
pocsric   (alt.: phixic) partially octa-contracted small rhombated icositetrachoron, partially hexadeca-expanded icositetrachoron, octa-augmented truncated tesseract ... 160, 512, 464, 112
... ike atop id atop srid atop ti 162, 600, 584, 146
... id - srid - F-ike - ti tower, thawro'd rox ... 162, 630, 714, 246
..., xFoFx3ooooo5xofox&#xt   (F=ff=x+f) bilunabirotundic rhombicosidodecahedron prism, castellated rhombicosidodecahedral prism 164, 492, 424, 96
... xooFxxFfooFoofo3xxFooFxxxFooFxx3ofooFoofFxxFoox&#xt 164, 588, 568, 144
pac grit partially (mono-)contracted great rhombated tesseract 168, 336, 216, 48
... edge-beveled hexadecachoron 168, 352, 224, 40
pacproh partially (mono-)contracted proh 168, 432, 336, 72
squippia squacu, K-4.109 square pyramid atop square cupola 1.847759 17, 40, 35, 12
ecubpy elongated cubical pyramid, heptadiminished icositetrachoron 1 17, 40, 36, 13
... reduced( ofx3/2oxx3ooo&xt by 2tet ) 0.874032 17, 42, 38, 13
... point atop tet atop co 17, 46, 48, 19
aubautipip augmented biaugmented-triangular-prism prism 17, 50, 51, 18
squippiaco, K-4.31 square-pyramid atop cuboctahedron 1 17, 52, 51, 16
... trigonal mibdi-laced wedge 1 17, 52, 52, 17
... oFxx3xxof3foxo3oofx&#zx 170, 690, 750, 230
... bitruncated Witting polychoron, complex polychoron o3-3-x3-3-x3-3-o3 17280, 34560, 10800, 480
... (small) rhombated Witting polychoron, complex polychoron x3-3-o3-3-x3-3-o3 17280, 69120, 32400, 2640
... Fxxx5ofxo xofx5oxox&#zx 175, 600, 625, 200
pretasto pentagonorhombic trisnub trisoctachoron 176, 624, 592, 144
... xfofxxfoFxfxo3ooxxoFxFoxxoo3oxfxFofxxfofx&xt (F=ff=x+f) 176, 636, 592, 132
... ooofxxFfooFoofo3oxFxoFxxxFooFxx3xfoxFoofFxxFoox&#xt 176, 696, 724, 204
thiddip, K-4.47 triangle - hexagon duoprism, hexagon - hip wedge 1.154701 18, 36, 27, 9
teddipe tridiminished-icosahedron prism 1.074481 18, 39, 31, 10
tricupe, K-4.45 triangular-cupola prism, triangular prism atop hexagonal prism 1.118034 18, 39, 31, 10
esquipyp elongated square-pyramidal-prism, elongated-square-pyramid prism, external blend of square-pyramidal prism and tesseract 18, 41, 34, 11
octatut, oct || tut, K-4.52 octahedron atop truncated tetrahedron, octahedral cap of small rhombated pentachoron 1.183216 18, 42, 34, 10
triddet triangular ditetragoltriate sqrt[(a2+b2)/3] 18, 45, 42, 15
haf, K-4.46 hexagonal antifastegium, hexagon - hap wedge, {6} || gyro hip 1.130454 18, 48, 45, 15
ecubedpy elongated cubical bipyramid, hexadiminished icositetrachoron 1 18, 48, 48, 18
tautipip triaugmented-triangular-prism prism 18, 51, 49, 16
retdip (old: retriddip) rectified triddip 1.290994 18, 54, 51, 15
... external blend of the square-antiprism prism and 2 cube-pyramids, cubic-pyramid-biaugmented square-antiprism prism 18, 56, 60, 22
... external blend of the square-antiprism prism and 2 squap-pyramids, squap-pyramid-biaugmented square-antiprism prism 18, 56, 68, 30
... cuboctahedral retro-cuploid 1 18, 60, 53, 15
octaco, K-4.29 octahedron atop cuboctahedron, half of icositetrachoron (its oct-first rotunda), rectified octahedron-pyramid 1 18, 60, 58, 16
... mono-augmented trigonal mibdi-laced wedge ... 18, 62, 72, 28
... tetra-augmented axially-tetrahedral ursachoron xofo3ooox3oxoo&#xt ... 18, 70, 90, 38
... general variant of triddap sqrt[(a2+b2)/3] 18, 72, 84, 30
triddap triangle duoantiprism, hemiated hiddip 1.414214 18, 72, 84, 30
... cyclo-hexagonally diminished ico, tegum sum of 2 bi-dual (x,q)-triddips 1 18, 72, 84, 30
traddet triangular antiditetragoltriate sqrt[(a22+b22)/3] 18, 72, 96, 42
tidagrid, tid || grid, K-4.173 truncated dodecahedron atop great rhombicosidodecahedron, truncated-dodecahedral cap of prismatorhombated hexacosichoron 9.744610 180, 390, 274, 64
qridaquit gissidu expanded axially-great-icosahedral ursachoron, (qrid,quit gissid)-based ursulate 1.020794 180, 450, 346, 76
sridatidu expanded axially-icosahedral ursachoron, (srid,tid)-based ursulate 3.077684 180, 450, 356, 76
cytid srico cyclotridiminished small rhombated icositetrachoron 2.613126 180, 468, 369, 81
twagy tiddip twelve-gyro-augmented truncated-icosidodecahedral prism 180, 540, 526, 166
twau tiddip twelve-(ortho-)augmented truncated-icosidodecahedral prism 180, 540, 526, 166
... oFxxx5Fofxo oxofx5ooxox&#zx 180, 650, 690, 220
... FAxoAFxoxx3FxAAoxFxox oxofofxFof3ooxofxfoFf&#zx 186, 612, 600, 174
... ooofxxFfooFxofx3oxFxoFxxxFoxFxo3xfoxFoofFxxfooo&#xt 188, 804, 880, 264
... oFfoo3ooxxF3Fxoxo3ooffx&#zx 190, 660, 650, 180
... oFFxx3xxoof3fooxo3ooffx&#zx 190, 870, 990, 310
... β3β3o4β (?) ... 192, 1056, 1152, 328
... β3o3β4β (?) ... 192, 1152, 1184, 296
thaquitoth tesseractihexadecaquasitruncated tesseractihexadecachoron 1.338990 192, 384, 200, 32
thatoth tesseractihexadecatruncated tesseractihexadecachoron 1.790840 192, 384, 200, 32
tico truncated icositetrachoron, cantitruncated hexadecachoron 2.645751 192, 384, 240, 48
gaqrit great quasirhombated tesseract 1.401594 192, 384, 248, 56
grit great rhombated tesseract, cantitruncated tesseract 3.005916 192, 384, 248, 56
girpdo great rhombiprismatodisoctachoron 1.174172 192, 480, 304, 48
girpith great rhombiprismated tesseractihexadecachoron 1.082392 192, 480, 304, 48
sirpdo small rhombiprismatodisoctachoron 2.370932 192, 480, 304, 48
sirpith small rhombiprismated tesseractihexadecachoron 2.613126 192, 480, 304, 48
... x3x3β4o (?) ... 192, 480, 304, 56
gichado great cubihexadecadisoctachoron 1.174172 192, 480, 320, 56
sichado small cubihexadecadisoctachoron 2.370932 192, 480, 320, 56
giphado great prismatohexadecadisoctachoron 1.082392 192, 480, 336, 64
siphado small prismatohexadecadisoctachoron 2.613126 192, 480, 336, 64
paqrit prismatoquasirhombated tesseract 1.174172 192, 480, 368, 80
prit prismatorhombated tesseract, prismatotruncated hexadecachoron, runcitruncated hexadecachoron 2.370932 192, 480, 368, 80
proh prismatorhombated hexadecachoron, prismatotruncated tesseract, runcitruncated tesseract 2.613126 192, 480, 368, 80
quiproh quasiprismatorhombated hexadecachoron 1.082392 192, 480, 368, 80
kavahto skewverted hexadecatrisoctachoron 1.414214 192, 576, 336, 40
... o3β3x4x (?) ... 192, 576, 392, 80
gikviphado great skewverted prismatohexadecadisoctachoron 1.414214 192, 576, 416, 56
skiviphado small skewverted prismatohexadecadisoctachoron 1.414214 192, 576, 416, 56
kaviphdit skewverted prismatohexadecadistesseract 1.414214 192, 576, 432, 64
... oxwQ wxoo3xxxx4oxxo&#zx ... 192, 576, 498, 114
retah (alt.: amtah) rectified/ambified tesseractihexadecachoron 4.123106 192, 576, 504, 120
... x3β3o4x (?) ... 192, 672, 512, 104
... x3o3β4x (?) ... 192, 672, 576, 136
... x3β4o3o (?) ... 192, 672, 576, 168
... x3β3β4o (?) ... 192, 672, 592, 128
... β3x3o4β (?) ... 192, 672, 640, 176
pysnet s3s3s4x, pyritosnub tesseract, edge-alternated great diprismated tesseractihexadecachoron, edge-snub hexadecachoron ... 192, 672, 656, 176
... o3β3x4β (?) ... 192, 768, 656, 152
... x3β3o4β (?) ... 192, 768, 656, 152
residpith (alt.: amsidpith) rectified/ambified small-disprismated-tesseractihexadecachoron 2.797933 192, 768, 720, 144
... xofxxFfooFxfo3xxxoFxxxFoxxx3ofxFoofFxxfox&#xt 192, 804, 888, 276
... β3o3β4x (?) ... 192, 864, 800, 200
bamic (old: apic) biambotetracontoctachoron, antiprismatotetracontoctachoron, triangle based biambotetracontoctachoron 1.732051 192, 864, 864, 192
snet s3s3s4s, snub tesseract, non-uniform alternation of gidpith ... 192, 864, 944, 272
... o3β3β4β (?) ... 192, 960, 1008, 256
idsid pixhi icositetra-diminished small disprismatohexacosihecatonicosachoron 5.236068 1920, 5040, 4272, 1152
... FAxoFFxxox3foFFxofxxo xoxFxFoAxF3oxxofxFoFf&#zx 198, 702, 705, 201
... x3β3o3o (?) ... 20, 100, 80, 20
... Shephard's 5-generalised hexadecachoron, complex polychoron x2-3-o2-3-o2-4-o5 , β5 4 20, 150, 500, 625
sistadip square-pentagram duoprism 0.881132 20, 40, 29, 9
squipdip, K-4.42 square-pentagon duoprism 1.106168 20, 40, 29, 9
tip (alt: tettum) truncated pentachoron, tet-based tutsatope, tet-based tutism 1.264911 20, 40, 30, 10
squipuf, K-4.105 square pucofastegium, square - octagon-prismatic wedge, square magnabicupolaic ring, {4} || op, {8} || squacu, square-cap of srit 1.847759 20, 44, 35, 11
pecuf, K-4.154 pentagonal cupofastegium, decagon - pentagon-prismatic wedge, pentagonal orthobicupolaic ring, {10} || pip, {5} || pecu, 2/5-luna of stawros 5.236068 20, 45, 38, 13
auteddipe augmented-tridiminished-icosahedron prism ... 20, 46, 38, 12
paw, K-4.133, {10} || pap antipentawedge, decagon - pentagonn-antiprismatic wedge, pentagonal gyrobicupolaic ring, {10} || pap, {5} || gyrated pecu 3.077684 20, 50, 43, 13
staw pentagrammic gyrobicupolaic ring, star antiwedge, {10/2} || stap 0.870153 20, 50, 43, 13
esquidpyp elongated square dipyramid prism, J15 prism ... 20, 50, 44, 14
mibdip metabidiminished-icosahedron prism 1.074481 20, 50, 44, 14
pappip, K-4.39 pentagonal-antiprism prism 1.074481 20, 50, 44, 14
stappip pentagramic-antiprism prism 0.825168 20, 50, 44, 14
squacufbil square-cupofastegia biluna, rotunda of quawros, square atop squobcu 20, 52, 51, 19
duhd decahemidecachoron, copyropodichoron 1 20, 60, 50, 15
pedpedip pentadiminished pentagonal duoprism 1.203002 20, 60, 55, 15
cubaco, cube || co, K-4.35 cube atop cuboctahedron, cubical cupola 1.031784 20, 60, 56, 16
nipdip spinoprismatodispentachoron 1 20, 60, 60, 20
phud prismatohemidecachoron 1 20, 60, 60, 25
hocoaso hollow cuboctahedron atop stella octangula, tetrahedral cupolaic blend 1 20, 60, 64, 23
piphid prismatopentahemidecachoron, copyrofacetoretropodichoron 1 20, 60, 70, 20
gyspid (alt: tetacobcu) gyrated small prismatodecachoron, orthobicupola of runcinated pentachoron, tetaco orthobicupola 1 20, 60, 70, 30
spid small prismatodecachoron, runcinated pentachoron, expanded pentachoron, pyroperichoron, tetaco gyrobicupola, vertex figure of cypit, lattice A4 contact polytope (span of its roots) 1 20, 60, 70, 30
cytau tes cyclotetraaugmented tesseract, cyclotetradiminished icositetrachoron 1 20, 64, 68, 24
cubaike, cube || ike, K-4.21 cube atop icosahedron 1 20, 66, 74, 28
... great-rhombated-pentachoron dual 20, 80, 120, 60
... small-rhombated-pentachoron dual 20, 80, 90, 30
... triaugmented trigonal mibdi-laced wedge ... 20, 82, 112, 50
apid (alt.: bamid) antiprismatodecachoron, biambodecachoron, triangle based biambodecachoron 0.774597 20, 90, 100, 30
... expanded augmented axially-icosahedral ursachoron ofxo3xooo5xxxx&#xt 200, 540, 478, 138
... xFfxo3xoxoF3fxooo3oofFx&#zx 200, 780, 760, 180
... Fxxox5ofxfo xofox5oxofx&#zx 200, 850, 950, 300
idim sidpixhi icosa-diminished small disprismatohexacosihecatonicosachoron 5.236068 2000, 5400, 4800, 1400
... xoofxxFfooFxofo3xxFxoFxxxFoxFxx3ofoxFoofFxxfoox&#xt 204, 924, 1104, 384
... oFxxox5Fofxfo oxofox5ooxofx&#zx 205, 900, 1015, 320
... Waterman polychoron number 5 wrt. primitive tesseractic lattice C4 centered at a hole 3 208, 672, 592, 128
hidicau pretasto hexadeca-diminished icositetra-augmented pentagonorhombic-trisnub-trisoctachoron 208, 872, 1000, 336
... n-fold dissected dodecahedron polytwister, n-fold dissected doter, dodecaswirlic 12n-choron ... 20n, 80n, 72n, 12n
gissidpy great-stellated-dodecahedral pyramid, vertex cap of gaghi 0.591923 21, 50, 42, 13
epippy elongated pentagonal-prismatic pyramid ... 21, 50, 44, 15
tricuatut, tricu || tut, K-4.50 triangular-cupola atop truncated-tetrahedron 1.183216 21, 51, 43, 13
... octatut,tricuf-blend 21, 54, 47, 14
... thawro wedge ... 21, 60, 60, 21
... external blend of the sphenocorona-prism and a cube-pyramid, cubic-pyramid-augmented sphenocorona-prism 21, 62, 62, 21
tridico (alt.: cytid ico) (cyclo)tridiminished ico 1 21, 72, 78, 27
pta cubaike cube-augmented cubaike 1 21, 74, 86, 33
ptaika cube ike-augmented cubaike 21, 78, 104, 47
ditdidpy ditdid pyramid, vertex pyramid of dittady 1 21, 80, 84, 25
gidtidpy gidtid pyramid, vertex pyramid of gidtixhi 1 21, 80, 92, 33
sidtidpy sidtid pyramid, vertex pyramid of sidtixhi 1 21, 80, 92, 33
... xofo3ofox5xoxx&#xt 3.077684 210, 750, 736, 196
... oxqw wxwx3ooxx4qwox&#zx 216, 600, 488, 104
... rectified Witting polychoron, complex polychoron o3-3-x3-3-o3-3-o3 2160, 17280, 8640, 480
idsrahi icositetra-diminished small rhombated hecatonicosachoron 6.735034 2160, 5040, 3600, 720
epipdapy elongated pentagonal-prismatic bipyramid ... 22, 60, 59, 21
gyepippip gyroelongated-pentagonal-pyramid prism 1.074481 22, 61, 57, 18
tetacoaoct octahedron atop (pseudo) cuboctahedron atop tetrahedron 1 22, 78, 86, 30
pabdico parabidiminished icositetrachoron, hexa-augmented tesseract 1 22, 80, 84, 26
baucubaike bi-augmented cubaike 22, 86, 116, 52
icau pretasto icositetra-augmented pentagonorhombic-trisnub-trisoctachoron 224, 1032, 1168, 360
poccont partially octa-contracted tetracontoctachoron 224, 480, 304, 48
... oxxFxoAFxxFoxFx3xofxxFoooFxxfox3xFxoFxxFAoxFxxo&#xt 228, 792, 780, 216
hossdap hollow small stellated dodecahedral antiprism, pseudo sissid atop pseudo sissid 0.707107 24, 120, 144, 36
sissidagad, sissid || gad small stellated decahedron atop great dodecahedron, sissid antiprism, gad antiprism 1 24, 120, 144, 56
gikaike great icosahedron atop icosahedron 1 24, 120, 160, 52
shiddip, K-4.54 square - hexagon duoprism 1.224745 24, 48, 34, 10
tuttip, K-4.57 truncated-tetrahedron prism 1.274755 24, 48, 34, 10
tistodip triangle - octagram duoprism, octagram - stop wedge 0.791345 24, 48, 35, 11
todip, K-4.59 triangle - octagon duoprism, octagon - op wedge 1.428440 24, 48, 35, 11
squacupe, K-4.69 square-cupola prism, cube atop octagonal prism 1.485633 24, 52, 40, 12
chope cubohemioctahedron prism 1.118034 24, 60, 44, 12
ohope octahemioctahedron prism 1.118034 24, 60, 48, 14
bidsrip bidiminished small rhombated pentachoron 1.183216 24, 60, 51, 15
mibdirit metabidiminished rectified tesseract, wedge-diminished rectified tesseract, bistratic cuboctahedron based wedge 1.224745 24, 60, 51, 15
cope, K-4.43 cuboctahedron prism 1.118034 24, 60, 52, 16
happip, K-4.53 hexagonal-antiprism prism 1.197085 24, 60, 52, 16
tobcupe, K-4.44 triangular-orthobicupola prism 1.118034 24, 60, 52, 16
tuta (alt.: pabdirit, tutcup, tutaltut), tut || inv tut, K-4.55 truncated tetrahedral alterprism, truncated tetrahedral cupoliprism, runcic snub cubic hosochoron, truncated tetrahedron atop inverted truncated tetrahedron, truncated tetrahedron atop alternate truncated tetrahedron, tetrahedrally medial part of rectified tesseract, parabidiminished rectified tesseract 1.224745 24, 60, 52, 16
dihipap dyad-hexagonal prismantiprismoid, s2s2s6x, edge-alternated sitwadip ... 24, 60, 58, 22
oaf, K-4.58 octagonal antifastegium, octagon - oap wedge, {8} || gyro op 1.409438 24, 64, 59, 19
octu axially-octahedral ursachoron ofx3xoo4ooo&#xt, oct-based ursulate, vertex figure of s3s4o3o4o 1.144123 24, 66, 58, 16
coatut, co || tut, K-4.48 cuboctahedron atop truncated tetrahedron, cuboctahedral cap of small rhombated pentachoron 1.183216 24, 66, 58, 16
octatutbicu octatut bicupola ... 24, 66, 60, 18
tobcuatut, tobcu || tut, K-4.49 triangular-orthobicupola atop truncated-tetrahedron 1.183216 24, 66, 61, 19
gaddip great-dodecahedron prism 1.074481 24, 72, 54, 14
sissiddip small-stellated-dodecahedron prism 0.771681 24, 72, 54, 14
retisdip (alt.: amtisdip) rectified/ambified tisdip 1.527525 24, 72, 67, 19
gipe great-icosahedron prism 0.771681 24, 72, 70, 22
ipe, K-4.36 icosahedron prism, vertex figure of rectified hyperbolic pentachoric honeycomb 1.074481 24, 72, 70, 22
hocucup hollow cuboid cupoliprism, six tepe blend, "coord-planes squares star" atop "coord-planes squares star" 0.790569 24, 72, 72, 18
quawros quadratic ({8} || cube-)wedge rosette, bridge cyclotetraaugmented tesseract, ring-augmented tesseract, cube || {8} || cube, {4} || squobcu || {4} 24, 72, 84, 36
tetacoa cube tetrahedron atop cuboctahedron atop cube ... 24, 78, 84, 30
tibbit triangular-bipyramidal triacontadichoron, rectified-tesseract dual, surtegmated hexadecachoron 24, 88, 96, 32
ghahoh great hexadecahemihexadecachoron 1 24, 96, 112, 24
shahoh small hexadecahemihexadecachoron 1 24, 96, 112, 24
pikap (alt.: snittap) pyritohedral icosahedral antiprism, snub-tetrahedral antiprism, non-uniform alternation of tope ... 24, 96, 112, 40
dod honho disoctidishemioctintercepted hemioctachoron 1 24, 96, 128, 28
hohoh hexadecoctihemihexadecachoron 1 24, 96, 128, 32
doh honho disoctihemihexadekintercepted hemioctachoron 1 24, 96, 136, 28
hodho hexadecoctidishemioctachoron 1 24, 96, 136, 32
ohuhoh octihexadecahemihexadecachoron 1 24, 96, 144, 32
hoh honho hexadecoctihemihexadekintercepted hemioctachoron 1 24, 96, 152, 36
ihi icositetrahemiicositetrachoron 1 24, 96, 168, 36
odho octidishemioctachoron 1 24, 96, 72, 16
oh octahemihexadecachoron 1 24, 96, 80, 16
ratho rectified tesseractihemioctachoron 1 24, 96, 88, 20
huhoh hexadecahemihexadecachoron 1 24, 96, 96, 24
ico (alt.: jot) icositetrachoron, 24-cell, xylochoron, octaplex, rectified hexadecachoron, birectified tesseract, hyperdiamond, joined tesseract, trisoctachoron, vertex figure of hext, Voronoi cell of lattice F4, Voronoi cell of lattice D4*, surtegmated tesseract, Gosset polytope 01,1,1, lattice B4 contact polytope (span of its small roots), lattice D4 contact polytope (span of its roots), lattice F4 contact polytope (span of its small roots) 1 24, 96, 96, 24
... xFfoo3xoxxF3fxoxo3ooffx&#zx 240, 1080, 1320, 480
... Witting polychoron, complex polychoron x3-3-o3-3-o3-3-o3 1 240, 2160, 2160, 240
idtiddip icosidodecatruncated-icosidodecahedron prism, icositruncated-dodecadodecahedron prism 2.061553 240, 480, 268, 46
quitdiddip quasitruncated-dodecadodecahedron prism 1.732051 240, 480, 288, 56
pextico partially (mono-)expanded tico 240, 480, 296, 56
gaquatiddip great-quasitruncated-icosidodecahedron prism 1.136572 240, 480, 304, 64
griddip, K-4.150 great-rhombicosidodecahedron prism 3.835128 240, 480, 304, 64
srida gridtum bistratic srid-cap of prahi, (srid,grid)-based tutsachoron, (srid,grid)-based tutism 8.278950 240, 540, 376, 76
arse biscrahi bistratic icosidodecahedron-first subsegment of small rhombihexacosachoron, around-symmetrically expanded biscrahi 6.073594 240, 570, 414, 84
tigikaike truncated gikaike 2.645751 240, 600, 424, 76
owau prit   (alt.: pox spic, alt.: phic prico) octa-augmented prismatorhombated tesseract, partially octa-expanded small prismated (dis)icositetrachoron, partially hexadeca-contracted prismatorhombated icositetrachoron 240, 768, 768, 240
arsdod depabdirox around-symmetrical dodecadiminishing of deep parabidiminished rox 3.077684 240, 780, 696, 156
... icositetrachoron-derived Gévay polychoron, rectified o3m4o3o ... 240, 864, 768, 144
gefidtethi great exofissary ditetrahedronary tetrakishecatonicosachoron 0.874032 2400, 10800, 6720, 480
sefidtethi small exofissary ditetrahedronary tetrakishecatonicosachoron 2.288246 2400, 10800, 6720, 480
sefradit thix small exofissary retroditetrahedronary triakishecatonicosihexacosachoron 2.288246 2400, 10800, 6720, 960
gefradit thix great exofissary retroditetrahedronary triakishecatonicosihexacosachoron 0.874032 2400, 10800, 6720, 960
gefirdit xethi great exofissary retroditetrahedronary hexacositrishecatonicosachoron 1.414214 2400, 10800, 7680, 960
gefridit xethi great exofissary retroinverted ditetrahedronary hexacositrishecatonicosachoron 1.414214 2400, 10800, 7680, 960
getit thix great tritrigonal trishecatonicosihexacosachoron 1.136572 2400, 10800, 7680, 960
getit xethi great tritrigonal hexacositrishecatonicosachoron 1.136572 2400, 10800, 7680, 960
git thixady great tritrigonal hecatonicosihexacosidishecatonicosachoron 1.136572 2400, 10800, 7680, 960
sit thixady small tritrigonal hecatonicosihexacosidishecatonicosachoron 3.835128 2400, 10800, 7680, 960
stut thix small tritrigonal trishecatonicosihexacosachoron 3.835128 2400, 10800, 7680, 960
stut xethi small tritrigonal hexacositrishecatonicosachoron 3.835128 2400, 10800, 7680, 960
geedatepthi great exoditetrahedrary prismatotrishecatonicosachoron 1.414214 2400, 10800, 7920, 1080
seedatepthi small exoditetrahedrary prismatotrishecatonicosachoron 1.414214 2400, 10800, 7920, 1080
getit dixady great tritrigonal dihexacosidihecatonicosachoron 1.136572 2400, 10800, 8640, 1440
stut dixady small tritrigonal dihexacosidihecatonicosachoron 3.835128 2400, 10800, 8640, 1440
gaedit pathi grand exoditetrahedronary prismatotriakishecatonicosachoron 0.874032 2400, 10800, 8880, 1080
sedit pathi small exoditetrahedronary prismatotriakishecatonicosachoron 2.288246 2400, 10800, 8880, 1080
getit pixady great tritrigonal prismatohexacosidihecatonicosachoron 1.136572 2400, 10800, 8880, 1560
stut pixady small tritrigonal prismatohexacosidihecatonicosachoron 3.835128 2400, 10800, 8880, 1560
gadtef pixady great ditetrahedronary exofissary prismatohexacosadishecatonicosachoron 0.874032 2400, 10800, 9840, 2040
getit phiddix great tritrigonal prismatohecatonicosidishexacosachoron 1.136572 2400, 10800, 9840, 2040
sadtef pixady small ditetrahedronary exofissary prismatohexacosadishecatonicosachoron 2.288246 2400, 10800, 9840, 2040
stut phiddix small tritrigonal prismatohecatonicosidishexacosachoron 3.835128 2400, 10800, 9840, 2040
... o3o3β5x (?) ... 2400, 12000, 9120, 1920
rapsady retroantiprismatosnub dishecatonicosachoron 1.618034 2400, 21600, 22080, 1680
... β3o3o5β (?) ... 2400, 21600, 23040, 5040
quit sishi quasitruncated small stellated hecatonicosachoron 2 2400, 4800, 2160, 240
tigaghi truncated great grand hecatonicosachoron 2 2400, 4800, 2160, 240
quit gogishi quasitruncated great grand stellated hecatonicosachoron 0.677481 2400, 4800, 3120, 720
thi truncated hecatonicosachoron 8.218334 2400, 4800, 3120, 720
idimsrahi icosa-diminished small rhombated hecatonicosachoron 6.735034 2400, 6000, 4520, 920
tahi triakishecatonicosachoron 2 2400, 7200, 4080, 360
gidthixhi great ditrigonary hecatonicosihexacosihecatonicosachoron 3.139124 2400, 7200, 4560, 840
gixhihy great hexacosihecatonicosihecatonicosachoron 0.763932 2400, 7200, 4560, 840
sidthixhi small ditrigonary hecatonicosihexacosihecatonicosachoron 1.773668 2400, 7200, 4560, 840
sixhihy small hexacosihecatonicosihecatonicosachoron 5.236068 2400, 7200, 4560, 840
gohihix great hecatonicosihecatonicosihexacosachoron 1.464888 2400, 7200, 5040, 540
shihix small hecatonicosihecatonicosihexacosachoron 2.975584 2400, 7200, 5040, 840
gixhidy great hexacosihecatonicosadishecatonicosachoron 1.464888 2400, 7200, 5280, 960
sixhidy small hexacosihecatonicosadishecatonicosachoron 2.975584 2400, 7200, 5280, 960
gadixady great dishexacosadishecatonicosachoron 3.139124 2400, 7200, 6240, 1440
sadixady small dishexacosadishecatonicosachoron 1.773668 2400, 7200, 6240, 1440
quadippady quasidisprismatodishecatonicosachoron, Unholey Terror 1.414214 2400, 7200, 6480, 1680
siddapady small disprismatodishecatonicosachoron 2 2400, 7200, 6480, 1680
six fipady small hexacosafaceted prismatodishecatonicosachoron 5.236068 2400, 7200, 7440, 1440
quad pagaxhi quasidisprismatogrand hexacosihecatonicosachoron 0.874032 2400, 7200, 7440, 2640
quidpixhi quasidisprismatohexacosihecatonicosachoron 0.763932 2400, 7200, 7440, 2640
sidpixhi small disprismatohexacosihecatonicosachoron, runcinated hecatonicosachoron, runcinated hexacosachoron 5.236068 2400, 7200, 7440, 2640
... x3o3o5v, variation of small disprismatohexacosihecatonicosachoron 3.835128 2400, 7200, 7440, 2640
gabbathi great blendic trishecatonicosachoron 2 2400, 8400, 4800, 360
sabbathi small blendic trishecatonicosachoron 2 2400, 8400, 4800, 360
tidtidohi truncated ditrigonary dishecatonicosachoron 2.645751 2400, 8400, 5280, 360
bithi blendic trishecatonicosachoron 2 2400, 8400, 5520, 360
badohi blendic dishecatonicosachoron 2 2400, 8400, 6240, 240
tiggidtixhi truncated great ditrigonary hexacosihecatonicosachoron 2.645751 2400, 8400, 6240, 840
tissidtixhi truncated small ditrigonary hexacosihecatonicosachoron 2.645751 2400, 8400, 6240, 840
ganbathi great spinoblendic trishecatonicosachoron 2 2400, 8400, 6480, 960
sanbathi small spinoblendic trishecatonicosachoron 2 2400, 8400, 6480, 960
ganbippady great spinoblendic prismatodishecatonicosachoron 2 2400, 8400, 6960, 960
sanbippady small spinoblendic prismatodishecatonicosachoron 2 2400, 8400, 6960, 960
gabbadipady great blendic disprismatodishecatonicosachoron 2 2400, 8400, 7200, 1680
sabbadipady small blendic disprismatodishecatonicosachoron 2 2400, 8400, 7200, 1680
gabippady (old: gabbippady) great blendic prismatodishecatonicosachoron 2 2400, 8400, 7200, 960
sabippady (old: sabbippady) small blendic prismatodishecatonicosachoron 2 2400, 8400, 7200, 960
... xxxFooAFxxAxxFx3oxFxxAxxxFooFxx3xfoxFoofFxxFoox&#xt 246, 768, 696, 174
... xoxFoFxox3oxoooooxo5ooxofoxoo&#xt 248, 1032, 1020, 236
... fooo3xxoF3xfxo *b3oxFo&#zx 248, 816, 784, 216
pedip pentagon-pentagon duoprism 1.203002 25, 50, 35, 10
stardip pentagram-pentagram duoprism 0.743496 25, 50, 35, 10
starpedip (old: stipdip, starpendip) pentagram-pentagon duoprism, stellar (pentagonal) pentagonal diprism 1 25, 50, 35, 10
pepuf, K-4.165 pentagonal pucofastegium, pentagon - decagon-prismatic wedge, pentagonal magnabicupolaic ring, {5} || dip, {10} || pecu, {5}-first cap of srahi 6.735034 25, 55, 43, 13
..., K-4.146 pentagon - pentagonal-rotunda wedge, {5} || pero 3.077684 25, 65, 58, 18
... augmented axially-octahedral ursachoron ofxo3xooo4oooo&#xt ... 25, 72, 70, 23
eikepy elongated icosahedral pyramid 25, 84, 100, 41
... omni-pecu-augmented (10,20)-duoprism 250, 650, 520, 120
... omni-pecu-gyroaugmented (10,20)-duoprism 250, 650, 520, 120
... FxFox5xFoFx xofox5oxofx&#zx 250, 750, 630, 130
... oFxFox5AxFoFx2oxofox5ooxofx&#zx 255, 800, 695, 150
... Shephard's 4-generalised tesseract, complex polychoron x4-4-o2-3-o2-3-o2 , γ4 4 256, 256, 96, 16
autpen augmented truncated pentachoron ... 26, 64, 56, 18
peppia pero, K-4.139 pentagonal-pyramid atop pentagonal-rotunda 3.077684 26, 75, 68, 19
eikedpy elongated icosahedral bipyramid 26, 96, 130, 60
... oFFxx3xxoof3fooxx3xxFFo&#zx 260, 900, 840, 200
... hexastratic ike-first cap of rectified hexacosachoron 3.077684 264, 1140, 1124, 248
... oxqwQ wxwxx3ooxxx4qwoxo&#zx 264, 768, 648, 144
etripuf elongated trigonal pucofastegium ... 27, 63, 53, 17
biscsrip bistratic trip-cap of srip, {3}-diminished small rhombated pentachoron 1.183216 27, 75, 66, 18
didamibdrox diminished deep metabidiminished rectified hexacosachoron 3.077684 270, 1020, 993, 243
tiscsrix tristratic icosidodecahedron-first cap of small rhombihexacosachoron 6.073594 270, 690, 516, 96
... tetra-augmented axially-octahedral ursachoron xoBo3ofox3xooo&#xt ... 28, 102, 118, 44
tetripau tuttip trip-wise tetra-augmented tuttip 28, 72, 70, 26
etetaco elongated tetaco ... 28, 78, 80, 30
coaop, co || op, K-4.63 cuboctahedron atop octagonal-prism 1.447009 28, 80, 72, 20
arse aurap around-symmetrically expanded augmented rectified pentachoron 28, 84, 80, 24
tetaco altut tetrahedron atop cuboctahedron atop inverted truncated tetrahedron ... 28, 84, 80, 24
... aoc3ddd3cao *b3oca&#ze, general variant of prismatorhombisnub icositetrachoron sqrt[(a2+ac+c2+2ad+2cd+2d2)/2] 288, 1008, 960, 240
prarsi prismatorhombiretrosnub icositetrachoron 1.328131 288, 1008, 960, 240
prissi prismatorhombisnub icositetrachoron, prismato-semistruncated icositetrachoron, runcic snub icositetrachoron 2.497212 288, 1008, 960, 240
... x3o4β3o (?) ... 288, 1152, 1056, 264
afdec antifrustic distetracontoctachoron 1.414214 288, 1152, 816, 96
girfaddic great retrofrustic distetracontoctachoron 1.414214 288, 1152, 816, 96
... o3β4x3o (?) ... 288, 1152, 960, 168
rafficdi retrofrustic tetracontoctadisicositetrachoron 1.414214 288, 1152, 960, 96
bipec biprismatotetracontoctachoron sqrt[a2+ab sqrt(2)+b2] 288, 1296, 1536, 528
... o3β4β3o (?) ... 288, 1728, 1632, 336
... β3o4β3o (?) ... 288, 1728, 1728, 432
cont tetracontoctachoron, octagonny, bitruncated icositetrachoron 3.414214 288, 576, 336, 48
gic great tetracontoctachoron, octagrammy 0.585786 288, 576, 336, 48
pabextico partially bi-expanded tico, partially bi-contracted gidpith 288, 576, 352, 64
pahtex prit partially demitesseractic-expanded prit, partially demitesseractic-contracted gidpith 288, 624, 416, 80
rawvaty retrosphenoverted triakisicositetrachoron 2.613126 288, 864, 576, 72
wavaty sphenoverted triakisicositetrachoron 1.082392 288, 864, 576, 72
qrico quasirhombated icositetrachoron 1.082392 288, 864, 720, 144
srico small rhombated icositetrachoron, cantellated icositetrachoron 2.613126 288, 864, 720, 144
rerico x3o4q3o, rectified rectified-icositetrachoron, variation of small rhombated icositetrachoron 3.316625 288, 864, 720, 144
idsrix icositetra-diminished small rhombated hexacosachoron 6.073594 2880, 7920, 6192, 1152
... external blend of the hebesphenomegacorona-prism and a cube-pyramid, cubic-pyramid-augmented hebesphenomegacorona-prism 29, 88, 87, 28
teddi adoe, teddi || doe, K-4.83 tridiminished-icosahedron atop dodecahedron, triminished segment of vertex-first hexacosachoron 1.618034 29, 90, 95, 34
n-pipy n-prism pyramid, general vertex pyramid of o-3-x-3-o-n-o 1/sqrt[3 - 1/sin2(π/n)] 2n+1, 5n, 4n+2, n+3
n-appy n-antiprismatical pyramid sqrt[(2-2 cos(π/n))/(5-6 cos(π/n))] 2n+1, 6n, 6n+2, 2n+3
n/d-pyp n/d-pyramidal prism, line || n/d-prism sqrt[1/4+1/(4-1/sin2[π d/n])] 2n+2, 5n+1, 4n+2, n+3
n-pidpy n-prismatic bipyramid 2n+2, 7n, 7n+2, 2n+4
n-apt (line-)n-antiprismatic tegum, n-antiprismatic bipyramid, n-pyramidal antiprism 2n+2, 8n, 10n+2, 4n+4
n/d,2n/d-dip n/d-gram - 2n/d-gram duoprism sqrt[1/(4 sin2(π d/n))+1/(4 sin2(π d/2n))] 2n2, 4n2, 2n2+3n, 3n
2n,m-dip 2n-gonal - m-gonal duoprism sqrt[1/(4 sin2(π/2n))+1/(4 sin2(π/m))] 2nm, 4nm, 2nm+2n+m, 2n+m
n-m-det (n,m)-ditetragoltriate ... 2nm, 5nm, 4nm+n+m, nm+n+m
n,m-dap n-gon - m-gon duoantiprism, hemiated 2n-gon - 2m-gon duoprism sqrt[A2/(4 sin2(π/2n))+B2/(4 sin2(π/2m))] 2nm, 8nm, 8nm+2n+2m, 2nm+2n+2m
mibdiadoe, mibdi || doe, K-4.82 metabidiminished icosahedron atop dodecahedron, metabidiminished segment of vertex-first hexacosachoron 1.618034 30, 100, 114, 44
papadoe, pap || doe, K-4.81 pentagonal-antiprism atop dodecahedron, parabidiminished segment of vertex-first hexacosachoron, pentagonal-antiprism-first cap of grand antiprism 1.618034 30, 100, 114, 44
haucope hexa-augmented cope 30, 108, 124, 46
... o3β3x3o (?) ... 30, 120, 90, 20
... o3β3β3o (?) ... 30, 180, 180, 40
... β3o3β3o (?) ... 30, 210, 200, 50
deca decachoron, bitruncated pentachoron, equatorial cross-section of (vertex first) q-pent 1.414214 30, 60, 40, 10
phiddip pentagon hexagon duoprism 1.312862 30, 60, 41, 11
tradedip, K-4.94 triangle - decagon duoprism, decagon - dip wedge 1.717954 30, 60, 43, 13
pecupe pentagonal-cupola prism, pentagonal-prism atop decagonal-prism 2.288246 30, 65, 49, 14
stacupe pentagrammic-cupola prism, stip atop 2pip 0.874032 30, 65, 49, 14
duspid small-prismated-decachoron dual, crystalic icosachoron 30, 70, 60, 20
octatoe, oct || toe (degenerate) octahedron atop truncated octahedron ∞   i.e. flat in euclidean space 30, 72, 58, 16
eoctatut elongated octatut 30, 72, 60, 18
octasirco, oct || sirco, K-4.107 octahedron atop small rhombicuboctahedron, octahedral cap of small prismatotetracontoctachoron 1.847759 30, 84, 82, 28
... pocuro wedge ... 30, 85, 83, 28
pippindip prismatopentintercepted dispentachoron 1.183216 30, 90, 115, 25
pinnipdip pentaintercepted prismatodispentachoron, prismatopentaintercepted dispentachoron 1.183216 30, 90, 115, 30
garpop grand rhombated prismatopentachoron 1.183216 30, 90, 65, 15
rawvtip retrosphenoverted triakispentachoron 1.183216 30, 90, 70, 15
sirdop small rhombidispentachoron 1.183216 30, 90, 70, 20
... pentachoron-derived Gévay polychoron, rectified o3m3o3o 1.095445 30, 90, 80, 20
srip small rhombated pentachoron, cantellated pentachoron 1.183216 30, 90, 80, 20
pirpop pseudorhombated prismatopentachoron 1.183216 30, 90, 85, 25
... diminished 1/10-luna of hexacosachoron 1.618034 30, 90, 93, 33
eoctaco elongated octaco 30, 96, 90, 24
bicypdrox (bistratic) bi-cyclopentadiminished rectified hexacosachoron 3.077684 300, 1000, 985, 285
... dodeca-diminished equatorial tetrastratic segment of rox 3.077684 300, 1140, 1128, 288
twagy griddip twelve-gyro-augmented great-rhombated-icosidodecahedral prism 300, 780, 676, 196
twau griddip twelve-(ortho-)augmented great-rhombated-icosidodecahedral prism 300, 780, 676, 196
... triaconta-sphenated id-first tristratic sub-cap of rahi ... 300, 840, 706, 166
... Fxo oxf3xox5xfo&zxt 300, 900, 776, 176
... xAFxx3ooxxF3Fxoxo3ooffx&#zx 300, 960, 910, 250
sidsrahi swirl-diminished small rhombated hecatonicosachoron, swirl-diminished cantellated hecatonicosachoron 6.735034 3000, 7800, 6240, 1440
idimsrix icosa-diminished small rhombated hexacosachoron 6.073594 3000, 8400, 6600, 1200
... 1/10-luna of hexacosachoron 1.618034 31, 100, 113, 44
gyepipa pero, K-4.140 gyroelongated pentagonal pyramid atop pentagonal rotunda 3.077684 31, 100, 93, 24
... reduced( ofx3/2oxx4ooo&xt by oct+6{4} ) 0.899454 31, 84, 69, 20
didpy, pt || did (degenerate) did pyramid ∞   i.e. flat in euclidean space 31, 90, 84, 25
... equatorial tetrastratic segment of rectified hexacosachoron 3.077684 312, 1260, 1248, 300
damibdrox deep metabidiminished rectified hexacosachoron 3.077684 312, 1270, 1245, 287
icau prissi icositetra-augmented prismatorhombisnub icositetrachoron 312, 1296, 1680, 696
... hecatonicosachoron-derived Gévay polychoron, rectified o5m3o3o ... 3120, 10800, 9600, 1920
coaescu, co || escu, K-4.62 cuboctahedron atop elongated square cupola 1.447009 32, 100, 92, 24
sissidadoe (degenerate) sissid atop doe ∞   i.e. flat in euclidean space 32, 120, 114, 26
gadadoe great dodecahedron atop dodecahedron 1.618034 32, 120, 142, 44
... taller great stellated dodecahedron atop small stellated dodecahedron 0.662791 32, 120, 142, 44
gissidasissid shallower great stellated dodecahedron atop small stellated dodecahedron 0.618034 32, 120, 142, 44
ikadoe (alt.: ikap), ike || doe, K-4.78 icosahedron atop dodecahedron, icosahedral antiprism, dodecahedral antiprism, segment of vertex-first hexacosachoron 1.618034 32, 120, 152, 64
gissidragike great stellated dodecahedron retroprism, great icosahedron retroprism, narrower great stellated dodecahedron atop great icosahedron 0.618034 32, 120, 152, 64
gissidagike great stellated dodecahedron antiprism, great icosahedron antiprism, taller great stellated dodecahedron atop great icosahedron 0.662791 32, 120, 152, 64
... o3o3β4o (?) ... 32, 240, 224, 56
sistodip square - octagram duoprism 0.890446 32, 64, 44, 12
sodip, K-4.70 square - octagon duoprism 1.485633 32, 64, 44, 12
titepe truncated tetrahedral prism sqrt[(5y2+12y+12)/8] 32, 64, 46, 14
cubatic, cube || tic (degenerate) cube atop truncated cube ∞   i.e. flat in euclidean space 32, 72, 56, 16
autodip augmented 3-8-duoprism ... 32, 76, 65, 21
oappip, K-4.65 octagonal-antiprism prism 1.463603 32, 80, 68, 20
squobcupe square orthobicupola prism, J28 prism ... 32, 80, 68, 20
... s4x2s4x (?) ... 32, 80, 72, 24
cubasirco, cube || sirco, K-4.71 cube atop small rhombicuboctahedron, cubical cap of small disprismatotesseractihexadecachoron 1.485633 32, 84, 80, 28
hinnit hexadekintercepted tesseract 1.224745 32, 96, 120, 24
gotto great trisoctachoron, great triakisoctachoron 1.224745 32, 96, 88, 24
rit rectified tesseract, rectified octachoron, birectified hexadecachoron, runcic tesseract 1.224745 32, 96, 88, 24
sto small trisoctachoron, small triakisoctachoron 1.224745 32, 96, 96, 24
firt facetorectified tesseract 1.224745 32, 96, 96, 32
pox tico partially octa-expanded truncated icositetrachoron 320, 640, 400, 80
... pentagonal double antitegmoid, pentaantitegmatoswirlic hectochoron, dual of great antiprism ... 320, 720, 500, 100
biscex bistratic vertex-first cap of hexacosachoron 1.618034 33, 132, 182, 83
biscpoxic bistratic vertex-first cap of poxic 33, 92, 86, 27
... oFFxx3xxoxf3Fxxox3oofFx&#zx 330, 1170, 1150, 310
... Fxox3xoxf3oFxx *b3oxfo&#zx 336, 1200, 1176, 312
... xoxxFxxox3oxoxoxoxo5ooxoooxoo&#xt 336, 1380, 1414, 370
pac gidpith partially (mono-)contracted gidpith 336, 672, 408, 72
tetaco ausrip tetaco-augmented srip 34, 108, 102, 28
... heptadiminished 2/10-luna of ex bidiminished inner pentadiminished 2/10-luna of ex 35, 100, 89, 24
stawros pentagrammic ({10} || pip-)wedge rosette, bridge cyclopentaaugmented starpedip, ring-augmented starpedip 35, 110, 130, 55
tehipau tuttip hip-wise tetra-augmented tuttip 36, 108, 110, 38
... triangular duoexpandoprism sqrt[(a2+3b2)/3] 36, 108, 120, 48
triddep triangular duoexpandoprism, expanded triddip, tegum sum of 2 alternated thiddips 1.154701 36, 108, 120, 48
coasirco, co || sirco, K-4.61 cuboctahedron atop small rhombicuboctahedron 1.447009 36, 120, 112, 28
pexic partially (mono-)expanded icositetrachoron ... 36, 132, 128, 32
... diminished thawro-wedged 1/6-luna of hexacosachoron, {6},ike-wedge, ike,thawro,thawro-multiwedge ... 36, 138, 171, 69
hiddip hexagonal-hexagonal duoprism, Voronoi cell of lattice A2×A2 1.414214 36, 72, 48, 12
titwadip triangle - dodecagon duoprism, dodecagon - twip wedge 2.016280 36, 72, 51, 15
tatriddip truncated triangular duoprism sqrt[(2y2+5y+5)/3] 36, 72, 51, 15
tutatoe, tut || toe, K-4.76 truncated tetrahedron atop truncated octahedron, truncated-tetrahedral cap of prismatorhombated pentachoron, tetrahedral canticupola 1.612452 36, 78, 58, 16
octum octahedron-first rotunda of truncated hexadecachoron, oct-based tutsatope, oct-based tutism 1.581139 36, 78, 58, 16
coatic, K-4.129 cuboctahedron atop truncated cube, cuboctahedral cap of small rhombated icositetrachoron 2.613126 36, 84, 64, 16
coatoe, co || toe, K-4.95 cuboctahedron atop truncated octahedron, cuboctahedral cap of rectified icosatetrachoron 1.732051 36, 84, 64, 16
esquipuf elongated square pucofastegium, square atop octagon-prism atop octagon-prism 36, 84, 69, 21
coatutu expanded axially-tetrahedral ursachoron, (co,tut)-based ursulate 1.328131 36, 90, 74, 20
cyte cubau sodip cyclotetra cubaugmented sodip ... 36, 96, 84, 24
... xxfoF3oxxFx3xFxxo3Fofxx&#zx 360, 1080, 900, 180
... xoofoox3ofxoxfo5xoxxxox&#xt 360, 1140, 1046, 266
... Ffxo xofo3ofox5xoxx&#zx 360, 1470, 1608, 498
... icosaswirlic hexacosachoron, thirtyfold dissected icosahedral polytwister, thirtyfold dissected ikter ... 360, 2160, 2400, 600
pinpixhi prismatointercepted prismatohexacontahecatonicosachoron 6.735034 3600, 10800, 12360, 2640
gwavathi great sphenoverted triakishecatonicosachoron 1.027486 3600, 10800, 5520, 360
srawvathi small retrosphenoverted triakishecatonicosachoron 4.352502 3600, 10800, 5520, 360
grawv ditathi great retrosphenoverted ditrigonary triakishecatonicosachoron 2.093315 3600, 10800, 6000, 360
grawv hidy great retrosphenoverted hecatonicosadishecatonicosachoron 1.589926 3600, 10800, 6000, 360
rawvathi retrosphenoverted triakishecatonicosachoron 2.689994 3600, 10800, 6000, 360
srawv hidy small retrosphenoverted hecatonicosadishecatonicosachoron 3.387054 3600, 10800, 6000, 360
swav ditathi small sphenoverted ditrigonary triakishecatonicosachoron 2.572554 3600, 10800, 6000, 360
wavathi sphenoverted triakishecatonicosachoron 1.662508 3600, 10800, 6000, 360
gwav ditathi great sphenoverted ditrigonary triakishecatonicosachoron 2.036148 3600, 10800, 6480, 360
grawvathi great retrosphenoverted triakishecatonicosachoron 2.572554 3600, 10800, 6960, 360
swavathi small sphenoverted triakishecatonicosachoron 2.093315 3600, 10800, 6960, 360
grawv hixhi great retrosphenoverted hecatonicosihexacosihecatonicosachoron 1.513868 3600, 10800, 6960, 840
gwavixady great sphenoverted hexacosadishecatonicosachoron 0.799575 3600, 10800, 6960, 840
mrawv hixhi medial retrosphenoverted hecatonicosihexacosihecatonicosachoron 3.963358 3600, 10800, 6960, 840
rawvid tixady retrosphenoverted ditrigonary hexacosadishecatonicosachoron 5.330704 3600, 10800, 6960, 840
srawvixady small retrosphenoverted hexacosadishecatonicosachoron 6.735034 3600, 10800, 6960, 840
wavdatixady sphenoverted ditrigonary hexacosadishecatonicosachoron 1.258409 3600, 10800, 6960, 840
sirgashi small rhombated grand stellated hecatonicosachoron 1.589926 3600, 10800, 7200, 960
sirghi small rhombated great hecatonicosachoron 3.387054 3600, 10800, 7200, 960
garawv hixhi great retrosphenoverted hecatonicosihexacosihecatonicosachoron 1.054256 3600, 10800, 7440, 840
grawvixady great retrosphenoverted hexacosadishecatonicosachoron 2.036148 3600, 10800, 7440, 840
srawv hixhi small retrosphenoverted hecatonicosihexacosihecatonicosachoron 6.073594 3600, 10800, 7440, 840
swavixady small sphenoverted hexacosadishecatonicosachoron 3.294556 3600, 10800, 7440, 840
srawv ditathi small retrosphenoverted ditrigonary triakishecatonicosachoron 3.294556 3600, 10800, 7680, 360
qrigfix (old: querfix) quasirhombated great faceted hexacosachoron 1.027486 3600, 10800, 7680, 960
sirfix small rhombated faceted hexacosachoron 4.352502 3600, 10800, 7680, 960
rawvhiddix retrosphenoverted hecatonicosadishexacosachoron 1.258409 3600, 10800, 7920, 1320
wavhiddix sphenoverted hecatonicosadishexacosachoron 5.330704 3600, 10800, 7920, 1320
sirgaghi small rhombated great grand hecatonicosachoron 1.513868 3600, 10800, 8160, 1440
sirsashi small rhombated small stellated hecatonicosachoron 3.963358 3600, 10800, 8160, 1440
qragishi (old: qraghi) quasirhombated grand stellated hecatonicosachoron 1.662508 3600, 10800, 8160, 960
sraghi small rhombated grand hecatonicosachoron 2.689994 3600, 10800, 8160, 960
... hexacosachoron-derived Gévay polychoron, rectified o3m3o5o 6.412847 3600, 10800, 8640, 1440
sirgax small rhombated grand hexacosachoron 1.054256 3600, 10800, 8640, 1440
srix small rhombated hexacosachoron, cantellated hexacosachoron 6.073594 3600, 10800, 8640, 1440
rerahi o3x3o5f, rectified rectified-hecatonicosachoron, variation of srahi 9.013835 3600, 10800, 9120, 1920
qrigogishi (old: qrahi) quasirhombated great grand stellated hecatonicosachoron 0.799575 3600, 10800, 9120, 1920
srahi small rhombated hecatonicosachoron, cantellated hecatonicosachoron 6.735034 3600, 10800, 9120, 1920
gipriphi great pseudorhombated prismatohecatonicosachoron 0.799575 3600, 10800, 9240, 2040
spriphi small pseudorhombated prismatohecatonicosachoron 6.735034 3600, 10800, 9240, 2040
sgysrahi swirl-gyrated small rhombated hecatonicosachoron, swirl-gyrated cantellated hecatonicosachoron 6.735034 3600, 10800, 9720, 2520
girfixthi great retrofrustic hexacositrishecatonicosachoron 2.236068 3600, 14400, 10080, 960
... o3x3β5o (?) ... 3600, 14400, 10320, 1920
gefdit dixdy great exofissary ditrigonal dihexacosadihecatonicosachoron 1.732051 3600, 14400, 11040, 1440
sefdit dixdy small exofissary ditrigonal dihexacosadihecatonicosachoron 1.732051 3600, 14400, 11040, 1440
sirfixthi small retrofrustic hexacositrishecatonicosachoron 2.236068 3600, 14400, 11280, 960
affixthi antifrustic hexacositrishecatonicosachoron 2.236068 3600, 14400, 9120, 960
raffixthi retrofrustic hexacositrishecatonicosachoron 2.236068 3600, 14400, 9120, 960
... o3β3x5o (?) ... 3600, 14400, 9360, 1440
... x3o3β5o (?) ... 3600, 18000, 14640, 2640
prishi prismatorhombisnub hecatonicosachoron 3.625437 3600, 21600, 20640, 3960
... o3β3β5o (?) ... 3600, 21600, 21120, 4320
... β3o3β5o (?) ... 3600, 25200, 23040, 5040
... o3β3o5β (?) ... 3600, 25200, 23520, 5520
gadsadox great disnub dihexacosachoron 0.726543 3600, 28800, 31200, 6000
sadsadox small disnub dihexacosachoron 3.077684 3600, 28800, 31200, 6000
ghihi great hecatonicosihecatonicosachoron 0.854102 3600, 7200, 3360, 240
shihi small hecatonicosihecatonicosachoron 5.854102 3600, 7200, 3360, 240
dahi dishecatonicosachoron 3 3600, 7200, 3840, 240
gixhi great hexacosihecatonicosachoron 1.244649 3600, 7200, 4320, 720
xhi hexacosihecatonicosachoron, bitruncated hecatonicosachoron, bitruncated hexacosachoron 7.579634 3600, 7200, 4320, 720
... outer pentadiminished 2/10-luna of hexacosachoron 1.618034 37, 116, 113, 34
... inner pentadiminished 2/10-luna of ex 1/5-luna of xfooo5xofxo oxofx5ooxox&#zx 37, 121, 133, 49
... thawro-wedged 1/6-luna of hexacosachoron ... 37, 150, 201, 88
octasircoacube oct atop sirco atop cube 38, 120, 136, 54
baudeca biaugmented decachoron 38, 96, 84, 26
... rico-derived polychoron incorporating does 2.802517 384, 1008, 768, 144
poc prico   (alt.: phex spic) partially octa-contracted prismatorhombated icositetrachoron, partially hexadeca-expanded small prismated (dis)icositetrachoron ... 384, 1056, 912, 240
... β3x3β4x (?) ... 384, 1152, 896, 200
... x3β3x4β (?) ... 384, 1152, 896, 200
... x3β3β4x (?) ... 384, 1152, 960, 208
... β3x3β4β (?) ... 384, 1344, 1184, 296
... x3β3β4β (?) ... 384, 1344, 1248, 304
... β3β3x4β (?) ... 384, 1344, 1248, 328
bitec (old: sidwapic) bitruncatotetracontoctachoron, snub disphenic antiprismatotetracontoctachoron, general variant of hull of tastic, tegum sum of 2 inverted (x,y)-ticoes sqrt(3y2+3y+1) 384, 1920, 2592, 1056
thaquitpath tesseractihexadecaquasitruncated prismatotesseractihexadecachoron 1.608038 384, 768, 416, 56
thatpath tesseractihexadecatruncated prismatotesseractihexadecachoron 2.326846 384, 768, 416, 56
gaquidpoth great quasidisprismatotesseractihexadecachoron 1.938391 384, 768, 464, 80
gidpith great disprismatotesseractihexadecachoron, great prismated tesseract, omnitruncated tesseract 3.498949 384, 768, 464, 80
pox srico partially octa-expanded small rhombated icositetrachoron 384, 960, 720, 144
... β3x3x4β (?) ... 384, 960, 736, 176
teddi aid, teddi || id, K-4.147 tridiminished icosahedron atop icosidodecahedron 3.077684 39, 120, 115, 34
3,n-dip, K-4.175 triangle - n-gon duoprism, n-gon - n-prismatic wedge sqrt[1/3+1/(4 sin2(π/n))] 3n, 6n, 4n+3, n+3
n-af, K-4.174 n-gonal antifastegium, n-gonal - n-antiprismatic wedge, {n} || gyro n-prism sqrt[(1+2 cos(π/n)-2 cos2(π/n))/(2+4 cos(π/n)-6 cos2(π/n))] 3n, 8n, 7n+3, 2n+3
n/d-af n/d-grammal antifastegium, n/d-grammal - n/d-antiprismatic wedge, {n/d} || gyro n/d-prism sqrt[(1+2 cos(π d/n)-2 cos2(π d/n))/(2+4 cos(π d/n)-6 cos2(π d/n))] 3n, 8n, 7n+3, 2n+3
dappip, K-4.96 decagonal-antiprism prism 1.747560 40, 100, 84, 24
... reduced( ofx3/2oxx3xxx&xt by 4x {6/2} ) 1.136572 40, 102, 78, 20
pexrit partially (mono-)expanded rit 40, 104, 88, 24
... expanded augmented axially-tetrahedral ursachoron ofxo3xooo3xxxx&#xt 40, 108, 102, 34
pacsid pith (alt: cuba sircobcu) partially (mono-) contracted sidpith, partially expanded quawros, cubasirco bicupola 40, 120, 134, 54
ditdiddip ditrigonal-dodecadodecahedron prism 1 40, 140, 108, 26
gidtiddip great-ditrigonary-icosidodecahedron prism 1 40, 140, 124, 34
sidtiddip small-ditrigonary-icosidodecahedron prism 1 40, 140, 124, 34
biped biprismatodecachoron sqrt[(2a2+ab+2b2)/5] 40, 140, 160, 60
ditdidap ditrigonary-dodecadodecahedron antiprism 0.951057 40, 180, 168, 26
gidtidap great-ditrigonary-icosidodecahedron antiprism 0.951057 40, 180, 184, 54
sidtidap small-ditrigonary-icosidodecahedron antiprism 0.951057 40, 180, 184, 54
... tegum sum of 2 mutually inverted (x,u)-tips 2 40, 200, 280, 120
bited (old: sidwapid) bitruncatodecachoron, snub disphenic antiprismatodecachoron, general variant of hull of tisted, tegum sum of 2 inverted (x,y)-tips sqrt[(3y2+3y+2)/5] 40, 200, 280, 120
pistodip pentagon - octagram duoprism 1.008216 40, 80, 53, 13
podip pentagon - octagon duoprism 1.559075 40, 80, 53, 13
starodip pentagram - octagon duoprism 1.408368 40, 80, 53, 13
stastodip pentagram - octagram duoprism 0.754511 40, 80, 53, 13
dope, K-4.74 dodecahedron prism 1.487792 40, 80, 54, 14
gissiddip great-stellated-dodecahedron prism 0.732444 40, 80, 54, 14
squadedip, K-4.97 square - decagon duoprism 1.765796 40, 80, 54, 14
pahtex tes partially demitesseractic-expanded tesseract, partially demitesseractic-contracted truncated tesseract, hexadecachorally truncated tesseract 40, 80, 56, 16
perope, K-4.92 pentagonal-rotunda prism 1.693527 40, 90, 69, 19
escupe, K-4.68 elongated-square-cupola prism 1.485633 40, 92, 72, 20
opatic, op || tic, K-4.106 octagonal prism atop truncated cube 1.847759 40, 92, 72, 20
... oooxfxooo3xoxoxoxox5ofxfofxfo&#xt 400, 1260, 1140, 280
... oxoofooxo3oofxoxfoo5xxoxxxoxx&#xt 400, 1320, 1310, 390
... ooofxfooo3xoxxoxxox5ofxofoxfo&#xt 400, 1500, 1468, 368
... oxofofoxo3oofoxofoo5xxoxxxoxx&#xt 400, 1650, 1872, 622
... oct atop tut atop toe 42, 102, 84, 24
sissidadid, sissid || did small stellated dodecahedron atop dodecadodecahedron, small-stellated-dodecahedral cupola 1.064815 42, 150, 126, 26
ikaid, ike || id, K-4.137 icosahedron atop icosidodecahedron, icosahedral cap of rectified hexacosachoron, icosahedral cupola 3.077684 42, 150, 142, 34
... 2/10-luna of hexacosachoron 1.618034 42, 171, 233, 104
..., xFoFx3xxxxx5xofox&#xt   (F=ff=x+f) bilunabirotundic great rhombicosidodecahedron prism 420, 1080, 828, 168
... Fxxx3xxoF3xfxo *b3oxFo&#zx 432, 1320, 1200, 312
risadi (alt.: idrox) rectified snub icositetrachoron, icositetradiminished rectified hexacosachoron 3.077684 432, 1440, 1248, 240
idprahi icositetra-diminished prismatorhombated hecatonicosachoron 8.278950 4320, 9360, 6192, 1152
... oxoxfxooo3xxxoxoxox5ooxfofxfo&#xt 440, 1410, 1280, 310
... oxofxfooo3xxxxoxxox5ooxofoxfo&#xt 440, 1710, 1800, 530
pibox tico partially bi-octa-expanded truncated icositetrachoron 448, 896, 560, 112
coatotum bistratic co-cap of prip, tut-diminished prip, Stott expansion of tip, (co,toe)-based tutsachoron, (co,toe)-based tutism 1.612452 48, 108, 80, 20
pabexrit partially bi-expanded rit, partially bi-contracted tat 48, 112, 88, 24
quercope quasirhombicuboctahedron prism 0.890446 48, 120, 100, 28
sircope, K-4.66 small-rhombicuboctahedron prism, medial (cube-first) subsegment of sidpith 1.485633 48, 120, 100, 28
toatic, toe || tic, K-4.98 truncated octahedron atop truncated cube 1.785406 48, 120, 100, 28
tutatoe gybcu tutatoe gyrobicupola 48, 120, 102, 30
tutatobcu tutatoe orthobicupola 48, 120, 102, 30
titho truncated tesseractihemioctachoron 1.581139 48, 120, 88, 20
goccope great-cubicuboctahedron prism 0.890446 48, 120, 88, 22
soccope small-cubicuboctahedron prism 1.485633 48, 120, 88, 22
thex truncated hexadecachoron, cantic tesseract 1.581139 48, 120, 96, 24
... rico-cap augmented thex-rotunda ... 48, 126, 108, 30
sircoatoe, sirco || toe, K-4.75 small rhombicuboctahedron atop truncated octahedron 1.582890 48, 132, 112, 28
sircoatic, sirco || tic, K-4.100 small rhombicuboctahedron atop truncated cube, small-rhombicuboctahedral cap of small rhombated tesseract 1.847759 48, 132, 112, 28
coaticbicu coatic bicupola 48, 132, 114, 30
coatobcu coatoe bicupola, equatorially contracted rectified icositetrachoron 48, 132, 114, 30
pysna s2s3s4x, pyritosnub alterprism, edge-alternated great-rhombicuboctahedronal prism, edge-snub octahedral hosochoron ... 48, 144, 136, 40
sniccup, K-4.60 snub-cube prism, snub-cuboctahedron prism 1.433724 48, 144, 136, 40
cyte opau sodip cyclotetra octagon-prism-augmented sodip ... 48, 144, 140, 44
tridex tri-icositetradiminished hexacosachoron, tetragonal-antiwedge heptacontadichoron 1.618034 48, 192, 216, 72
sniccap s2s3s4s, snub-cubic antiprism, non-uniform alternation of gircope ... 48, 192, 220, 76
tabene trigonal-bipyramidal enneacontahexachoron, rectified-icositetrachoron dual, surtegmated icositetrachoron 48, 240, 288, 96
... x3β3o4o (?) ... 48, 312, 240, 48
bicont (old: ducont) bitetracontoctachoron, tetracontoctachoron dual, bi-apiculated icositetrachoron, tetradisphenoidal 288-cell 1.306563 48, 336, 576, 288
histodip hexagon - octagram duoprism 1.137055 48, 96, 62, 14
hodip hexagon - octagon duoprism 1.645329 48, 96, 62, 14
quithip quasitruncated-hexahedron prism 0.765367 48, 96, 64, 16
sitwadip square - dodecagon duoprism 2.057195 48, 96, 64, 16
ticcup, K-4.99 truncated-cube prism 1.847759 48, 96, 64, 16
tope, K-4.89 truncated-octahedron prism 1.658312 48, 96, 64, 16
pibox srico partially bi-octa-expanded small rhombitetracontoctachoron 480, 1056, 720, 144
hidhi hecatonicosa-diminished hecatonicosachoron 3.702459 480, 1440, 1200, 240
... oxoxfxoxo3xxxoxoxxx5ooxfofxoo&#xt 480, 1560, 1420, 340
... Ffxo oxFx3xfox5xoxx&#zx 480, 1560, 1518, 438
ridimex (alt.: idimrox) rectified icosidiminished hexacosachoron, icosidiminished rectified hexacosachoron 3.077684 480, 1800, 1640, 320
... oxofxfoxo3xxxxoxxxx5ooxofoxoo&#xt 480, 1920, 2132, 692
hedip heptagonal-heptagonal duoprism 1.629715 49, 96, 63, 14
n-aw, {2n} || n-ap anti-n-wedge, n-gonal anti-wedge, 2n-gon - n-antiprismatic wedge, n-gonal gyrobicupolaic ring, {2n} || n-antiprism, {n} || gyrated n-cupola sqrt[(3-2 cos(π/n))/(5-6 cos(π/n))] 4n, 10n, 8n+3, 2n+3
n-appip, K-4.176 n-antiprism prism sqrt[(5-4 cos(π/n))/(8-8 cos(π/n))] 4n, 10n, 8n+4, 2n+4
n/d-appip n/d-antiprism prism sqrt[(5-4 cos(π d/n))/(8-8 cos(π d/n))] 4n, 10n, 8n+4, 2n+4
... n/d-grammic retroantiprismatic hemiantiprism 0.707107 4n, 12n, 10n+4, 2n+4
2,n-dap digon - n-gon duoantiprism, hemiated square - 2n-gon duoprism sqrt[A2/2+B2/(4 sin2(π/2n))] 4n, 14n, 16n+4, 6n+4
... n-fold dissected tetrahedral polytwister, n-fold dissected tetter, tetraswirlic 4n-choron ... 4n, 16n, 16n, 4n
4,n-dip, K-4.177 square - n-gonal duoprism sqrt[1/2+1/(4 sin2(π/n))] 4n, 8n, 5n+4, n+4
4,n/d-dip square - n/d-gramal duoprism sqrt[1/2+1/(4 sin2(πd/n))] 4n, 8n, 5n+4, n+4
n-cuf n-gonal cupofastegium, 2n-gon - n-prismatic wedge, n-gonal orthobicupolaic ring, {2n} || n-prism, {n} || n-cupola sqrt[(5+2 cos(π/n)-4cos2(π/n))/(8-12 cos2(π/n))] 4n, 9n, 7n+3, 2n+3
n/d-cuf n/d-grammal cupofastegium, 2n-gon - n/d-prismatic wedge, n/d-grammal orthobicupolaic ring, {2n/d} || n/d-prism, {n/d} || n/d-cupola sqrt[(5+2 cos(π d/n)-4cos2(π d/n))/(8-12 cos2(π d/n))] 4n, 9n, 7n+3, 2n+3
n-dep n-gonal duoexpandoprism, expanded n-n-duoprism, tegum sum of 2 alternated n-2n-duoprisms sqrt[1/(4 sin2(π/2n))+1/(4 sin2(π/n))] 4n2, 12n2, 12n2+4n, 4n2+4n
(n,2m)-pap n-gon - 2m-gon prismantiprismoid, s-n-s-2-s-2m-x, edge-alternated 2n-gon - 4m-gon duoprism ... 4nm, 12nm, 10nm+2n+4m, 2nm+2n+4m
... (n,m)-double antiprismatoid ... 4nm, 20nm, 28nm+2n+2m, 12nm+2n+2m
2n,2m-dip 2n-gonal - 2m-gonal duoprism sqrt[1/(4 sin2(π/2n))+1/(4 sin2(π/2m))] 4nm, 8nm, 4nm+2n+2m, 2n+2m
... Shephard's p-generalised hexadecachoron, complex polychoron x2-3-o2-3-o2-4-op , βp 4 4p, 6p2, 4p3, p4
... rectified Shephard's tesseract, complex polychoron op-4-x2-3-o2-3-o2 4p3, 6p4, 2p2(2p2+3), p(p3+4)
... truncated generalized Shephard tesseract, complex polychoron xp-4-x2-3-o2-3-o2 4p4, 2p3(3p+2), 2p2(2p2+3), p(p3+4)
... maximally expanded generalized Shephard tesseract, complex polychoron xp-4-o2-3-o2-3-x2 4p4, 6p3(p+2), 4p2(p2+3p+3), p(p3+4p2+6p+4)
pen, K-4.1 pentachoron, 4D simplex (α4), 5-cell, pyroter(id), tetrahedral pyramid, triangle-pyramidal pyramid, regular triangle-scalene, regular line-tettene, regular (point-)pennene, 3 tet rosette, vertex figure of hix, Gosset polytope 03, 5-2-stepprism 0.632456 5, 10, 10, 5
... qo3oo3oo&#x, shallower variant of tetrahedral pyramid, vertex pyramid of tes 1 5, 10, 10, 5
... xo3oo ox&#q, q-laced trigonal scalene 0.804400 5, 10, 10, 5
... xo3oo3oo&#q, taller variant of tetrahedral pyramid 0.784465 5, 10, 10, 5
padedip pentagon - decagon duoprism 1.828016 50, 100, 65, 15
pistadedip pentagon - decagram duoprism 1.051462 50, 100, 65, 15
stardedip pentagram - decagon duoprism 1.701302 50, 100, 65, 15
stastidedip pentagram - decagram duoprism 0.811393 50, 100, 65, 15
didadoe did atop doe 1.414214 50, 150, 126, 26
doaid, doe || id, K-4.77 dodecahedron atop icosidodecahedron, dodecahedral cupola 1.618034 50, 150, 134, 34
gissidagid, gissid || gid great stellated dodecahedron atop great icosidodecahedron, great stellated dodecahedral cupola 0.692924 50, 150, 134, 34
pautpen penta-augmentated truncated pentachoron ... 50, 160, 160, 50
gudap (old: gedap) great duoantiprism, (old: great double antiprism – but not: great antiprism) 1 50, 200, 220, 70
pedap pentagonal duoantiprism ... 50, 200, 220, 70
gocap great cycloantiprism 1 50, 200, 260, 110
tocap toroidal cycloantiprism 1 50, 200, 260, 110
bicyte ausodip bicyclotetraugmented square-octagon duoprism ... 52, 176, 164, 40
owaudope omni-augmented dodecahedral-prism 52, 200, 234, 86
... tetracontoctachoron-derived Gévay polychoron ... 528, 2496, 2880, 912
arsted diddidex around-symmetrical tridiminishing of (axial) duo-disdodeca-icosa-diminished hexacosachoron 1.618034 53, 129, 100, 24
... 3/10-luna of hexacosachoron 1.618034 53, 242, 353, 164
hoddated ex (shallow-)hexa-octa-diminished deep-tetra-diminished hexacosachoron 1.618034 54, 138, 112, 28
hautope hexa-augmented tope 54, 144, 136, 46
... ooxf3xfox3oxFx&#xt 54, 150, 128, 32
eocta sirco elongated octasirco ... 54, 156, 156, 54
iku (1,0,20,0,0)-diminished vertex-first-rotunda of ex, (full-symmetrical) icosiena -diminished vertex-first-rotunda of ex, axially-icosahedral ursachoron ofx3xoo5ooo&#xt, ike-based ursulate 1.618034 54, 162, 142, 34
giku gike-based ursachoron 0.965407 54, 162, 144, 34
dapabdi poxic (alt.: hau sircope) deep parabidiminished poxic, hexa-augmented sircope 54, 168, 148, 34
... (1,0,8,12,0)-diminished vertex-first-rotunda of ex, (subsymmetrical) icosiena -diminished vertex-first rotunda of hexacosachoron 1.618034 54, 168, 166, 52
sidrebcu stellidodecahedral rectibicupola, orbiform bistratc stack of small stellated dodecahedron atop pseudo dodecadodecahedron atop great dodecahedron 1.064815 54, 240, 228, 50
rite (alt.: ikaidbicu) rectified ite, ikaid bicupola ... 54, 240, 252, 66
... (0,0,20,0,0)-diminished vertex-first-rotunda of ex, icosi-diminished vertex-first-rotunda of ex, mono-augmented axially-icosahedral ursachoron ofxo3xooo5oooo&#xt 1.618034 55, 174, 172, 53
pactat partially (mono-)contracted tat 56, 120, 88, 24
... thawro-wedged 2/6-luna of hexacosachoron ... 56, 264, 379, 171
iquatoc icositetraquasitruncated tetracontoctachoron 2 576, 1152, 576, 72
gaqri great quasirhombated icositetrachoron 1.230739 576, 1152, 720, 144
grico great rhombated icositetrachoron, cantitruncated icositetrachoron 4.299451 576, 1152, 720, 144
bimtec bimesotruncatotetracontoctachoron sqrt[3a2+4ab sqrt(2)+3b2] 576, 1440, 1056, 192
paqri prismatoquasirhombated icositetrachoron 1.938391 576, 1440, 1104, 240
prico prismatorhombated icositetrachoron, runcitruncated icositetrachoron 3.498949 576, 1440, 1104, 240
diquitdi disicositetraquasitruncated disicositetrachoron 1.608038 576, 1440, 816, 96
ditdi disicositetratruncated disicositetrachoron 2.326846 576, 1440, 816, 96
girpdi great rhombiprismic disicosatetrachoron 1.938391 576, 1440, 912, 144
sirpdi small rhombiprismic disicosatetrachoron 3.498949 576, 1440, 912, 144
gipti great prismatotriakisicositetrachoron 1.938391 576, 1440, 960, 168
sipti small prismatotriakisicositetrachoron 3.498949 576, 1440, 960, 168
guti great tetrakisicositetrachoron 2.326846 576, 1440, 960, 96
suti small tetrakisicositetrachoron 1.608038 576, 1440, 960, 96
... x3x4β3o (?) ... 576, 1728, 1344, 264
... x3β4o3x (?) ... 576, 1728, 1430, 360
recont rectified tetracontoctachoron 6.754807 576, 1728, 1488, 336
... β3x4β3o (?) ... 576, 2304, 2016, 432
respic rectified small prismated tetracontoctachoron 3.557647 576, 2304, 2112, 384
... x3β4o3β (?) ... 576, 2304, 2112, 528
sni (old: snico) / snoc s3s4s3s, (fully) snubbed icositetrachoron (but not sadi) / snubbed tetracontoctachoron, non-uniform alternation of gippic ... 576, 2592, 2832, 816
... β3β4β3o (?) ... 576, 2880, 2976, 744
sabric small birhombatotetracontoctachoron sqrt[a2 + 2 sqrt(2) ab + 3b2] 576, 2880, 3168, 864
gabric great birhombatotetracontoctachoron sqrt[a2 + 2 sqrt(2) ab + 3b2] 576, 2880, 3360, 1056
mabric medial birhombatotetracontoctachoron sqrt[a2 + 2 sqrt(2) ab + 3b2] 576, 2880, 3552, 1248
... β3β4o3β (?) ... 576, 3168, 3456, 936
idprix icositetra-diminished prismatorhombated hexacosachoron 9.744610 5760, 12960, 8832, 1632
... (1,0,4,12,0)-diminished vertex-first-rotunda of ex, heptadeca-diminished vertex-first rotunda of hexacosachoron 1.618034 58, 204, 214, 68
5,n-dip pentagon - n-gon duoprism sqrt[(5+sqrt(5))/10+1/(4 sin2(π/n))] 5n, 10n, 6n+5, n+5
n-puf n-gonal pucofastegium, n-gon - 2n-prismatic wedge, n-gonal magnabicupolaic ring, {n} || 2n-prism, {2n} || n-cupola sqrt[(2 cos2(π/n)-2 cos(π/n)-3)/(6 cos2(π/n)-2)] 5n, 11n, 8n+3, 2n+3
n-cufbil n-gonal cupofastegia biluna 5n, 13n, 12n+4, 4n+4
squasc (old: squippypy, alt: edihex), 4pyr-pyr, K-4.4 square-scalene, square-pyramidal pyramid, line atop fully orthogonal square, 1/4-luna of hex, 4 tet rosette, edge-diminished hex 0.707107 6, 13, 13, 6
tete (old: tedpy) (line-)tetrahedron-tegum, tetrahedral bipyramid 6, 14, 16, 8
triddit triangle duotegum, dual of triangle duoprism, 6-2-stepprism 0.707107 6, 15, 18, 9
hadedip hexagon - decagon duoprism 1.902113 60, 120, 76, 16
grip great rhombated pentachoron, cantitruncated pentachoron 1.843909 60, 120, 80, 20
etutatoe elongated tutatoe ... 60, 138, 108, 30
cytid rico cyclotridiminished rectified-icositetrachoron, metatridiminished rectified-icositetrachoron 1.732051 60, 144, 111, 27
ripdip rhombiprismato dispentachoron 1.612452 60, 150, 100, 20
diddip dodecadodecahedron prism 1.118034 60, 150, 108, 26
pittip prismatotriakispentachoron 1.612452 60, 150, 110, 25
geihiddip great-icosihemidodecahedron prism 0.794963 60, 150, 112, 28
bimted (old: bimtid) bimesotruncatodecachoron sqrt[(3a2+4ab+3b2)/5] 60, 150, 120, 30
prip prismatorhombated pentachoron, runcitruncated pentachoron 1.612452 60, 150, 120, 30
giddip great-icosidodecahedron prism 0.794963 60, 150, 124, 34
gyprip gyrated prip 1.612452 60, 150, 124, 34
iddip, K-4.90 icosidodecahedron prism 1.693527 60, 150, 124, 34
gidhiddip great-dodecahemidodecahedron prism 0.794963 60, 150, 96, 20
tau tope tetra-augmented tope 60, 156, 140, 44
tutatoa sirco truncated tetrahedron atop truncated octahedron atop small rhombicuboctahedron ... 60, 174, 158, 42
... x3x3β3o (?) ... 60, 180, 130, 30
redeca rectified decachoron 2.828427 60, 180, 160, 40
... omni-pippy-augmented (5,10)-duoprism 60, 200, 205, 65
... x3β3o3x (?) ... 60, 210, 170, 40
... β3x3β3o (?) ... 60, 240, 200, 50
dastop dodeca-star toroidi-prism 0.707107 60, 240, 204, 36
hog dhidicup hollow gidhid cupoliprism 0.732444 60, 240, 216, 36
respid rectified small prismated decachoron 1.732051 60, 240, 230, 50
... Waterman polychoron number 3 wrt. cyclo-pentachoric lattice A4 centered at a lattice point 1.732051 60, 240, 230, 50
... decachoron-derived Gévay polychoron, Waterman polychoron number 4 wrt. cyclo-pentachoric lattice A4 centered at a lattice point 2 60, 260, 300, 100
... x3β3o3β (?) ... 60, 270, 240, 60
snip / snad s3s3s3s, snub pentachoron / snub decachoron, non-uniform alternation of gippid ... 60, 270, 300, 90
... β3β3β3o (?) ... 60, 300, 320, 85
sabred small birhombatodecachoron sqrt[(2a2+2ab+3b2)/5] 60, 300, 340, 100
gabred great birhombatodecachoron sqrt[(2a2+2ab+3b2)/5] 60, 300, 360, 120
mabred medial birhombatodecachoron sqrt[(2a2+2ab+3b2)/5] 60, 300, 380, 140
... β3β3o3β (?) ... 60, 360, 380, 100
gogishi, gaspD great grand stellated hecatonicosachoron, greatened aggrandized stellated polydodecahedron 0.540182 600, 1200, 720, 120
hi, pD hecatonicosachoron, 120-cell, dodecacontachoron, twelftychoron, cosmochoron, dodecaplex, polydodecahedron, hyperdodecahedron 3.702459 600, 1200, 720, 120
... squashed hexaconta-sphenated id-first deep parabidiminished rahi ... 600, 1740, 1488, 348
... xoxFxFxox3oxfoxofxo5xxoxxxoxx&#xt 600, 2040, 1978, 538
... dodecaswirlic triacosihexacontachoron, thirtyfold dissected dodecahedral polytwister, thirtyfold dissected doter ... 600, 2400, 2160, 360
spidrox (alt.: hidrox) swirlprismatodiminished rectified hexacosachoron, 120-diminished rectified hexacosachoron 3.077684 600, 2400, 2640, 840
sporraggix swirlprismatoreplenished rectified grand hexacosachoron 0.726543 600, 2400, 2640, 840
gadatady grand ditetrahedral dishecatonicosachoron 0.874032 600, 3600, 2160, 240
siddatady small ditetrahedral dishecatonicosachoron 2.288246 600, 3600, 2160, 240
dattady ditetrahedronary dishecatonicosachoron 1.414214 600, 3600, 2640, 240
giddatady great ditetrahedronary dishecatonicosachoron 1.414214 600, 3600, 2640, 240
dattathi ditetrahedronary trishecatonicosachoron 1.414214 600, 3600, 2880, 360
radatathi retroditetrahedronary dishecatonicosachoron 1.414214 600, 3600, 2880, 360
gadtaxhi great ditetrahedronary hexacosihecatonicosachoron 0.874032 600, 3600, 3120, 720
sidtaxhi small ditetrahedronary hexacosihecatonicosachoron 2.288246 600, 3600, 3120, 720
gardatady grand retroditetrahedral dishecatonicosachoron 0.874032 600, 3600, 3840, 240
sirdatady small retroditetrahedral dishecatonicosachoron 2.288246 600, 3600, 3840, 240
gadtaxady grand ditetrahedronary hexacosadishecatonicosachoron 0.874032 600, 3600, 3840, 840
gardtaxady grand retroditetrahedronary hexacosidishecatonicosachoron 0.874032 600, 3600, 3840, 840
sidtaxady small ditetrahedronary hexacosidishecatonicosachoron 2.288246 600, 3600, 3840, 840
sirdtaxady small retroditetrahedronary hexacosidishecatonicosachoron 2.288246 600, 3600, 3840, 840
dittafady ditetrahedrofissary dishecatonicosachoron 1.414214 600, 3600, 4080, 240
mardatathi medial retroditetrahedral triakishecatonicosachoron 1.414214 600, 3600, 4080, 360
ridatathi retroinverted ditetrahedral triakishecatonicosachoron 1.414214 600, 3600, 4080, 360
gadtifady (old: gadtafady) great ditetrahedronarofissary dishecatonicosachoron 0.874032 600, 3600, 4560, 240
sadtifady small ditetrahedronarofissary dishecatonicosachoron 2.288246 600, 3600, 4560, 240
sridtathi small retroinverted ditetrahedronary trishecatonicosachoron 2.288246 600, 3600, 4560, 360
gardatathi grand retroditetrahedronary trishecatonicosachoron 0.874032 600, 3600, 5280, 360
grad tathi great retroditetrahedronary trishecatonicosachoron 1.414214 600, 3600, 5280, 360
gridtathi great retroinverted ditetrahedronary trishecatonicosachoron 1.414214 600, 3600, 5280, 360
sand tathi small intercepted ditetrahedronary trishecatonicosachoron 2.288246 600, 3600, 5280, 360
gard tadhix grand retroditetrahedronary dishecatonicosihexacosachoron 0.874032 600, 3600, 5280, 840
sradditdahix small retroditetrahedronary dishecatonicosihexacosachoron 2.288246 600, 3600, 5280, 840
dittadphi ditetrahedronary disprismatohecatonicosachoron 1.414214 600, 3600, 6480, 1560
dard tipady diretroditetrahedronary prismatodishecatonicosachoron 1.414214 600, 3600, 6480, 960
gidard tipady great diretroditetrahedronary prismatodishecatonicosachoron 1.414214 600, 3600, 6480, 960
gardtapaxhi grand retroditetrahedronary hexacosidishecatonicosachoron 0.874032 600, 3600, 7440, 1440
siddit paxhi small ditetrahedronary hexacosidishecatonicosachoron 2.288246 600, 3600, 7440, 1440
datcathi ditetrahedronary coincidic trishecatonicosachoron 1.414214 600, 7200, 5280, 360
gadathiphi grand ditetrahedronary hecatonicosaprismatohecatonicosachoron 0.874032 600, 7200, 7440, 1440
sirdtapady small retroditetrahedronary prismatodishecatonicosachoron 2.288246 600, 7200, 7440, 1440
ikadoaid (1,0,0,12,0)-diminished vertex-first-rotunda of ex, trideca-diminished vertex-first rotunda of hexacosachoron, ike atop (pseudo) doe atop id 1.618034 62, 240, 262, 84
twau doaid deep mono-diminished rotunda of ex, 12-augmented doe || id 1.618034 62, 270, 374, 166
... Shephard's 5-generalised tesseract, complex polychoron x5-4-o2-3-o2-3-o2 , γ5 4 625, 500, 150, 20
... (0,0,0,12,0)-diminished vertex-first-rotunda of ex, dodeca-diminished vertex-first rotunda of hexacosachoron 1.618034 63, 252, 292, 103
odip octagon-octagon duoprism 1.847759 64, 128, 80, 16
ostodip octagon-octagram duoprism 1.414214 64, 128, 80, 16
stodip octagram-octagram duoprism 0.765367 64, 128, 80, 16
... o3o3q4x, variation of tat 2.645751 64, 128, 88, 24
quitit quasitruncated tesseract 0.615370 64, 128, 88, 24
tat truncated tesseract 2.149726 64, 128, 88, 24
gittith great tesseractitesseractihexadecachoron 0.890446 64, 192, 136, 32
steth small tesseractitesseractihexadecachoron 1.485633 64, 192, 136, 32
gnappoth great spinoprismatotesseractihexadecachoron 0.890446 64, 192, 184, 56
snappoth small spinoprismatotesseractihexadecachoron 1.485633 64, 192, 184, 56
gaquipadah great quasiprismatodishexadecachoron 0.890446 64, 192, 200, 72
iquipadah inverted quasiprismatodishexadecachoron 1.485633 64, 192, 200, 72
gahfipto great hexadecafeceted prismatotesseractioctachoron 0.890446 64, 192, 208, 48
gittifcoth great tesseractifaceted cubitesseractihexadecachoron 0.890446 64, 192, 208, 48
shafipto small hexadecafaceted prismatotesseractioctachoron 1.485633 64, 192, 208, 48
stefacoth small tesseractifaceted cubitesseractihexadecachoron 1.485633 64, 192, 208, 48
... q3o3o4x, variation of sidpith 1.732051 64, 192, 208, 80
... Q3o3o4x, variation of sidpith 2.645751 64, 192, 208, 80
quidpith (old: qippith) quasi(dis)prismatotesseractihexadecachoron 0.890446 64, 192, 208, 80
sidpith small disprismatotesseractihexadecachoron, runcinated tesseract, small prismated tesseract 1.485633 64, 192, 208, 80
... x3o3o4q, variation of sidpith 1.870829 64, 192, 208, 80
dippit disprismatotesseract 1.485633 64, 192, 232, 64
picnut prismatocubiintercepted tesseract 0.890446 64, 192, 232, 64
... Waterman polychoron number 5 wrt. primitive tesseractic lattice C4 centered at a lattice point 64, 312, 352, 104
... 4/10-luna of hexacosachoron 1.618034 64, 313, 473, 224
... o3o3β4x (?) ... 64, 320, 272, 56
... β3o3o4β (?) ... 64, 480, 576, 176
... truncated Witting polychoron, complex polychoron x3-3-x3-3-o3-3-o3 6480, 19440, 8640, 480
... maximally expanded Witting polychoron, complex polychoron x3-3-o3-3-o3-3-x3 6480, 34560, 30240, 4800
thawrorh thawro rhombochoron ... 66, 246, 262, 82
arsted biscrox around-symmetrically tridiminished bistratic icosahedron-first cap of rectified hexacosachoron 3.077684 69, 195, 165, 39
6,n-dip hexagon - n-gonal duoprism sqrt[1+1/(4 sin2(π/n))] 6n, 12n, 7n+6, n+6
n/d-cupe n/d-cupola prism, n/d-prism atop 2n/d-prism sqrt[(5+2 cos(π d/n)-4 cos2(π d/n))/(6-8 cos2(π d/n))] 6n, 13n, 9n+4, 2n+4
n-gytpuf n-gonal gyrotegmicupolafastegium, n-cupola atop inverted gyrated n-cupola, 2n-prismatic gyrated bi-wedge 6n, 16n, 14n+4, 4n+4
n-tepuf n-gonal tegmipucofastegium, n-cupola atop inverted ortho n-cupola, 2n-prismatic ortho bi-wedge 6n, 16n, 14n+4, 4n+4
... n-fold dissected octahedral polytwister, n-fold dissected octer, octaswirlic 8n-choron ... 6n, 30n, 32n, 8n
... rectified Shephard's hexadecachoron, complex polychoron op-4-o2-3-x2-3-o2 6p2, 12p3, 4p3(p+1), p(p3+4)
... (small) rhombated generalized Shephard tesseract, complex polychoron xp-4-o2-3-x2-3-o2 6p4, 12p3(p+1), 2p2(4p2+6p+3), p(p3+4p2+4)
trippy, K-4.7 trigonal-prismatic pyramid, vertex pyramid of the rectified pentachoron 0.774597 7, 15, 14, 6
pesc (old: peppypy), K-4.86 pentagon scalene, pentagon-pyramidal pyramid, line atop fully orthogonal pentagon, 5 tet rosette 1.618034 7, 16, 16, 7
stasc (old: stappypy) stellar scalene, pentagrammic scalene, pentagram-pyramidal pyramid, line atop fully orthogonal pentagram, 5 tet two-step rosette 0.618034 7, 16, 16, 7
... vertex figure of great spinocelliprismated penteract 0.920055 7, 18, 19, 8
octpy, K-4.3 octahedral pyramid, half of hex (its vertex-first rotunda) 0.707107 7, 18, 20, 9
... general 7-2-stepprism sqrt(A2+B2) 7, 21, 28, 14
doa pabidrid, doe || pabidrid, K-4.155 dodecahedron atop parabidiminished rhombicosidodecahedron 5.236068 70, 170, 144, 44
bicypdrahi (bistratic) bi-cyclopentadiminished rectified hecatonicosachoron 4.534568 700, 1800, 1410, 310
hitwadip hexagon - dodecagon duoprism 2.175328 72, 144, 90, 18
ticagirco, K-4.128 truncated cube atop great rhombicuboctahedron, truncated-cubical cap of prismatorhombated hexadecachoron, cuboctahedral supra-cap of small rhombated icositetrachoron 2.613126 72, 156, 112, 28
toagirco, toe || girco, K-4.149 truncated octahedron atop great rhombicuboctahedron, truncated octahedral cap of prismatorhombated icositetrachoron 3.498949 72, 156, 112, 28
quithaquitco quasitruncated hexahedron atop quasitruncated cuboctahedron 1.082392 72, 156, 112, 28
tutatoe augrip tutatoe-augmented grip 72, 162, 118, 28
goccoa cotco great cubicuboctahedron atop cubotruncated cuboctahedron 1.414214 72, 168, 112, 22
sircoagirco, sirco || girco (degenerate) small rhombicuboctahedron atop great rhombicuboctahedron ∞   i.e. flat in euclidean space 72, 168, 124, 28
sissid || 3doe (degenerate) sissid atop 3doe ∞   i.e. flat in euclidean space 72, 180, 126, 26
pex thex partially (mono-)expanded thex ... 72, 180, 140, 32
quercoa quithu (querco,quith)-based ursachoron 0.986869 72, 180, 142, 34
sirco aticu expanded axially-octahedral ursachoron, (sirco,tic)-based ursulate 1.806144 72, 180, 142, 34
esircoatic elongated sircoatic, diminished srit 72, 192, 156, 36
pabdirico parabidiminished rectified icosatetrachoron, bistratic co-first central segment of rico, axis-orthogonal partial Stott expanded rit 1.732051 72, 192, 156, 36
... wx ox3xx4oo&#zx 72, 192, 164, 44
sissidaraded, sissid || raded small stellated dodecahedron atop rhombidodecadodecahedron, sissid-first cap of padohi 2.497212 72, 210, 186, 56
bidex bi-icositetradiminished hexacosachoron 1.618034 72, 216, 192, 48
birgax bi-icositetra-replenished grand hexacosachoron 0.618034 72, 216, 192, 48
dapabdi spic deep parabidiminished small prismatotetracontoctachoron, hexa-gyro-augmented truncated-cube prism 1.847759 72, 216, 202, 58
hau ticcup hexa-(ortho-)augmented ticcup 72, 216, 214, 70
... oxFxoo3xooxFx3ofxfox&#xt   (F=ff=x+f) 72, 222, 202, 52
pacsrit partially (mono-)contracted small rhombated tesseract ... 72, 228, 204, 48
... oxFxoo3xfoxFx3ooxfox&#xt   (F=ff=x+f) 72, 228, 210, 54
poxic   (alt.: phic srico, alt.: owau sidpith) partially octa-expanded icositetrachoron, partially hexadeca-contracted small rhombated icositetrachoron, octa-augmented small diprismated tesseractithexadecachoron ... 72, 256, 256, 72
twau iddip twelve-augmented icosidodecahedral-prism 72, 270, 304, 106
spidrico swirlprismatodiminished rectified icositetrachoron, 24-diminished rectified icositetrachoron 1.732051 72, 288, 288, 72
... octaswirlic enneacontahexachoron, twelvefold dissected octahedral polytwister, twelvefold dissected octer 1.255926 72, 360, 384, 96
... oxofxfoxo3xxFxoxFxx5xxoxFxoxx&#xt 720, 2160, 1912, 472
tibbic triangular-bipyramidal chilliadiacosichoron, rectified-hecatonicosachoron dual, surtegmated hexacosachoron 720, 3120, 3600, 1200
griphi great retropental hecatonicosachoron 1.175571 720, 3600, 1920, 120
mriphi medial retropental hecatonicosachoron 1.902113 720, 3600, 1920, 120
giprapivady great pentagonal retroprismatoverted dishecatonicosachoron 1.902113 720, 3600, 2160, 240
ragashi rectified grand stellated hecatonicosachoron 1.175571 720, 3600, 2160, 240
righi rectified great hecatonicosachoron 1.902113 720, 3600, 2160, 240
spapivady small pentagrammal antiprismatoverted dishecatonicosachoron 1.175571 720, 3600, 2160, 240
graphi grand retropental hecatonicosachoron 0.726543 720, 3600, 2520, 120
sriphi small retropental hecatonicosachoron 3.077684 720, 3600, 2520, 120
rigfix rectified great faceted hexacosichoron 0.726543 720, 3600, 2640, 240
rofix rectified faceted hexacosichoron 3.077684 720, 3600, 2640, 240
gippapivady great pentagrammal antiprismatoverted dishecatonicosachoron 0.726543 720, 3600, 3120, 240
raghi rectified grand hecatonicosachoron 1.902113 720, 3600, 3120, 240
ragishi rectified great stellated hecatonicosachoron 1.175571 720, 3600, 3120, 240
sprapivady small pentagonal retroprismatoverted dishecatonicosachoron 3.077684 720, 3600, 3120, 240
quiphi quasiprismatohecatonicosachoron 0.726543 720, 3600, 3240, 840
sophi small prismatohecatonicosachoron 3.077684 720, 3600, 3240, 840
pibhaki pentagonal-bipyramidal heptacosiicosachoron, rectified-hexacosachoron dual, surtegmated hecatonicosachoron 720, 3600, 3600, 720
papvixhi pentagonal prismatoverted hexacosahecatonicosachoron 1.902113 720, 3600, 3600, 720
prap vixhi pentagonal retroprismatoverted hexacosahecatonicosachoron 1.175571 720, 3600, 3600, 720
raggix rectified grand hexacosachoron 0.726543 720, 3600, 3600, 720
rox rectified hexacosachoron 3.077684 720, 3600, 3600, 720
frogfix faceted rectified great faceted hexacosichoron 0.726543 720, 3600, 4320, 720
rixhi retroinverted hexacosahecatonicosachoron 3.077684 720, 3600, 4320, 720
frox faceted rectified hexacosichoron 3.077684 720, 3600, 4440, 840
ripahi retroinverted prismatohecatonicosachoron 4.534568 720, 3600, 4440, 840
ipixady invertopental hexacosadishecatonicosachoron 3.077684 720, 3600, 5760, 840
omfapaxady omnicircumfacetopental hexacosadishecatonicosachoron 0.726543 720, 3600, 5760, 840
gipdohiny great pental dishecatonicosaintercepted hecatonicosachoron 0.726543 720, 3600, 6360, 360
sirphinady small inverted retropental hecatonicosaintercepted dishecatonicosachoron 3.077684 720, 3600, 6360, 360
mif pixady circumfacetopental hexacosadishecatonicosachoron 0.726543 720, 3600, 6840, 840
nipixady intercepted invertopental hexacosadishecatonicosachoron 3.077684 720, 3600, 6840, 840
lifpipixhi polar facetopental prismatohexacosahecatonicosachoron 3.077684 720, 3600, 7560, 1440
ofpipixhi omnifacetopental prismatohexacosahecatonicosachoron 0.726543 720, 3600, 7560, 1440
dahiquatady dishecatonicosiquasitruncated dishecatonicosachoron 4.134026 7200, 14400, 6000, 360
dahitady dishecatonicositruncated dishecatonicosachoron 2.431014 7200, 14400, 6000, 360
hihiquatady hecatonicosihecatonicosiquasitruncated dishecatonicosachoron 3.605551 7200, 14400, 6480, 360
hixquathix hecatonicosihexacosaquasitruncated hecatonicosihexacosachoron 2.174739 7200, 14400, 6960, 840
hixthix hecatonicosihexacositruncated hecatonicosihexacosachoron 6.186316 7200, 14400, 6960, 840
gaqrigafix great quasirhombated great faceted hexacosachoron 1.080363 7200, 14400, 7680, 960
girfix great rhombated faceted hexacosachoron 7.404918 7200, 14400, 7680, 960
gaqrigaghi great quasirhombated great grand hecatonicosachoron 1.679184 7200, 14400, 8160, 1440
gaqrisashi great quasirhombated small stellated hecatonicosachoron 5.018002 7200, 14400, 8160, 1440
gaqrigashi great quasirhombated great stellated hecatonicosachoron 2.700333 7200, 14400, 8160, 960
graghi great rhombated grand hecatonicosachoron 4.550627 7200, 14400, 8160, 960
graggix great rhombated grand hexacosachoron 1.658546 7200, 14400, 8640, 1440
grix great rhombated hexacosachoron, cantitruncated hexacosachoron 9.124101 7200, 14400, 8640, 1440
gaqrigagishi great quasirhombated great grand stellated hecatonicosachoron 1.179024 7200, 14400, 9120, 1920
grahi great rhombated hecatonicosachoron, cantitruncated hecatonicosachoron 11.252107 7200, 14400, 9120, 1920
xhidy hexacosihecatonicosadishecatonicosachoron 3 7200, 18000, 10080, 960
gapthi grand prismatotriakishecatonicosachoron 2.400819 7200, 18000, 10320, 1080
gid thipady great ditrigonary hecatonicosiprismatodishecatonicosachoron 4.087567 7200, 18000, 10320, 1080
giphidy great prismated hecatonicosadishecatonicosachoron 1.348948 7200, 18000, 10320, 1080
mipthi medial prismatotriakishecatonicosachoron 3.199386 7200, 18000, 10320, 1080
sid thipady small ditrigonary hecatonicosiprismatodishecatonicosachoron 1.814331 7200, 18000, 10320, 1080
siphidy small prismated hecatonicosadishecatonicosachoron 4.917351 7200, 18000, 10320, 1080
gipthi great prismatotriakishecatonicosachoron 3.531591 7200, 18000, 10320, 1560
sipthi small prismatotriakishecatonicosachoron 1.878261 7200, 18000, 10320, 1560
girpixhi great rhombiprismic hexacosahecatonicosachoron 1.021064 7200, 18000, 11040, 1440
gripady great rhombiprismic dishecatonicosachoron 1.207883 7200, 18000, 11040, 1440
sirpaxhi small rhombiprismic hexacosahecatonicosachoron 9.744610 7200, 18000, 11040, 1440
sripady small rhombiprismic dishecatonicosachoron 8.278950 7200, 18000, 11040, 1440
ghipady great hecatonicosiprismatodishecatonicosachoron 4.087567 7200, 18000, 11280, 1080
shipady small hecatonicosiprismatodishecatonicosachoron 1.814331 7200, 18000, 11280, 1080
gid tipathi great ditrigonal prismatotriakishecatonicosachoron 2.920251 7200, 18000, 11280, 1560
giphihix great prismatohecatonicosahecatonicosahexacosachoron 1.893038 7200, 18000, 11280, 1560
gippixady great prismatohexacosadishecatonicosachoron 1.207883 7200, 18000, 11280, 1560
gixipady great hexacosiprismatodishecatonicosachoron 1.624598 7200, 18000, 11280, 1560
sid tipathi small ditrigonary prismatotriakishecatonicosachoron 4.179968 7200, 18000, 11280, 1560
sixipady small hexacosiprismatodishecatonicosachoron 6.881910 7200, 18000, 11280, 1560
sphihix small prismatohecatonicosahecatonicosahexacosachoron 5.515107 7200, 18000, 11280, 1560
spixady small prismatohexacosadishecatonicosachoron 8.278950 7200, 18000, 11280, 1560
gixathi great hexacositriakishecatonicosachoron 3.804226 7200, 18000, 11280, 960
hixady hecatonicosihexacosidishecatonicosachoron 3 7200, 18000, 11280, 960
sixathi small hexacositriakishecatonicosachoron 2.351141 7200, 18000, 11280, 960
pirghi prismatorhombated great hecatonicosachoron 4.917351 7200, 18000, 11520, 1680
quippirgashi quasiprismatorhombated grand stellated hecatonicosachoron 1.348948 7200, 18000, 11520, 1680
giphiddix great prismatohecatonicosadishexacosachoron 1.624598 7200, 18000, 12240, 2040
giphixhi great prismatohecatonicosihexacosihecatonicosachoron 2.920251 7200, 18000, 12240, 2040
gippixhihy great prismatohexacosihecatonicosihecatonicosachoron 1.021064 7200, 18000, 12240, 2040
sphiddix small prismatohecatonicosadishexacosachoron 6.881910 7200, 18000, 12240, 2040
sphixhi small prismatohecatonicosihexacosihecatonicosachoron 4.179968 7200, 18000, 12240, 2040
spixhihy small prismatohexacosihecatonicosihecatonicosachoron 9.744610 7200, 18000, 12240, 2040
paqrigshi (old: paqraghi) prismatoquasirhombated great stellated hecatonicosachoron (prismatoquasirhombated grand hecatonicosachoron) 3.199386 7200, 18000, 12480, 1680
quippirghi quasiprismatorhombated grand hecatonicosachoron 2.400819 7200, 18000, 12480, 1680
paqrigafix (old: paquerfix) prismatoquasirhombated great facetted hexacosachoron 1.878261 7200, 18000, 12480, 2160
pirgaghi prismatorhombated great grand hecatonicosachoron 1.893038 7200, 18000, 12480, 2160
pirshi prismatorhombated (small) stellated hecatonicosachoron 5.515107 7200, 18000, 12480, 2160
quippirfix quasiprismatorhombated faceted hexacosachoron 3.531591 7200, 18000, 12480, 2160
paqrigagishi (old: paqrahi) prismatoquasirhombated great grand stellated hecatonicosachoron 1.207883 7200, 18000, 13440, 2640
prahi prismatorhombated hecatonicosachoron, runcitruncated hexacosachoron 8.278950 7200, 18000, 13440, 2640
prix prismatorhombated hexacosichoron, runcitruncated hecatonicosachoron 9.744610 7200, 18000, 13440, 2640
quippirgax quasiprismatorhombated grand hexacosachoron 1.021064 7200, 18000, 13440, 2640
hixquitixhi hecatonicosihexacosiquasitruncated hexacosihecatonicosachoron 2.351141 7200, 18000, 9120, 960
hixtixhi hecatonicosihexacositruncated hexacosihecatonicosachoron 3.804226 7200, 18000, 9120, 960
gik vixathi great skewverted hexacositriakishecatonicosachoro 2.013884 7200, 21600, 13680, 960
sik vixathi small skewverted hexacositriakishecatonicosachoro 4.684471 7200, 21600, 13680, 960
gik vipathi great skewverted prismatotriakishecatonicosachoron 2.828427 7200, 21600, 13920, 1080
sik vipathi small skewverted prismatotriakishecatonicosachoron 2.828427 7200, 21600, 13920, 1080
... o3β3x5x (?) ... 7200, 21600, 14160, 2640
gik vadixady great skewverted dishexacosidishecatonicosachoron 2.013884 7200, 21600, 14640, 1440
sik vadixady small skewverted dishexacosidishecatonicosachoron 4.684471 7200, 21600, 14640, 1440
... x3x3β5o (?) ... 7200, 21600, 14640, 2640
gikkiv datapixady great skewverted ditrigonary prismatohexacosadishecatonicosachoron 2.013884 7200, 21600, 14880, 1560
kavipathi skewverted prismatotrishecatonicosachoron 2.828427 7200, 21600, 14880, 1560
skiv datapixady small skewverted ditrigonary prismatohexacosadishecatonicosachoron 4.684471 7200, 21600, 14880, 1560
rexhi (alt.: amxhi) rectified/ambified hexacosihecatonicosachoron 15.126249 7200, 21600, 18720, 4320
... x3β3o5x (?) ... 7200, 25200, 18480, 3360
... x3o3β5x (?) ... 7200, 25200, 19440, 3840
... β3x3β5o (?) ... 7200, 28800, 23040, 5040
... prishi+120x 2did (?) ... 7200, 28800, 23520, 4080
... o3β3x5β (?) ... 7200, 28800, 23520, 5520
... β3x3o5β (?) ... 7200, 28800, 25440, 5040
... x3β3β5o (?) ... 7200, 28800, 25440, 5040
residpixhi (alt.: amsidpixhi) rectified/ambified small-disprismated-hexacosihecatonicosachoron 10.424281 7200, 28800, 26640, 5040
... x3β3o5β (?) ... 7200, 32400, 27840, 6240
... β3o3β5x (?) ... 7200, 32400, 27840, 6420
snixhi (old: snahi) s3s3s5s, snub hexacosihecatonicosachoron, (snub hecatonicosachoron (but not shi)), non-uniform alternation of gidpixhi ... 7200, 32400, 35040, 9840
... o3β3β5β (?) ... 7200, 36000, 36240, 9240
... β3β3β5o (?) ... 7200, 36000, 37440, 9240
... β3o3β5β (?) ... 7200, 43200, 43680, 10560
... β3β3o5β (?) ... 7200, 43200, 44640, 11040
... mono-diminished vertex-first rotunda of hexacosachoron 1.618034 74, 372, 562, 264
cythdex cyclical triangularily-hexagonally diminished hexacosachoron 1.618034 75, 306, 366, 135
... vertex-first rotunda of hexacosachoron 1.618034 75, 384, 592, 283
... oxFxofx3xooxFxo3ofxfooo&#xt   (F=ff=x+f) 76, 258, 250, 68
... oxFxofx3xfoxFxo3ooxfooo&#xt   (F=ff=x+f) 76, 264, 258, 70
..., doe || 6-dim-id || f-ike || doe axially-pyritohedral (2,24,12,6)-diminishing of ex 1.618034 76, 300, 356, 132
pox prico partially octa-expanded prismatorhombated icositetrachoron 768, 1728, 1200, 240
... tetracontadisdiminished ex 1.618034 78, 276, 300, 102
tewau thawrorh tetra-augmented thawro rhombochoron ... 78, 342, 410, 146
... f x3o3o, variation of tetrahedron prism, vertex figure of rectified hyperbolic hecatonicosachoric honeycomb 1.014647 8, 16, 14, 6
... q x3o3o, variation of tetrahedron prism, vertex figure of rectified penteract 0.935414 8, 16, 14, 6
tepe, K-4.9 (alt: dycuf) tetrahedron prism, line || trip, square - square bi-wedge, digonal orthobicupolaic ring, vertex figure of rix, dyadic cupolafastegium 0.790569 8, 16, 14, 6
bidrap, K-4.8 bidiminished rectified pentachoron, antiduowedge, square - tetrahedral wedge, digonal gyrobicupolaic ring, {4} || tet, line || ortho trip 0.774597 8, 18, 17, 7
... longer antiduowedge, vertex figure of cellirhombated dodecateron 0.953463 8, 18, 17, 7
... vertex figure of lepidosphenary hexateron 0.921954 8, 18, 17, 7
hatho hemitesseractihemioctachoron 0.707107 8, 20, 20, 8
tript trigonal-prismatic (line-)tegum, trigonal-prismatic dipyramid ... 8, 21, 23, 10
... vertex figure of great dispinocellirhombated penteract 0.907821 8, 22, 24, 10
tedope tetra(hedrally) diminished octahedronal prism 0.866025 8, 22, 26, 12
koho skew octahemioctachoron 0.707107 8, 24, 28, 12
... vertex figure of cellihemidodecateron 0.866025 8, 24, 32, 12
... vertex figure of dodecabiprismatohemidodecateron 0.866025 8, 24, 32, 12
tho tesseractihemioctachoron, octahemioctachoron, vertex figure of hehad 0.707107 8, 24, 32, 12
... vertex figure of triacontadipenteract 0.935414 8, 24, 32, 12
... vertex figure of great facetosphenary penteract 0.776106 8, 24, 32, 16
hex, K-4.2 (alt: octit, trapt) hexadecachoron, tetracross (β4), orthoplex, hemitesseract, hemioctachoron, 16-cell, aeroter(id), tetrahedral antiprism, vertex figure of tac, (line-)octahedral tegum, (line-)trigonal-antirprismatic tegum, Gosset polytope 11,1, 8-3-stepprism, lattice C4 contact polytope (span of its small roots) 0.707107 8, 24, 32, 16
... vertex figure of quasicellated penteractitriacontiditeron 1.118034 8, 24, 32, 16
... xo3oo3ox&#q, longer variant of tetrahedral antiprism, vertex figure of scad 0.866025 8, 24, 32, 16
... vertex figure of great biprismatodiscellipenteract 1.118034 8, 28, 38, 18
... vertex figure of retrosphenary cellihexateron 0.921954 8, 28, 38, 18
odedip octagon-decagon duoprism 2.079697 80, 160, 98, 18
cyted srit cyclotetradiminished small rhombitesseract, cyclotetraugmented octagonal duoprism 1.847759 80, 208, 172, 44
dusidpith small-prismated-tesseractihexadecachoron dual, triangular antitegmatic hexacontatetrachoron 80, 208, 192, 64
doasrid, doe || srid, K-4.152 dodecahedron atop small rhombicosidodecahedron, dodecahedral cap of small disprismatohexacosihecatonicosachoron 5.236068 80, 210, 194, 64
... expanded augmented axially-octahedral ursachoron ofx3xoo4xxx&#xt 80, 216, 196, 60
raded adoe rhombidodecadodecahedron atop dodecahedron 1.432173 80, 240, 126, 56
arspabd biscrox around-symmetrically parabidiminished bistratic icosahedron-first cap of rectified hexacosachoron 3.077684 80, 260, 234, 54
... Shephard's 3-generalised tesseract, complex polychoron x3-4-o2-3-o2-3-o2 , γ3 4 81, 108, 54, 12
iktum bistratic icosahedron-first cap of truncated hexacosachoron, ike-based tutsatope, ike-based tutism 4.643523 84, 192, 142, 34
biscsrico bistratic cuboctahedron-first cap of small rhombated icositetrachoron 2.613126 84, 204, 156, 36
dirico diminished rectified icosatetrachoron 1.732051 84, 240, 198, 42
... ofoxFxo3xxFxoox3xoofxfo&#xt   (F=ff=x+f) 84, 318, 362, 128
... oxFxofo3xfoxFxx3ooxfoox&#xt   (F=ff=x+f) 84, 324, 370, 130
... triacontapenta-diminished hexacosachoron, fooo5ofxo xofx5oxox&#zx 1.618034 85, 335, 360, 110
... hexaconta-sphenated id-first deep parabidiminished rahi ... 860, 2520, 2180, 520
tisadi (alt.: idtex) truncated snub icositetrachoron, icositetradiminished truncated hexacosachoron 4.643523 864, 1872, 1248, 240
... tesseract-derived Gévay polychoron, rectified o4m3o3o ... 88, 288, 256, 56
4,2n-dip square - 2n-gon duoprism sqrt[1/2+1/(4 sin2(π/2n))] 8n, 16n, 10n+4, 2n+4
4,2n/d-dip square - 2n/d-gram duoprism sqrt[1/2+1/(4 sin2(πd/2n))] 8n, 16n, 10n+4, 2n+4
8,n-dip octagon - n-gonal duoprism sqrt[(2+sqrt(2))/2+1/(4 sin2(π/n))] 8n, 16n, 9n+8, n+8
(2,2n)-pap dyad - 2n-gon prismantiprismoid, s2s2s-2n-x, edge-alternated square - 4n-gon duoprism ... 8n, 20n, 18n+4, 6n+4
... n-fold dissected cubic polytwister, n-fold dissected cubiter, cubiswirlic 6n-choron ... 8n, 32n, 30n, 6n
triddip, K-4.10 triangle-triangle duoprism, triangle - trip wedge, vertex figure of dot, Delone cell of lattice A2×A2 0.816497 9, 18, 15, 6
cubpy, K-4.26 cubical pyramid, vertex-pyramid of ico 1 9, 20, 18, 7
etepy elongated tetrahedral pyramid 9, 20, 20, 9
shasc small heptagrammic scalene, small-heptagrammic-pyramidal pyramid, line atop fully orthogonal small heptagramm 0.658240 9, 22, 22, 9
autepe augmented tetrahedral prism 9, 22, 23, 10
traf, K-4.6 triangular antifastegium, triangle oct wedge, {3} || gyro trip, {3} || oct, (vertex-) diminished rap 0.774597 9, 24, 24, 9
... vertex figure of great pteroprismated penteract 0.837186 9, 24, 24, 9
... vertex figure of spikifacetospinodishexadecateron 0.951190 9, 24, 24, 9
... q-laced {3} || gyro trip, vertex figure of srix 0.907485 9, 24, 24, 9
... vertex figure of topax 0.907485 9, 24, 24, 9
squappy square-antiprismatical pyramid 0.879465 9, 24, 26, 11
... vertex figure of biprismatododecateron 0.816497 9, 36, 42, 15
... vertex figure of biprismatointercepted dodecateron 0.816497 9, 36, 45, 15
... vertex figure of cellidishexateron 0.816497 9, 36, 48, 15
... vertex figure of cellibiprismatohexateron 0.816497 9, 36, 48, 21
... vertex figure of great prismated biprismatopenteract 0.837186 9, 36, 48, 21
diddatigid, did || tigid dodecadodecahedron atop truncated great dodecahedron, did-first cap of sirfix 4.352502 90, 210, 138, 26
idati, id || ti, K-4.158 icosidodecahedron atop truncated icosahedron, icosidodecahedral cap of small rhombated hexacosachoron 6.073594 90, 210, 154, 34
resrip (alt.: amsrip) rectified/ambified srip 2.144761 90, 270, 230, 50
dida raded, did || raded dodecadodecahedron atop rhombidodecadodecahedron 1.336349 90, 300, 258, 56
idasrid, id || srid, K-4.131 icosidodecahedron atop small rhombicosidodecahedron, icosidodecahedron cupola, ike-first supra-cap of rox 3.077684 90, 300, 274, 64
... xfooo5xofxo oxofx5ooxox&#zx, icosapentadiminished ex 95, 445, 600, 250
cotcope cuboctatruncated-cuboctahedron prism, cubitruncated-cuboctahedron prism 1.414214 96, 192, 112, 22
otwadip octagon - dodecagon duoprism 2.332200 96, 192, 116, 20
tah tesseractihexadecachoron, bitruncated tesseract, bitruncated hexadecachoron, runcicantic tesseract 2.121320 96, 192, 120, 24
gircope, K-4.125 great-rhombicuboctahedron prism 2.370932 96, 192, 124, 28
quitcope quasitruncated-cuboctahedron prism 1.174172 96, 192, 124, 28
sircoa gircotum bistratic cap of prismatorhombated tesseract, rhombicuboctahedral rotunda, (sirco,girco)-based tutschoron, (sirco,girco)-based tutism 2.370932 96, 216, 154, 34
tica gircobcu ticagirco bicupola 96, 240, 198, 54
toagircoatic toe atop girco atop tic 96, 240, 198, 54
gaqript grand quasirhombated prismatotesseract 0.765367 96, 288, 192, 32
garpit grand rhombated dishexadecachoron 1.847759 96, 288, 192, 32
rawvatoth retrosphenoverted tesseractitesseractihexadacachoron 1.847759 96, 288, 200, 32
wavitoth sphenoverted tesseractitesseractihexadecachoron 0.765367 96, 288, 200, 32
rawvhitto retrosphenoverted hexadecatesseractioctachoron 1.732051 96, 288, 208, 32
frico facetorectified icositetrachoron 1.732051 96, 288, 240, 48
rico rectified icosatetrachoron, cantellated hexadecachoron, hexadecachoron-derived Gévay polychoron 1.732051 96, 288, 240, 48
... o3q3o4x, variation of srit 2.236068 96, 288, 248, 56
rerit o3x3o4q, rectified rectified-tesseract, variation of srit 2.236068 96, 288, 248, 56
qrit quasirhombated tesseract 0.765367 96, 288, 248, 56
srit small rhombated tesseract, cantellated tesseract 1.847759 96, 288, 248, 56
gapript great pseudorhombated prismatotesseract 0.765367 96, 288, 256, 64
spript small pseudorhombated prismatotesseract 1.847759 96, 288, 256, 64
bipgy srit bipara(bi)gyrated small rhombitesseract, pseudo cantellated tesseract 1.847759 96, 288, 260, 68
bicyte gysrit bicyclotetragyrated small rhombitesseract 1.847759 96, 288, 264, 72
cyte gysrit cyclotetragyrated small rhombitesseract 1.847759 96, 288, 264, 72
ini icositetrintercepted icositetrachoron 1.732051 96, 288, 336, 48
pinpith prismatointercepted prismatotesseractihexadecachoron 1.847759 96, 288, 344, 80
pybiscrox pyritohedral bistratic icosahedron-first cap of rectified hexacosachoron 3.077684 96, 330, 318, 84
... o3x3β4o (?) ... 96, 336, 256, 56
... o3β3x4o (?) ... 96, 384, 264, 48
... x3o3β4o (?) ... 96, 384, 304, 56
... cubiswirlic heptacontidichoron, twelvefold dissected cubic polytwister, twelvefold dissected cubiter 1.538189 96, 384, 360, 72
... β3β3x *b3o (?) ... 96, 432, 368, 72
... aoc3ooo3cao *b3oca&#zd sqrt[(a2+ac+c2)/2] 96, 432, 480, 144
rasdi retrosnub icositetrachoron, retrosnub disicositetrachoron 0.618034 96, 432, 480, 144
sadi   (alt.: idex) snub icositetrachoron, snub disicositetrachoron, semistruncated icositetrachoron, icositetradiminished hexacosachoron, snub rhombatohexadecachoron 1.618034 96, 432, 480, 144
... o3β3β4o (?) ... 96, 528, 544, 128
... o3β4o3o (?) ... 96, 576, 576, 168
... o3β3o4β (?) ... 96, 624, 608, 152
mesdi medial snub disicositetrachoron 1 96, 720, 864, 144
rappisdi retroantiprismatosnub disicositetrachoron 1 96, 720, 864, 144
disdi disnub disicositetrachoron 1 96, 816, 1248, 240
poc gippic partially octa-contracted great prismatotetracontoctachoron 960, 2016, 1296, 240
tidimex (alt.: idimtex) truncated icosidiminished hexacosachoron, icosidiminished truncated hexacosachoron 4.643523 960, 2280, 1640, 320
... BAVFfxoo xFofxFVo3xxFxooxo5xooxFfoV&#zx 980, 3120, 2780, 640
n-sc, n-pyr-pyr {n}-scalene, {n}-pyramidal pyramid, n tet rosette, line atop fully orthogonal {n} sqrt[(4 sin2(π/n)-1)/(3 sin2(π/n)-1)]/2 n+2, 3n+1, 3n+1, n+2
n,n-dip n-gon - n-gon duoprism 1/(sqrt(2) sin(π/n)) n2, 2n2, n2+2n, 2n
n,m-dip n-gon - m-gon duoprism sqrt[1/(4 sin2(π/n))+1/(4 sin2(π/m))] nm, 2nm, nm+n+m, n+m
n/d,m/b-dip n/d-gram - m/b-gram duoprism sqrt[1/(4 sin2(π d/n))+1/(4 sin2(π b/m))] nm, 2nm, nm+n+m, n+m
... complex polychoron sp-4-o2-3-o2-3-o2 , (γp 4)/p p3, 6p3, 2p2(2p+3), p(p2+4)
... Shephard's p-generalised tesseract, complex polychoron xp-4-o2-3-o2-3-o2 , γp 4 p4, 4p3, 6p2, 4p

Count of actually available polytopes: 1440


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 5D
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Acronym Name Circumradius Face vector
penp pentachoron prism, vertex figure of ril 0.806226 10, 25, 30, 20, 7
... q x3o3o3o, variation of pentachoron prism, vertex figure of rectified hexeract 0.948683 10, 25, 30, 20, 7
triddippy trigonal-duoprismatic pyramid, vertex pyramid of the dodecateron 0.866025 10, 27, 33, 21, 7
cubasc (degenerate) cubical scalene, line atop fully orthogonal cube ∞   i.e. flat in euclidean space 10, 29, 38, 25, 8
editetaf edge-diminished tetaf, (top base) edge-diminishing of tet-first rotunda of hin 0.790569 10, 29, 38, 25, 8
squasquasc {4} atop squasc 0.790569 10, 29, 38, 25, 8
trafpy triangular antifastegium pyramid, (triangular prism, gyro triangular pyramid)-disphenoid 0.790569 10, 33, 48, 33, 10
..., {5} || perp {5/2} (degenerate) pentagon atop fully perpendicular pentagram ∞   i.e. flat in euclidean space 10, 35, 52, 35, 10
stadow pentagrammic disphenoid, pentagram atop fully orthogonal pentagram 0.623054 10, 35, 52, 35, 10
hehad hexadecahemidecateron, vertex figure of thox 0.707107 10, 40, 80, 80, 21
tac triacontiditeron, pentacross (β5), aeropet(id), pentachoral antiprism, vertex figure of gee, Gosset polytopes 21,1, lattice C5 contact polytope (span of its small roots) 0.707107 10, 40, 80, 80, 32
... xo3oo3oo3ox&#q, longer variant of pentachoral antiprism, vertex figure of staf 0.866025 10, 40, 80, 80, 32
pedoe pentagon-dodecahedron duoprism 1.639247 100, 250, 230, 95, 17
pabex rat partially biexpanded rectified triacontiditeron ... 100, 528, 852, 504, 82
5,n-dippip pentagon - n-gon duoprismatic prism sqrt[(15+2 sqrt(5))/20+1/(4 sin2(π/n))] 10n, 25n, 22n+10, 8n+15, n+7
penatrip pentachoron atop trigonal prism, (edge,perp triangle,trip)-trigonic 1 11, 31, 39, 25, 8
squippyippy square-pyramidal-prismatic pyramid, half of vertex pyramid of rectified triacontiditeron 1 11, 31, 39, 25, 8
ditetaf (alt.: traltepe, penaltrip) diminished tetaf, triangle atop gyrated tepe, pen atop gyrated trip, (edge,perp triangle,gyro trip)-trigonic 0.790569 11, 37, 54, 37, 11
rappy rectified-pentachoric pyramid, vertex cap of hin 0.790569 11, 40, 60, 40, 11
ritathexu rit-based ursateron 1.627127 112, 392, 456, 208, 34
..., tes || srit (degenerate) tes atop srit ∞   i.e. flat in euclidean space 112, 416, 560, 312, 58
pexnit partially expanded penteractitriacontiditeron ... 112, 608, 800, 360, 58
..., tes || sadi tes atop sadi ∞   i.e. flat in euclidean space 112, 656, 1176, 808, 178
gricope (old: gripe) great-rhombated-icositetrachoron prism, cantitruncated-icositetrachoron prism 4.328427 1152, 2880, 2592, 1008, 146
pricope (old: pripe) prismatorhombated-icositetrachoron prism, runcitruncated-icositetrachoron prism 3.534493 1152, 3456, 3648, 1584, 242
gricoa (old: gricoalgrico) great-rhombated-icositetrachoron alterprism, great-rhombated-icositetrachoron atop alternate great-rhombated-icositetrachoron 4.311477 1152, 3456, 3744, 1680, 242
..., prico || gyro grico (degenerate) prico atop gyrated grico ∞   i.e. flat in euclidean space 1152, 3744, 4128, 1776, 242
ditdia disicositetratruncated-disicositetrachoron alterprism 2.352869 1152, 4032, 3936, 1296, 98
sutia small-tetrakisicositetrachoron alterprism 1.677756 1152, 4032, 4224, 1440, 98
pricoa (old: pricoalprico) prismatorhombated-icositetrachoron alterprism, prismatorhombated-icositetrachoron atop alternate prismatorhombated-icositetrachoron 3.522336 1152, 4032, 4512, 1872, 242
tratet (alt.: tettet tettric) triangle - tetrahedron duoprism, triangle duofastegium, vertex figure of bril, (tet,tet,tet)-trigonic 0.841625 12, 30, 34, 21, 7
squascop squasc prism, square-scalene prism, square atop cube 0.866025 12, 32, 39, 25, 8
tetcubedaw (alt.: daworsquip) (tet,cube)-disphenoid, 1/6-lune of dodecateron, digonal antiprism atop axis-orthogonal square prism 0.866025 12, 34, 42, 26, 8
tedrix tridiminished rectified hexateron, square triorthowedge, lace simplex of 3 mutually orthogonal squares 0.816497 12, 36, 47, 30, 9
... vertex figure of spil 0.924211 12, 39, 52, 33, 10
trial triddip {3} atop gyrated triddip, {3}-first cap of rix 0.816497 12, 39, 52, 33, 10
triddaf triangular duoantifastegium, digonal-triangular duoantiwedge, trip atop bidual trip 0.790569 12, 42, 58, 36, 10
tedhin tetradiminished hemipenteract, square || hex 0.790569 12, 44, 73, 56, 17
tetaf (alt.: tetaltepe, tettet altettric) tetrahedral antifastegium, tet atop inverted tepe, tet-first rotunda of hin, (tet,tet,dual tet)-trigonic 0.790569 12, 46, 78, 59, 17
rapt rectified-pentachoric (line-)tegum, rectified-pentachoric dipyramid ... 12, 50, 90, 70, 20
bidot bidodecateron, triangular duotegmatic icosateron, triangular duotegmatic alterprism, dodecateron dual 0.790569 12, 60, 120, 90, 20
hadoe hexagon - dodecahedron duoprism 1.721489 120, 300, 272, 108, 18
grippip great-rhombated-pentachoron prism 1.910497 120, 300, 280, 120, 22
garx great rhombated hexateron, cantitruncated hexateron 2 120, 300, 290, 135, 27
ticca gircope truncated-cube atop great-rhombicuboctahedron-prism 3.239235 120, 324, 330, 153, 29
prippip prismatorhombated-pentachoron prism 1.688194 120, 360, 390, 180, 32
squid square-icosidodecahedron duoprism 1.765796 120, 360, 398, 192, 36
pripagrip prip atop grip 1.870829 120, 390, 440, 200, 32
pripalgrip prip atop alternate grip 1.848423 120, 390, 440, 200, 32
racpix retrocelliprismated hexateron 1.632993 120, 420, 450, 195, 33
sripal pripu (srip,inv.prip)-based ursateron 1.637956 120, 420, 480, 210, 32
pripa (old: pripalprip) prip alterprism, prip atop inverted prip, medial segment of card 1.658312 120, 420, 480, 210, 32
cappix (old: happix) celliprismated hexateron, cellitruncated hexateron, hedratoprismated hexateron, steritruncated hexateron 1.632993 120, 420, 570, 330, 62
..., ico || srit (degenerate) ico atop srit ∞   i.e. flat in euclidean space 120, 480, 632, 328, 58
icarico (degenerate) ico atop rico ∞   i.e. flat in euclidean space 120, 576, 720, 312, 50
rescad rectified scad 1.732051 120, 720, 1170, 660, 92
..., ico || sadi ico atop sadi ∞   i.e. flat in euclidean space 120, 816, 1584, 1128, 242
gogiship great-grand-stellated-hecatonicosachoron prism 0.736068 1200, 3000, 2640, 960, 122
hipe hecatonicosachoron prism 3.736068 1200, 3000, 2640, 960, 122
gadtaxhiap grand ditetrahedrary hexacontahecatonicosachoron antiprism 0.951057 1200, 9600, 13440, 6960, 1322
sidtaxhiap small ditetrahedrary hexacontahecatonicosachoron antiprism 2.321762 1200, 9600, 13440, 6960, 1322
gadtaxadiap grand ditetrahedronary hexacosadishecatonicosachoron atop alternate grand ditetrahedronary hexacosadishecatonicosachoron, grand ditetrahedronary hexacosadishecatonicosachoron alterprism 0.951057 1200, 9600, 14880, 7920, 1442
sirdtaxadiap small retroditetrahedronary hexacosidishecatonicosachoron atop alternate small retroditetrahedronary hexacosidishecatonicosachoron, small retroditetrahedronary hexacosidishecatonicosachoron alterprism 2.321762 1200, 9600, 14880, 7920, 1442
n,grid-dip n-gon - great-rhombicosidodecahedron duoprism sqrt[(31+12 sqrt(5))/4+1/(4 sin2(π/n))] 120n, 300n, 242n+120, 63n+180, n+62
gaghipy, pt || gaghi (degenerate) gaghi pyramid ∞   i.e. flat in euclidean space 121, 1320, 1920, 840, 121
sishipy, pt || sishi (degenerate) sishi pyramid ∞   i.e. flat in euclidean space 121, 1320, 1920, 840, 121
gidtixhipy, pt || gidtixhi (degenerate) gidtixhi pyramid ∞   i.e. flat in euclidean space 121, 1320, 3600, 3120, 721
sidtixhipy, pt || sidtixhi (degenerate) sidtixhi pyramid ∞   i.e. flat in euclidean space 121, 1320, 3600, 3120, 721
quititip quasitruncated-tesseract prism 0.792893 128, 320, 304, 136, 26
tattip truncated-tesseract prism 2.207107 128, 320, 304, 136, 26
ritatah, rit || tah (degenerate) rit atop tah ∞   i.e. flat in euclidean space 128, 384, 400, 168, 26
gittithip great-tesseractitesseractihexadecachoron prism 1.021221 128, 448, 464, 200, 34
stethip small-tesseractitesseractihexadecachoron prism 1.567516 128, 448, 464, 200, 34
sidpithip small-disprismatotesseractihexadecachoron prism, runcinated-tesseract prism, small-prismated-tesseract prism, central segment of scant 1.567516 128, 448, 608, 368, 82
pextot partially expanded truncated triacontaditeron ... 128, 448, 616, 352, 58
ritarico rectified-tesseract atop rectified-icositetrachoron, rectified-tesseract-first segment of small-prismated-triacontiditeron 1.870829 128, 480, 616, 312, 50
..., sidpith || tat (degenerate) sidpith atop tat ∞   i.e. flat in euclidean space 128, 512, 776, 472, 82
ritasrit, rit || srit rectified-tesseract atop small-rhombated-tesseract 2.632865 128, 576, 720, 328, 58
n,tut-dip n-gon - truncated-tetrahedron duoprism sqrt[11/8+1/(4 sin2(π/n))] 12n, 30n, 26n+12, 9n+18, n+8
n,co-dip n-gon - cuboctahedron duoprism sqrt[1+1/(4 sin2(π/n))] 12n, 36n, 38n+12, 15n+24, n+14
n,ike-dip n-gon - icosahedron duoprism sqrt[(5+sqrt(5))/8+1/(4 sin2(π/n))] 12n, 42n, 50n+12, 21n+30, n+20
tisdippy triangle-square-duoprism pyramid, vertex pyramid of nit 1.224745 13, 36, 43, 26, 8
opepy octahedral-prismatic pyramid, vertex pyramid of rectified triacontiditeron 1 13, 42, 58, 38, 11
bidrix bidiminished rectified hexateron 0.816497 13, 44, 59, 36, 10
roxahi, rox || hi (degenerate) rox atop hi ∞   i.e. flat in euclidean space 1320, 8400, 15120, 9960, 1922
trippyp trigonal-prismatic pyramid prism, lacing edge cap of the rectified-pentachoron prism 0.921954 14, 37, 43, 26, 8
cubasquasc cube atop squasc 1 14, 41, 51, 31, 9
octpyp, line||ope octahedron-prismatic wedge, line atop ope, octahedral-pyramid prism, half of hexip 0.866025 14, 43, 58, 38, 11
octatepe (alt.: tettet octtric) oct atop tepe, diminished rix, (tet,tet,oct)-trigonic 0.816497 14, 52, 70, 41, 11
bostarpglassdit bowtie - pentagrammic-retroprismatic-hourglass duotegum 0.707107 14, 52, 72, 43, 11
opet octahedral-prism tegum, (line, octahedral prism) duotegum ... 14, 54, 88, 66, 20
sissidisc small-stellated-dodecahedral scalene, small-stellated-dodecahedral-pyramid pyramid, line atop fully orthogonal small stellated dodecahedron 0.636010 14, 55, 84, 55, 14
bidhin (alt.: octahex, tetalrap, tetaltet octtric) bidiminished hemipenteract, oct || hex, tet || inverted rap, (tet,dual tet,oct)-trigonic 0.790569 14, 60, 100, 69, 17
shadow small heptagrammic disphenoid, small heptagramm atop fully orthogonal small heptagramm 0.674163 14, 63, 100, 63, 14
hatic (old: hittic) hexagon truncated-cube duoprism 2.040640 144, 360, 324, 126, 20
hatoe (old: hittoe) hexagon truncated-octahedron duoprism 1.870829 144, 360, 324, 126, 20
tragirco triangle - great-rhombicuboctahedron duoprism 2.388442 144, 360, 342, 153, 29
thexagtah thex atop gyrated tah 2.371708 144, 408, 408, 168, 26
hasirco (old: hissirco) hexagon small-rhombicuboctahedron duoprism 1.719624 144, 432, 468, 210, 32
thexatah (degenerate) thex atop tah ∞   i.e. flat in euclidean space 144, 504, 600, 288, 50
icou icositetrachoron-based ursateron, ico-based ursulate, vertex figure of s3s4o3o4o3o 1.738546 144, 600, 720, 312, 50
thexarico thex atop rico, ico-first subsegment of sart 1.732051 144, 600, 720, 312, 50
pexgyetac partially expanded gyroelongated-triacontaditeron ... 144, 624, 816, 392, 58
ragashia rectified grand stellated hecatonicosachoron alterprism 1.248606 1440, 10800, 11520, 3360, 242
righia rectified great hecatonicosachoron alterprism 1.917564 1440, 10800, 11520, 3360, 242
dittadiu dittady-based ursateron 1.008123 1440, 10920, 16080, 5880, 362
gidtixhiu gidtixhi-based ursateron 1.008123 1440, 10920, 17040, 7800, 842
sidtixhiu sidtixhi-based ursateron 1.008123 1440, 10920, 17040, 7800, 842
sophip small-prismatohecatonicosachoron prism 3.118034 1440, 7920, 10080, 4920, 842
roxip rectified-hexacosachoron prism 3.118034 1440, 7920, 10800, 5040, 722
grixip great-rhombated-hexacosachoron prism 9.137791 14400, 36000, 31680, 11520, 1442
grahip (old: grahipe) great-rhombated-hecatonicosachoron prism, cantitruncated-hecatonicosachoron prism 11.263210 14400, 36000, 32640, 12960, 1922
prahip (old: prahipe) prismatorhombated-hexacosachoron prism, runcitruncated-hexacosachoron prism 8.294035 14400, 43200, 44880, 18720, 2642
prixip prismatorhombated-hexacosachoron prism, runcitruncated-hexacosachoron prism 9.757429 14400, 43200, 44880, 18720, 2642
..., grix || prix (degenerate) grix atop prix ∞   i.e. flat in euclidean space 14400, 46800, 50880, 21120, 2642
..., prahi || grix (degenerate) prahi atop grix ∞   i.e. flat in euclidean space 14400, 46800, 50880, 21120, 2642
pirghia prismatorhombated great hecatonicosachoron alterprism 4.923348 14400, 50400, 51840, 18480, 1682
sphiddixa small prismatohecatonicosadishexacosachoron alterprism 6.893126 14400, 50400, 53280, 19920, 2042
tisquippy triangle-squippy douprism, half of troct, (triangle,trip,trip)-trigonic 0.912871 15, 39, 44, 26, 8
pexhix (alt.: triddipah, tripotricudaw) partially expanded hexateron, triangle-triangle duoprism atop hexagon, (trip, ortho tricu)-disphenoid 1 15, 42, 52, 33, 10
tripgytricudaw (trip, gyro tricu)-disphenoid 1 15, 48, 61, 36, 10
taope triangle atop octahedral-prism 0.866025 15, 51, 68, 41, 11
traltisdip triangle atop gyrated tisdip 1 15, 51, 68, 41, 11
firx facetorectified hexateron 0.816497 15, 60, 105, 90, 31
rix rectified hexateron, vertex figure of hax, Gosset polytope 03,1 0.816497 15, 60, 80, 45, 12
dihin (alt.: penalrap) (vertex-)diminished hemipenteract, pentachoron atop alternate rectified pentachoron 0.790569 15, 70, 130, 95, 22
..., deca || gippid (degenerate) deca atop gippid ∞   i.e. flat in euclidean space 150, 420, 430, 190, 32
pid pentagon - icosidodecahedron duoprism 1.828016 150, 450, 490, 225, 37
pabexnit partially biexpanded penteractitriacontiditeron ... 152, 752, 968, 440, 74
pabac span partially bicontracted small prismated penteract ... 152, 756, 1192, 700, 114
..., fix || padohi (degenerate) fix atop padohi ∞   i.e. flat in euclidean space 1560, 9360, 15840, 9720, 2162
gofixa quipdohi (degenerate) gofix atop quipdohi ∞   i.e. flat in euclidean space 1560, 9360, 15840, 9720, 2162
squatet square-tetrahedron duoprism, square duofastegium, 2,4-duoprism cupoliprism, vertex figure of brox 0.935414 16, 40, 44, 26, 8
tepacube tepe || cube, bidrap prism, bi-edge-dimin. rappip, wedge-faceted rappip 0.921954 16, 44, 52, 31, 9
teddot tetradiminished dodecateron, bidrap alterprism, bidrap atop gyroinverted bidrap 0.866025 16, 54, 78, 54, 16
squiddaf square duoantifastegium, digonal-square duoantiwedge, square prism atop bidual square prism 0.895420 16, 56, 76, 46, 12
hexip hexadecachoron prism, vertex figure of rag 0.866025 16, 56, 88, 64, 18
teta ope (alt.: octarap, tetoct octtric) tetrahedron atop octahedron-prism, octahedron atop rectified-pentachoron, half of dodecateron (its tet-first rotunda), (tet,oct,oct)-trigonic 0.866025 16, 60, 80, 45, 11
hin hemipenteract, demipenteract, hemitesseractic gyroprism, tetrahedral altersquarism, vertex figure of jak, Gosset polytope 12,1 0.790569 16, 80, 160, 120, 26
dah dishexadecateron, vertex figure of kaje 0.790569 16, 80, 160, 120, 32
han hexadecapenteract, vertex figure of daj 0.790569 16, 80, 160, 160, 26
hit hexadecateron 0.790569 16, 80, 220, 120, 16
radah retrodishexadecateron 0.790569 16, 80, 220, 160, 32
rinah retropenteractihexadecateron 0.790569 16, 80, 220, 200, 26
odoe octagon - dodecahedron duoprism 1.915889 160, 400, 356, 134, 20
quittin quasitruncated penteract 0.649286 160, 400, 400, 200, 42
tan truncated penteract 2.465447 160, 400, 400, 200, 42
thin truncated hemipenteract, cantic penteract 1.903943 160, 560, 640, 280, 42
quacant quasicellated penteractitriacontiditeron 1.021221 160, 640, 1040, 800, 242
scant small cellated penteractitriacontiditeron, stericated penteract, stericated pentacross 1.567516 160, 640, 1040, 800, 242
gabdacan great biprismatodiscellipenteract 1.021221 160, 640, 1120, 840, 210
ginnont great penteractipenteractitriacontiditeron 1.021221 160, 640, 640, 280, 52
sinnont small penteractipenteractitriacontiditeron 1.567516 160, 640, 640, 280, 52
kafandoh spikifacetospinodishexadecateron 1.620185 160, 720, 800, 280, 32
sirhin small rhombihemipenteract, cantellated demipenteract, runcic penteract 1.620185 160, 720, 880, 360, 42
..., ico || spic (degenerate) ico atop spic ∞   i.e. flat in euclidean space 168, 816, 1344, 936, 242
... tetrahedral - 2n-prismantiprismoid ... 16n, 64n, 100n+8, 64n+12, 12n+6
tespy (degenerate) tes pyramid ∞   i.e. flat in euclidean space 17, 48, 56, 32, 9
... point || hex || gyro hex, Dutour polyteron type A 17, 88, 184, 144, 33
..., grico || gippic (degenerate) grico atop gippic ∞   i.e. flat in euclidean space 1728, 4608, 4416, 1776, 242
tratrip (old: triddippip) triangle triangular-prism duoprism, triangle-triangle duoprismatic prism, vertex figure of ram 0.957427 18, 45, 48, 27, 8
cubpyp cubpy prism 1.118034 18, 49, 56, 32, 9
triphipdaw (alt.: tripalhip) (trip,hip)-disphenoid, trip atop lacing-orthogonal hip 1.274755 18, 51, 61, 36, 10
octhipdaw (alt.: traporhip) (oct,hip)-disphenoid, trigonal antiprism atop axis-orthogonal hexagonal prism 1.224745 18, 54, 64, 36, 10
troct (alt.: octoct octtric) triangle-octahedron duoprism, vertex figure of brag, (oct,oct,oct)-trigonic 0.912871 18, 54, 66, 39, 11
tisdipah tisdip atop hexagon 1 18, 54, 68, 41, 11
traffip traf prism, trip atop inverted tisdip 0.921954 18, 57, 72, 42, 11
opeah ope atop hexagon, (trip,gyro trip,hexagon)-trigonic 1 18, 60, 77, 44, 11
tridafup (alt.: pabdidot) triangular duoantifastegiaprism, triangular duoantiwedge, triddip atop bidual triddip, central segment of vertex first dot, parabidiminished dot 0.866025 18, 72, 102, 60, 14
pex tac partially expanded triacontaditeron ... 18, 72, 136, 128, 48
gyetac gyroelongated triacontaditeron ... 18, 96, 208, 168, 40
gibrid (old: gadrid) great birhombated dodecateron, bicantitruncated hexateron 2.179449 180, 450, 420, 180, 32
trati triangle - truncated-icosahedron duoprism 2.544388 180, 450, 426, 189, 35
tratid triangle - truncated-dodecahedron duoprism 3.025056 180, 450, 426, 189, 35
gripagippid grip atop gippid, grip-first cap of cograx 2.327373 180, 480, 470, 200, 32
pripa gippid prip atop gippid, prip-first cap of pattit 2.738613 180, 510, 510, 210, 32
sripa gippidtum srip-first bistratic cap of pithin, (srip,gippid)-based tutsateron, (srip,gippid)-based tutism 2.371708 180, 510, 510, 210, 32
rapirx retroprismatorhombated hexateron 1.914854 180, 540, 540, 225, 38
pripal gripu (prip,grip)-based ursateron 1.904375 180, 540, 570, 245, 37
pirx prismatorhombated hexateron, runcicantellated hexateron 1.914854 180, 540, 570, 255, 47
hid hexagon icosidodecahedron duoprism 1.902113 180, 540, 582,258, 38
trasrid triangle - small-rhombicosidodecahedron duoprism 2.306383 180, 540, 606, 309, 65
pattix prismatotruncated hexateron, runcitruncated hexateron 1.848423 180, 630, 720, 315, 47
trasnid triangle - snub-dodecahedron duoprism 2.231808 180, 630, 786, 429, 95
recard retrocellirhombated dodecaateron 1.658312 180, 720, 780, 300, 44
rocrax (old: sircrax) (small) retrocellirhombated hexateron 1.658312 180, 720, 840, 360, 53
card (old: scard, shard) (small) cellirhombated dodecateron, small hedratorhombated dodecateron, stericantellated hexateron 1.658312 180, 720, 900, 420, 62
hiarahi, hi || rahi (degenerate) hi atop rahi ∞   i.e. flat in euclidean space 1800, 7200, 8640, 3960, 722
ricoasadi rico atop sadi 1.738546 192, 1008, 1584, 912, 146
otic (old: ottic) octagon - truncated-cube duoprism 2.207107 192, 480, 424, 156, 22
otoe (old: otto) octagon truncated-octahedron duoprism 2.051123 192, 480, 424, 156, 22
stotoe octagram truncated-octahedron duoprism, star-octagon truncated-octahedron duoprism 1.671195 192, 480, 424, 156, 22
tahp tesseractihexadecachoron prism, bitruncated-tesseract prism, bitruncated-hexadecachoron prism 2.179449 192, 480, 432, 168, 26
squagirco square great-rhombicuboctahedron duoprism 2.423081 192, 480, 440, 180, 30
osirco octagon small-rhombicuboctahedron duoprism 1.914214 192, 576, 616, 264, 34
taha (old: tahagtah), tah || gyro tah tah alterprism, tah atop gyro tah 2.150581 192, 576, 624, 288, 50
ricatah rico atop tah, rico-first cap of sibrant 2.236068 192, 672, 744, 312, 50
ricope rectified-icositetrachoron prism 1.802776 192, 672, 768, 336, 50
srittip small-rhombated-tesseract prism 1.914214 192, 672, 784, 360, 58
ricoa (old: ricoalrico), rico || gyro rico rectified icositetrachoron alterprism, rectified icositetrachoron atop gyrated rectified icositetrachoron 1.778824 192, 864, 1056, 432, 50
ricasrit, rico || srit rectified-icositetrachoron atop small-rhombated-tesseract 1.847759 192, 960, 1256, 568, 82
sadip snub-icositetrachoron prism, snub-disicositetrachoron prism, semistruncated-icositetrachoron prism 1.693527 192, 960, 1392, 768, 146
pysnan pyritosnub penteract, edge-alternation of great cellated penteractitriacontiditeron ... 1920, 10560, 15360, 7920, 1202
snan snub penteract, alternation of great cellated penteractitriacontiditeron ... 1920, 13440, 21600, 12240, 2162
gadinnert great dispenteractirhombated triacontaditeron 2.336045 1920, 4800, 3760, 1080, 92
sadinnert small dispenteractirhombated triacontaditeron 2.010695 1920, 4800, 3760, 1080, 92
noqrant penteractiquasirhombated penteractitriacontaditeron 1.849749 1920, 4800, 4000, 1320, 132
nurrant penteractirhombated penteractitriacontaditeron 3.013043 1920, 4800, 4000, 1320, 132
gippit great prismated triacontiditeron, omnitruncated hemipenteract 3.872983 1920, 4800, 4160, 1440, 162
gaquapan great quasiprismated penteract 2.527061 1920, 4800, 4240, 1530, 202
gippin great prismated penteract, runcicantitruncated penteract 4.371952 1920, 4800, 4240, 1560, 202
narptint penteractiretroprismatotruncated penteractitriacontaditeron 2.621320 1920, 5760, 5200, 1600, 142
noqraptant penteractiquasiretroprismatotruncated penteractitriacontaditeron 1.621320 1920, 5760, 5200, 1600, 142
gibcotdin great biprismatocellitriacontadiadispenteract 2.001839 1920, 5760, 5440, 1840, 172
gircaptint (old: grecaptint) great retrocelliprismatotruncated penteractitriacontaditeron 1.949424 1920, 5760, 5440, 1840, 172
sibcotdin small biprismatocellitriacontadiadispenteract 3.534493 1920, 5760, 5440, 1840, 172
sircaptint (old: srecaptint) small retrocelliprismatotruncated penteractitriacontaditeron 3.701317 1920, 5760, 5440, 1840, 172
naquiptant penteractiquasiprismatotruncated penteractitriacontaditeron 1.621320 1920, 5760, 5520, 1920, 172
niptant penteractiprismatotruncated penteractitriacontaditeron 2.621320 1920, 5760, 5520, 1920, 172
gorcrin great retrocelligreat rhombated penteract 2.143163 1920, 5760, 5680, 2080, 212
srocgrin small retrocelligreat rhombated penteract 3.988340 1920, 5760, 5680, 2080, 212
captint celliprismatotruncated penteractitriacontiditeron, steriruncitruncated penteract, steriruncitruncated pentacross 3.701317 1920, 5760, 5760, 2160, 242
quicpatint quasicelliprismatotruncated penteractitriacontiditeron 1.949424 1920, 5760, 5760, 2160, 242
cogart (old: gocart) celligreatorhombated triacontiditeron, (great cellirhombated triacontiditeron), stericantitruncated pentacross 3.534493 1920, 5760, 5920, 2320, 242
quicgrat (old: cogqrit) quasicelligreat rhombated triacontiditeron, (celligreat quasirhombated triacontiditeron) 2.001839 1920, 5760, 5920, 2320, 242
cogrin (old: gocrin) celligreatorhombated penteract (great cellirhombated penteract), stericantitruncated penteract 3.988340 1920, 5760, 6000, 2400, 242
quacgarn quasicelligreatorhombated penteract 2.143163 1920, 5760, 6000, 2400, 242
petet pentagon-tetrahedron duoprism, pentagon duofastegium 1.048144 20, 50, 54, 31, 9
squasquippy square-squippy duoprism, squippyp prism 1 20, 52, 57, 32, 9
tepatut (alt.: tettet tuttric) tepe atop tut, tepe-first wedge of siphin, (tet,tet,tut)-trigonic 1.274755 20, 58, 70, 41, 11
tepaco (alt.: tettet cotric) tepe atop co, 0.217953-luna of scad, (tet,tet,co)-trigonic, partial Stott expansion of hix 1 20, 64, 88, 59, 17
penu pentachoron-based ursateron, pen-based ursulate, vertex figure of o3o3o3o4s3s 1.029086 20, 65, 80, 45, 12
cutep cubical-tegum prism, prism of tepepy ... 20, 66, 88, 54, 14
... squap - square duoprism, {4}-wedge of tessap 1.050501 20, 68, 89, 52, 13
rappip rectified-pentachoron prism, vertex figure of rojak 0.921954 20, 70, 90, 50, 12
hexaco hexadecachoron atop cuboctahedron, 0.147584-luna of rectified triacontiditeron 1 20, 72, 106, 68, 17
dot (alt.: rapa) dodecateron, birectified hexateron, equatorial cross-section of (vertex first) 1/q-ax, rap alterprism, rap atop inverted rap, vertex figure of mo, Gosset polytope 02,2 0.866025 20, 90, 120, 60, 12
cubaope cube atop octahedral-prism 0.895420 20, 90, 154, 111, 29
bad biprismatododecateron 0.866025 20, 90, 210, 150, 32
bend biprismatointercepted dodecateron 0.866025 20, 90, 210, 150, 32
caddix cellidishexateron 0.866025 20, 90, 210, 165, 27
cabbix cellibiprismatohexateron 0.866025 20, 90, 210, 165, 41
gappip great-antiprism prism 1.693527 200, 1100, 1940, 1360, 322
pabextot partially biexpanded truncated triacontaditeron ... 200, 700, 936, 516, 82
pabac sirn partially bicontracted small rhombated penteract ... 200, 912, 1144, 520, 90
n,doe-dip n-gon - dodecahedron duoprism sqrt[(9+3 sqrt(5))/8+1/(4 sin2(π/n))] 20n, 50n, 42n+20, 13n+30, n+12
trathiddip triangle atop thiddip, triangle-first cap of sarx 1.290994 21, 57, 64, 36, 10
triddipa hip triddip atop hip, (triangle,trip,hip)-trigonic 1.190238 21, 60, 71, 41, 11
trial tricupe triangle atop gyrated tricupe, (triangle,gyro trip,hip)-trigonic 1.224745 21, 66, 80, 44, 11
spidpy (degenerate) spid pyramid ∞   i.e. flat in euclidean space 21, 80, 130, 100, 31
..., padohi || rofix (degenerate) padohi atop rofix ∞   i.e. flat in euclidean space 2160, 18000, 28080, 14880, 2162
..., rigfix || quipdohi (degenerate) rigfix atop quipdohi ∞   i.e. flat in euclidean space 2160, 18000, 28080, 14880, 2162
rapatut (alt.: tetoct tuttric) rap atop tut, (tet,oct,tut)-trigonic 1.190238 22, 72, 86, 45, 11
rapaco (alt.: tetoct cotric) rap atop co, 0.176208-luna of rat, (tet,oct,co)-trigonic 1 22, 90, 128, 75, 17
pac span partially contracted small prismated penteract ... 224, 1056, 1624, 944, 154
gippiccup great-prismatotetracontoctachoron prism, omnitruncated-icositetrachoron prism 5.194028 2304, 5760, 5088, 1872, 242
opeaco octahedron-prism atop cuboctahedron, diminished 1/4-lune of rat 1 24, 102, 138, 75, 17
tessap tesseract antiprism, hexadecachoron antiprism 1.050501 24, 120, 248, 232, 82
... triangular,tetrahedral duoantiprism ... 24, 132, 248, 174, 36
tracube triangle - cube duoprism 1.040833 24, 60, 62, 33, 9
hatet (old: hittet, alt. hipdaw) hexagon-tetrahedron duoprism, hexagon duofastegium, hip disphenoid 1.172604 24, 60, 64, 36, 10
tricufip tricuf prism 1.118034 24, 66, 75, 42, 11
tripa thiddip trip atop thiddip, (hexagon,trip,hip)-trigonic 1.190238 24, 69, 80, 44, 11
opeatut (alt.: octoct tuttric) ope atop tut, (oct,oct,tut)-trigonic 1.190238 24, 72, 84, 45, 11
trawp (alt.: opea hip) traw prism, ope atop hip, 1/6-lune of icope 1.118034 24, 72, 84, 45, 11
squoct square-octahedron duoprism, vertex figure of brinoh 1 24, 72, 86, 48, 12
howoh hexadecasphenohexadecateron, cantellated hexadecahemidecateron 1.732051 240, 1200, 1440, 560, 71
sart small rhombated triacontiditeron, cantellated pentacross 1.732051 240, 1200, 1520, 640, 82
ricoaspic rectified icositetrachoron atop small prismated icositetrachoron 1.847759 240, 1440, 2352, 1392, 242
gohip great hexacosachoron prism 1.693527 240, 1560, 2160, 960, 122
exip hexacosachoron prism 1.693527 240, 1560, 3120, 2400, 602
gashia grand stellated hecatonicosachoron antiprism, grand stellated hecatonicosachoron alterprism, grand stellated hecatonicosachoron atop dual grand stellated hecatonicosachoron 0.707107 240, 2880, 8640, 6720, 1682
..., gaghi || gofix (degenerate) gaghi atop gofix, (degenerate) gaghi antiprism, (degenerate) gofix antiprism ∞   i.e. flat in euclidean space 240, 3360, 9120, 7680, 2162
..., sishi || fix (degenerate) sishi atop fix, (degenerate) sishi antiprism, (degenerate) fix antiprism ∞   i.e. flat in euclidean space 240, 3360, 9120, 7680, 2162
sishia small stellated hecatonicosachoron alterprism, narrower sishi atop sishi 1.074481 240, 3840, 8640, 3840, 362
gippiddip great-prismatodecachoron prism 2.291288 240, 600, 540, 210, 32
squati square - truncated-icosahedron duoprism 2.576932 240, 600, 548, 222, 36
squatid square - truncated-dodecahedron duoprism 3.052479 240, 600, 548, 222, 36
pripro prip-first rotunda of captid 2.236068 240, 660, 640, 255, 37
ictum (degenerate) ico-based tutsateron, ico-first bistratic "cap" of thext ∞   i.e. flat in euclidean space 240, 696, 720, 312, 50
bittit bitruncated triacontiditeron, Voronoi cell of lattice D5* 2.121320 240, 720, 720, 280, 42
oid octagon-icosidodecahedron duoprism 2.079697 240, 720, 766, 324, 40
squasrid square - small-rhombicosidodecahedron duoprism 2.342236 240, 720, 788, 372, 66
..., thex || prit (degenerate) thex atop prit ∞   i.e. flat in euclidean space 240, 792, 944, 472, 82
squasnid square - snub-dodecahedron duoprism 2.268840 240, 840, 1028, 522, 96
tiscad truncated small-cellated-dodecateron sqrt[(3y2+12y+14)/3] 240, 840, 1170, 660, 92
sitpodadia small (intersected) tripesic dodecahedronary dishecatonicosachoron alterprism 1.074481 240, 8640, 13440, 6000, 362
rasishia rasishi alterprism 2.829949 2400, 14400, 18720, 5520, 362
rahipe rectified-hecatonicosachoron prism 4.562051 2400, 8400, 9840, 4560, 722
n,tic-dip n-gon - truncated-cube duoprism sqrt[sqrt(2)+7/4+1/(4 sin2(π/n))] 24n, 60n, 50n+24, 15n+36, n+14
n,toe-dip n-gon truncated-octahedron duoprism sqrt[5/2+1/(4 sin2(π/n))] 24n, 60n, 50n+24, 15n+36, n+14
n,sirco-dip n-gon small-rhombicuboctahedron duoprism sqrt[(5+2 sqrt(2))/4+1/(4 sin2(π/n))] 24n, 72n, 74n+24, 27n+48, n+26
repenp (alt.: ampenp) rectified/ambified penp 1.264911 25, 100, 130, 70, 17
octpy || octaco 1/4-lune of rectified triacontiditeron, octahedron-pyramid atop octhedron-first-rotunda-of-icositetrachoron 1 25, 114, 156, 83, 18
icopy (degenerate) ico pyramid ∞   i.e. flat in euclidean space 25, 120, 192, 120, 25
pennatip pen atop tip, pen-first cap of rin 1.414214 25, 70, 80, 45, 12
penaspid pentachoron atop small prismated decachoron, pen-first rotunda of scad 1 25, 90, 140, 105, 32
pacsirn partially contracted small rhombated penteract ... 256, 1088, 1328, 600, 106
..., tat || grit (degenerate) tat atop grit ∞   i.e. flat in euclidean space 256, 704, 720, 328, 58
..., sidpith || prit (degenerate) sidpith atop prit ∞   i.e. flat in euclidean space 256, 864, 1056, 528, 82
..., tat || prit (degenerate) tat atop prit ∞   i.e. flat in euclidean space 256, 992, 1224, 568, 82
starpedippy, pt || starpedip (degenerate) starpedip pyramid ∞   i.e. flat in euclidean space 26, 75, 85, 45, 11
..., rahi || tex (degenerate) rahi atop tex ∞   i.e. flat in euclidean space 2640, 15120, 21120, 10080, 1442
tritricu triangle-tricu duoprism, half of traco 1.154701 27, 72, 78, 42, 11
trashiddip triangle atop shiddip 1.732051 27, 75, 83, 44, 11
triddip althiddip triddip atop gyrated thiddip 1.190238 27, 90, 114, 63, 14
coates cuboctahedron atop tesseract 1.050501 28, 104, 134, 73, 17
teta tuttip (alt.: tettut tuttric) tet atop tuttip, tet-first cap of sirhin, (tet,tut,tut)-trigonic 1.620185 28, 78, 86, 45, 11
tetacope tet atop cope, tet-first segment of spix 1.190238 28, 90, 116, 69, 17
tetco tuttric (tet,co,tut)-trigonic 1.274755 28, 96, 128, 75, 17
pabex gyetac partially bi-expanded gyroelongated-triacontaditeron ... 288, 1008, 1200, 560, 82
..., srit || proh (degenerate) srit atop proh ∞   i.e. flat in euclidean space 288, 1152, 1384, 600, 82
cydispan cubically cyclodiminished small-prismated-penteract 1.914214 288, 1200, 1752, 1020, 182
spiccup small-prismatotetracontoctachoron prism, runcinated-icositetrachoron prism 1.914214 288, 1296, 1920, 1152, 242
horico adisti hollow rectified icositetrachoron atop disnub tetrakisicositetrachoron, snub disicositetrachoric cupolaic blend 1.738546 288, 1728, 2688, 1440, 241
hagirco (old: higgirco) hexagon great-rhombicuboctahedron duoprism 2.524147 288, 720, 636, 234, 32
haquitco hexagon - quasitruncated-cuboctahedron duoprism 1.459000 288, 720, 636, 234, 32
tahatico tah atop tico, tah-first segment of pirt 3 288, 768, 744, 312, 50
..., tah || grit (degenerate) tah atop grit ∞   i.e. flat in euclidean space 288, 768, 752, 328, 58
ricoatico (degenerate) rico atop tico ∞   i.e. flat in euclidean space 288, 864, 864, 336, 50
..., rico || proh (degenerate) rico atop proh ∞   i.e. flat in euclidean space 288, 960, 1088, 496, 82
texip truncated-hexacosachoron prism 4.749980 2880, 10080, 11520, 5040, 722
sid pippadia sid pippady alterprism 2.527959 2880, 21600, 34560, 14880, 1082
gidpixhip great-disprismatohexacosihecatonicosachoron prism, omnitruncated-hexacosachoron prism 12.796423 28800, 72000, 62880, 22320, 2642
n/d-dow n/d-grammal disphenoid, n/d-grammal biwedge, {n/d} || perp {n/d} sqrt[1+1/(2 sin2(π d/n))]/2 2n, n2+2n, 2n2+2, n2+2n, 2n
n,n-dippip n-gon - n-gon duoprismatic prism sqrt[1/4+1/(2 sin2(π/n))] 2n2, 5n2, 4n2+4n, n2+6n, 2n+2
n,m-dippip n-gon - m-gon duoprismatic prism sqrt[1/4+1/(4 sin2(π/n))+1/(4 sin2(π/m))] 2nm, 5nm, 4nm+2n+2m, nm+3n+3m, n+m+2
(n,m-ap)-dip n-gon - m-antiprism - duoprism sqrt[1/(4 sin2(π/n))+(3-2 cos(π/m))/(8-8 cos(π/m))] 2nm, 6nm, 6nm+2n+2m, 2nm+3n+4m, n+2m+2
n,m-dafup (n,m)-duoantifastegiaprism, (n,m)-duoantiwedge, (n,m)-dip atop bidual (n,m)-dip sqrt([2+1/(1-cos(pi/n))+1/(1-cos(pi/m))]/8) 2nm, 8nm, 10nm+2n+2m, 4nm+4n+4m, 2n+2m+2
..., {5} || gyro pedip (degenerate) pentagon atop gyrated pedip ∞   i.e. flat in euclidean space 30, 105, 136, 75, 16
octco tuttric (oct,co,tut)-trigonic 1.224745 30, 114, 144, 75, 17
dehad dodecahemidodecateron 1 30, 120, 140, 75, 18
retratet (alt.: amtratet) rectified/ambified tratet 1.354006 30, 120, 144, 81, 19
octacope oct atop cope, oct-first cap of nit 1.224745 30, 120, 156, 81, 17
dacox dodecacellihexateron 1 30, 120, 210, 135, 33
bacox biprismatocellihexateron 1 30, 120, 210, 165, 41
chad cellihemidodecateron 1 30, 120, 210, 180, 36
dibhid dodecabiprismatohemidodecateron 1 30, 120, 210, 180, 38
scad (old: shad) small cellated dodecateron, small hedrated dodecateron, stericated hexateron, expanded hexateron, vertex figure of cyxh, lattice A5 contact polytope (span of its roots) 1 30, 120, 210, 180, 62
rapaltip (degenerate) rap atop inverted tip ∞   i.e. flat in euclidean space 30, 130, 180, 100, 22
rapaspid rectified pentachoron atop small prismated decachoron, rap-first half of rat 1 30, 150, 250, 160, 32
trapip (old: trapedippip) triangle pentagonal-prism duoprism, triangle-pentagon duoprismatic prism 1.143215 30, 75, 76, 39, 10
tix (alt.: pentum) truncated hexateron, pen-based tutism 1.322876 30, 75, 80, 45, 12
hisquippy hexagon-squippy douprism, half of hoct 1.224745 30, 78, 83, 44, 11
tripufip (alt.: tripa shiddip) tripuf prism, trip-first cap of srippip 1.284523 30, 81, 87, 45, 11
octatuttip (alt.: octtut tuttric) oct atop tuttip, (oct,tut,tut)-trigonic 1.414214 30, 84, 90, 45, 11
rapatip rap atop tip, rap-first cap of sarx 0.774597 30, 90, 100, 50, 12
poct pentagon - octahedron duoprism 1.106168 30, 90, 106, 57, 13
stoct pentagram - octahedron duoprism 0.881132 30, 90, 106, 57, 13
octa tutcup, oct || tutcup oct atop tuta 1.274755 30, 96, 120, 69, 17
pabacca pin partially bicontracted celliprismated penteract ... 304, 1064, 1396, 752, 118
n,id-dip n-gon - icosidodecahedron duoprism sqrt[(3+sqrt(5))/2+1/(4 sin2(π/n))] 30n, 90n, 92n+30, 33n+60, n+32
tepeacope tepe atop cope, tepe-first half of spiddip 1.118034 32, 100, 126, 74, 18
cubacope cube atop cuboctahedron-prism 1.120019 32, 120, 154, 81, 17
... tetrahedral - square-prismantiprismoid ... 32, 128, 208, 140, 30
pabex tac partially biexpanded triacontaditeron ... 32, 128, 230, 204, 72
..., ofx3xoo4ooo&#xt || o3o4x cube atop (oct,co)-ursachoron, (oct,co)-ursachoron based wedge 1.994779 32, 150, 244, 159, 35
hexaico, hex || ico hexadecachoron-first rotunda of rectified triacontiditeron, hexadecachoron atop icositetrachoron, rectified hexadecachoron-pyramid 1 32, 168, 248, 136, 26
pent penteract, decateron, 5D measure-polytope (γ5), geopet(id) 1.118034 32, 80, 80, 40, 10
otet octagon-tetrahedron duoprism, octagon duofastegium 1.442951 32, 80, 84, 46, 12
stotet octagram-tetrahedron duoprism, octagram duofastegium 0.817247 32, 80, 84, 46, 12
tepeatuttip tepe atop tuttip, tetatut-prism 1.322876 32, 88, 96, 50, 12
squicuffip squicuf prism, tes atop op 1.567516 32, 88, 98, 53, 13
pirhin prismatorhombated hemipenteract, runcicantellated demipenteract, steriruncic penteract 2.150581 320, 1120, 1280, 560, 82
rawn (old: rawvanant) retrosphenary penteract 2.207107 320, 1280, 1280, 440, 52
wavinant sphenoverted penteractipenteractitriacontaditeron 0.792893 320, 1280, 1280, 440, 52
quarn quasirhombated penteract 0.792893 320, 1280, 1520, 680, 122
rerin rectified rectified-penteract 2.645751 320, 1280, 1520, 680, 122
sirn small rhombated penteract, cantellated penteract 2.207107 320, 1280, 1520, 680, 122
gafwan great facetosphenary penteract 0.792893 320, 1280, 1840, 1120, 210
fawdint frustisphenary dispenteractitriacontaditeron, fastegiverted dispenteractitriacontaditeron 0.914214 320, 1440, 1440, 480, 52
sirpin small retroprismated penteract 1.914214 320, 1440, 1440, 480, 52
gatopin great pteroprismated penteract 0.914214 320, 1440, 1680, 560, 50
spat small prismated triacontiditeron, runcinated pentacross 1.870829 320, 1440, 2160, 1200, 162
quappin quasiprismated penteract 0.914214 320, 1440, 2160, 1240, 202
span small prismated penteract, runcinated penteract 1.914214 320, 1440, 2160, 1240, 202
gipbin great prismated biprismatopenteract 0.914214 320, 1440, 2880, 1880, 322
bittin bitruncated penteract 2.549510 320, 800, 720, 280, 42
pex sart partially expanded small rhombated triacontiditeron ... 336, 1584, 2000, 848, 98
... rectification/ambification of icoap 1.847759 336, 2304, 3744, 2064, 290
penasrip pen atop srip 1.274755 35, 130, 180, 105, 22
penalsrip, pen || inv srip (degenerate) pen atop inverted srip ∞   i.e. flat in euclidean space 35, 160, 240, 145, 32
gyepcuro, J47 gyroelongated pentagonal cupolarotunda 35, 80, 47
opeatuttip ope atop tuttip, octatut-prism, ope-first cap of srippip 1.284523 36, 102, 110, 54, 12
hoct hexagon octahedron duoprism 1.224745 36, 108, 126, 66, 14
pabex hix (alt.: thiddipcup) partially bi-expanded hexateron, thiddip cupoliprism 1.190238 36, 108, 126, 66, 14
traco (alt.: cocoe cotric) triangle - cuboctahedron duoprism, (co,co,co)-trigonic 1.154701 36, 108, 126, 69, 17
tutaf (old: tutaltuttip) tut alterfastegium, tut atop inverted tuttip 1.274755 36, 114, 138, 75, 17
coatuttip co atop tuttip, co-first cap of sarx 1.290994 36, 120, 144, 75, 17
copatut cope atop tut 1.190238 36, 126, 156, 81, 17
trike triangle - icosahedron duoprism 1.112583 36, 126, 162, 93, 23
coa tutcup, co || tutcup co atop tuta 1.224745 36, 132, 162, 81, 17
opeacope ope atop cope, octaco-prism, ope-first half of icope 1.118034 36, 138, 176, 90, 18
tedrat (cyclo-)tetra-diminished rat 1 36, 192, 328, 212, 42
hossidgyt hollow small-stellated-dodecahedral gyrotrigonism 0.742632 36, 270, 516, 288, 39
trahip (old: thiddippip) triangle hexagonal-prism duoprism, triangle-hexagon duoprismatic prism 1.258306 36, 90, 90, 45, 11
tratut (alt.: tuttut tuttric) triangle truncated-tetrahedron duoprism, (tut,tut,tut)-trigonic 1.307032 36, 90, 90, 45, 11
squatricu square-tricu duoprism 1.224745 36, 96, 101, 51, 12
recaptid retrocelliprismatotruncated dodecateron 2.236068 360, 1080, 1050, 390, 48
rocgrax retrocelligreat rhombated hexateron 2.327373 360, 1080, 1080, 420, 53
captid (old: hiptid) celliprismatotruncated dodecateron, hedratoprismatotruncated dodecateron, steriruncitruncated hexateron 2.236068 360, 1080, 1110, 450, 62
cograx (old: gocrax, goharx) celligreatorhombated hexateron (great cellirhombated hexateron, great hedratorhombated hexateron), stericanitruncated hexateron 2.327373 360, 1080, 1140, 480, 62
hasrid hexagon - small-rhombicosidodecahedron duoprism 2.446644 360, 1080, 1152, 498, 68
resibrid rectified sibrid 2.645751 360, 1440, 1680, 720, 122
snod (snix) snub dodecateron (snub hexateron), alternation of great cellated hexateron ... 360, 2520, 4080, 2340, 422
hati hexagon - truncated-icosahedron duoprism 2.672186 360, 900, 792, 288, 38
hatid hexagon - truncated-dodecahedron duoprism 3.133309 360, 900, 792, 288, 38
gippix great prismated hexateron, runcicantitruncated hexateron 2.581989 360, 900, 810, 315, 47
tragrid triangle - great-rhombicosidodecahedron duoprism 3.845977 360, 900, 846, 369, 65
..., ragaghi || tigaghi (degenerate) ragaghi atop tigaghi ∞   i.e. flat in euclidean space 3600, 10800, 9120, 2640, 242
rahia sidpixhi (degenerate) rahi atop sidpixhi ∞   i.e. flat in euclidean space 3600, 18000, 28560, 16800, 2642
ricoa ticotum rico-based tutsatope, rico-based tutism, rico-first bistratic cap of pattit 2.738613 384, 1152, 1168, 456, 58
prittip prismatorhombated-tesseract prism, prismatotruncated-hexadecachoron prism, runcitruncated-hexadecachoron prism, central segment of cappin 2.423081 384, 1152, 1216, 528, 82
prohp prismatorhombated-hexadecachoron prism, prismatotruncated-tesseract prism, runcitruncated-tesseract prism, central segment of carnit 2.660531 384, 1152, 1216, 528, 82
..., prit || grit (degenerate) prit atop grit ∞   i.e. flat in euclidean space 384, 1248, 1384, 600, 82
prohagrit proh atop grit, proh-first segment of pattin 3.239235 384, 1248, 1384, 600, 82
sritaprohu (srit,proh)-based ursateron 2.706827 384, 1344, 1504, 624, 82
..., rico || gyro srico (degenerate) rico atop gyrated srico ∞   i.e. flat in euclidean space 384, 1440, 1824, 912, 146
pysneta pyritosnub tesseractic alterprism, edge-snub hexadecachoric hosoteron ... 384, 1920, 2848, 1584, 274
ogirco octagon - great-rhombicuboctahedron duoprism 2.660531 384, 960, 832, 288, 34
ticope truncated-icositetrachoron prism 2.692582 384, 960, 864, 336, 50
grittip truncated-tesseract prism, central segment of prin 3.047217 384, 960, 880, 360, 58
..., tex || sidpixhi (degenerate) tex atop sidpixhi ∞   i.e. flat in euclidean space 3840, 18720, 29040, 16800, 2642
danpit dispenteractiprismated triacontaditeron 2.5 3840, 9600, 7680, 2160, 132
nippant penteractiprismated penteractitriacontaditeron 3.505073 3840, 9600, 7680, 2160, 172
noquapant penteractiquasiprismated penteractitriacontaditeron 2.283521 3840, 9600, 7680, 2160, 172
gacnet great cellated penteractitriacontiditeron, omnitruncated penteract, omnitruncated pentacross 4.829189 3840, 9600, 8160, 2640, 242
gaquacint great quasicellated penteractitriacontiditeron 3.029675 3840, 9600, 8160, 2640, 242
tippip truncated-pentachoron prism 1.360147 40, 100, 100, 50, 12
pecube pentagon-cube duoprism 1.213922 40, 100, 98, 47, 11
rapadeca rap atop deca, rap-first cap of sirhin 1.620185 40, 120, 130, 60, 12
spiddip small-prismatodecachoron prism 1.118034 40, 140, 200, 130, 32
rapalsrip rap atop inverted srip, rap-first cap of spix 1.190238 40, 150, 200, 110, 22
hexalrit hex atop gyrated rit, hex-first cap of siphin 1.274755 40, 152, 216, 128, 26
spidatip small-prismate-pentachoron atop alternate truncated-pentachoron 1.274755 40, 160, 250, 160, 32
hexu hexadecachoron-based ursateron, hex-based ursulate, vertex figure of s3s4o3o3o4o 1.144123 40, 176, 248, 136, 26
rapasrip rectified pentachoron atop small rhombated pentachoron, rap-first cap of nit 1.224745 40, 180, 230, 110, 22
hexarit (degenerate) hex atop rit ∞   i.e. flat in euclidean space 40, 216, 408, 280, 50
icates, ico || tes icositetrachoron atop tesseract 1.050501 40, 216, 408, 288, 58
rhohid rectified hexadecahemidecateron 1 40, 240, 400, 200, 31
rat rectified triacontiditeron, rectified pentacross, vertex figure of hinoh, lattice B5 contact polytope (span of its small roots), lattice D5 contact polytope (span of its roots) 1 40, 240, 400, 240, 42
ratchet retrotriacontidicellihemitriacontaditeron 1 40, 240, 600, 560, 88
..., spic || srico (degenerate) spic atop srico ∞   i.e. flat in euclidean space 432, 2016, 2832, 1488, 242
..., rigfix || sirgaghi (degenerate) rigfix atop sirgaghi ∞   i.e. flat in euclidean space 4320, 18000, 21600, 9840, 1442
..., rofix || sirsashi (degenerate) rofix atop sirsashi ∞   i.e. flat in euclidean space 4320, 18000, 21600, 9840, 1442
coarit co atop rit 1.224745 44, 168, 222, 121, 25
..., doe || ipe (degenerate) doe atop ipe ∞   i.e. flat in euclidean space 44, 222, 382, 267, 65
pacca pin partially contracted celliprismated penteract ... 448, 1568, 2032, 1080, 170
triddippa hiddip triddip atop hiddip, triddip-first cap of card 1.658312 45, 126, 135, 66, 14
pabex sart partially biexpanded small rhombated triacontiditeron ... 456, 2040, 2560, 1096, 122
hacube (old: hiccube) hexagon cube duoprism 1.322876 48, 120, 116, 54, 12
squatut square - truncated-tetrahedron duoprism 1.369306 48, 120, 116, 54, 12
tuttipa toe (alt.: tuttut totric) tuttip atop toe, (tut,tut,toe)-trigonic 1.632993 48, 132, 144, 75, 17
copatoe (alt.: coco totric) cope atop toe, (co,co,toe)-trigonic 1.870829 48, 144, 162, 81, 17
tutcupa toe (alt.: tutaltut toetric) tuta atop toe, (tut,inv tut,toe)-trigonic 1.620185 48, 144, 162, 81, 17
squaco square-cuboctahedron duoprism 1.224745 48, 144, 164, 84, 18
tutcupip tuttip atop inverted tuttip, tuta-prism, medial segment of rittip 1.322876 48, 144, 164, 84, 18
owoct octagon octahedron duoprism 1.485633 48, 144, 166, 84, 16
stowoct octagram octahedron duoprism 0.890446 48, 144, 166, 84, 16
cotut totric (co,tut,toe)-trigonic 1.732051 48, 150, 168, 81, 17
copea tuttip cope atop tuttip, cope-first monostratic cap of srippip 1.284523 48, 156, 182, 90, 18
squike square-icosahedron duoprism 1.185120 48, 168, 212, 114, 24
tessarit tesseract atop rectified tesseract 1.227160 48, 192, 240, 120, 26
pexhin (old: tutas) partially expanded hemipenteract, truncated tetrahedron altersquarism, tuta alterprism, cyclodiminished siphin 1.274755 48, 192, 296, 188, 38
... tetrahedral - hexagon-prismantiprismoid ... 48, 192, 308, 204, 42
sirco acope small-rhombicuboctahedron atop cuboctahedron-prism 1.502958 48, 204, 270, 141, 29
icope icositetrachoron prism 1.118034 48, 216, 288, 144, 26
ica tutcup, ico || tutcup icositetrachoron atop truncated-tetrahedral-cupoliprism 1.224745 48, 228, 304, 148, 26
gicalico great icositetrachoron atop dual icositetrachoron, blend of 3 icateses 1.050501 48, 336, 744, 600, 122
hosiap hollow stellated icosatetrachoric antiprism, pseudo stico atop pseudo stico 0.790569 48, 336, 768, 624, 144
icoap (alt.: icoalico) icositetrachoral antiprism, icositetrachoron atop dual icositetrachoron 1.050501 48, 336, 768, 720, 242
oti octagon - truncated-icosahedron duoprism 2.801372 480, 1200, 1036, 354, 40
otid octagon - truncated-dodecahedron duoprism 3.244185 480, 1200, 1036, 354, 40
girhin great rhombated hemipenteract, cantitruncated demipenteract, runcicantic penteract 2.761340 480, 1200, 1040, 360, 42
squagrid square - great-rhombicosidodecahedron duoprism 3.867584 480, 1200, 1088, 432, 66
osrid octagon - small-rhombicosidodecahedron duoprism 2.587117 480, 1440, 1516, 624, 70
gart great rhombated triacontiditeron, cantitruncated pentacross 2.645751 480, 1440, 1520, 640, 82
pithin prismatotruncated hemipenteract, runcitruncated demipenteract, stericantic penteract 2.371708 480, 1680, 1840, 720, 82
sibrant small birhombated penteractitriacontiditeron, bicantellated penteract, bicantellated pentacross 2.236068 480, 1920, 2160, 840, 122
..., tico || prissi tico atop prissi 2.647378 480, 1968, 2640, 1392, 242
prohalsrico proh atop srico 2.632865 480, 2112, 2624, 1168, 178
thipe truncated-hecatonicosachoron prism 8.233530 4800, 12000, 11040, 4560, 722
sidpixhip small-disprismatohexacosihecatonicosachoron prism, runcinated-hecatonicosachoron prism, runcinated-hexacosachoron prism 5.259887 4800, 16800, 22080, 12720, 2642
stut phiddixa small tritrigonal prismatohecatonicosidishexacosachoron alterprism 3.855219 4800, 28800, 41280, 19920, 2042
n,girco-dip n-gon - great-rhombicuboctahedron duoprism sqrt[(13+6 sqrt(2))/4+1/(4 sin2(π/n))] 48n, 120n, 98n+48, 27n+72, n+26
n,tet-dip n-gon - tetrahedron duoprism, n-gonal duofastegium, n-gonal prism disphenoid sqrt[3/8+1/(4 sin2(π/n))] 4n, 10n, 10n+4, 5n+6, n+4
n/d-daf n/d-duoantifastegium, (2,n)-duoantiwedge, n/d-p atop bidual n/d-p sqrt([3+1/(1-cos(pi d/n))]/8) 4n, 14n, 18n+4, 10n+6, 2n+4
n/d,2n/d-dipcup n/d,2n/d-dip cupoliprism sqrt([7+4 cos(π d/n)-2 cos2(π d/n)]/[8-8 cos2(π d/n)]) 4n2, 12n2, 12n2+6n, 4n2+10n, 4n+2
pepip pentagon duoprismatic prism 1.302772 50, 125, 120, 55, 12
tipadeca tip atop deca, 2nd segment of rin in pen-first orientation 1.414214 50, 160, 190, 100, 22
rapu rectified-pentachoron-based ursateron, rap-based ursulate 1.258489 50, 190, 230, 110, 22
sripatip srip atop tip, srip-first segment of sarx 1.290994 50, 190, 230, 110, 22
sripaltip srip atop inverted tip 1.274755 50, 190, 260, 150, 32
spidasrip spid atop srip, spid-first cap of spix 1.190238 50, 210, 300, 170, 32
spidadeca, spid || deca (degenerate) spid atop deca ∞   i.e. flat in euclidean space 50, 240, 350, 190, 32
raggixu raggix-based ursateron 1.175984 5040, 22320, 26640, 10800, 1442
..., ike || dope (degenerate) ike atop dope ∞   i.e. flat in euclidean space 52, 230, 374, 259, 65
hatricu hexagon-tricu duoprism, trip-first half of haco 1.414214 54, 144, 147, 69, 14
cuba sircope cube atop small-rhombicuboctahedron-prism 1.695040 56, 180, 226, 129, 29
hexathex (degenerate) hex atop thex ∞   i.e. flat in euclidean space 56, 192, 248, 136, 26
pabac scant partially bicontracted small cellated penteractitriacontiditeron ... 56, 224, 386, 324, 108
squadinit square-diminished nit 1.224745 56, 240, 344, 200, 42
icarit, ico || rit icositetrachoron atop rectified tesseract, ico-first half of nit 1.224745 56, 288, 376, 168, 26
contip tetracontoctachoron prism, bitruncated-icositetrachoron prism 3.450631 576, 1440, 1248, 432, 50
..., tico || gidpith (degenerate) tico atop gidpith ∞   i.e. flat in euclidean space 576, 1536, 1472, 592, 82
gritta gidpith grit atop gidpith, grit-first segment of cogrin 3.988340 576, 1536, 1480, 600, 82
..., proh || gidpith (degenerate) proh atop gidpith ∞   i.e. flat in euclidean space 576, 1632, 1600, 624, 82
..., srico || cont (degenerate) srico atop cont ∞   i.e. flat in euclidean space 576, 2016, 2208, 912, 146
sricope (old: sripe) small-rhombated-icositetrachoron prism, cantellated-icositetrachoron prism 2.660531 576, 2016, 2304, 1008, 146
sricoa (old: sricoalsrico), srico || gyro srico small-rhombated-icositetrachoron alterprism, small-rhombated-icositetrachoron atop gyrated small-rhombated-icositetrachoron 2.632865 576, 2880, 3744, 1680, 242
hix hexateron, 5D simplex (α5), pyropet(id), pentachoral pyramid, regular tet-scalene, regular triangle-tettene, regular line-pennene, regular (point-)hixene, digonal gyrotrigonism, vertex figure of hop, Gosset polytope 04 0.645497 6, 15, 20, 15, 6
siddy small dodekicosahedron 1.721489 60, 120, 32
bittix (old: dittox) bitruncated hexateron 1.554563 60, 150, 140, 60, 12
decap decachoron prism 1.5 60, 150, 140, 60, 12
tradoe triangle - dodecahedron duoprism 1.515539 60, 150, 146, 69, 15
tutatope tut atop tope, tut-first cap of pattix 1.848423 60, 162, 168, 81, 17
coatope (alt.: cotoe totric) co atop tope, (co,toe,toe)-trigonic, co-first cap of sibrant at (rico,rico)-margin 2.236068 60, 168, 174, 81, 17
peco pentagon-cuboctahedron duoprism 1.312862 60, 180, 202, 99, 19
sripadeca srip atop deca, srip-first half of sibrid 1.414214 60, 210, 240, 110, 22
srippip small-rhombated-pentachoron prism 1.284523 60, 210, 250, 120, 22
pike pentagon-icosahedron duoprism 1.275976 60, 210, 262, 135, 25
rawx retrosphenary hexateron 1.290994 60, 240, 260, 105, 18
lawx lepidosphenary hexateron 1.290994 60, 240, 270, 135, 27
sarx small rhombated hexateron, cantellated hexateron 1.290994 60, 240, 290, 135, 27
coasircope cuboctahedron atop small-rhombicuboctahedron prism 1.847759 60, 240, 306, 153, 29
rawcax (old: rawvdipdopdix) retrosphenary cellihexateron, (retrosphenoverted disprismatoduoprismatodiakishexateron) 1.290994 60, 240, 440, 285, 62
rippix retroprismated hexateron 1.190238 60, 270, 300, 120, 18
topax pteroprismated hexateron 1.190238 60, 270, 330, 135, 21
spix small prismated hexateron, runcinated hexateron 1.190238 60, 270, 420, 255, 47
mibdinit metabidiminished nit, rectified bidhin 1.224745 60, 300, 394, 183, 31
sripa (alt: pabdinit, old: sripalsrip) small rhombated pentachoron alterprism, small rhombated pentachoron atop inverted small rhombated pentachoron, parabidiminished nit, equatorial segment of nit 1.224745 60, 300, 400, 190, 32
pabac carnit partially bicontracted cellirhombated penteractitriacontiditeron ... 600, 2568, 3200, 1384, 154
..., xhi || thi (degenerate) xhi atop thi ∞   i.e. flat in euclidean space 6000, 19200, 21840, 10560, 1922
..., sidpixhi || srix (degenerate) sidpixhi atop srix ∞   i.e. flat in euclidean space 6000, 25200, 34080, 17520, 2642
n,ti-dip n-gon - truncated-icosahedron duoprism sqrt[(29+9 sqrt(5))/8+1/(4 sin2(π/n))] 60n, 150n, 122n+60, 33n+90, n+32
n,tid-dip n-gon - truncated-dodecahedron duoprism sqrt[(37+15 sqrt(5))/8+1/(4 sin2(π/n))] 60n, 150n, 122n+60, 33n+90, n+32
n,srid-dip n-gon - small-rhombicosidodecahedron duoprism sqrt[sqrt(5)+11/4+1/(4 sin2(π/n))] 60n, 180n, 182n+60, 63n+120, n+62
ocube octagon - cube duoprism 1.567516 64, 160, 152, 68, 14
hextum hex-based tutsatope, hex-based tutism, hex-first rotunda of tot, truncation of hexpy 1.581139 64, 200, 248, 136, 26
rittip rectified-tesseract prism 1.322876 64, 224, 272, 136, 26
bodnit bi-octa-diminished penteractitriacontiditeron 1.224745 64, 288, 440, 272, 58
rita (old: ritag rit) rit atop gyro rit, medial segment of hex-first siphin 1.274755 64, 288, 464, 288, 50
pex rat partially expanded rectified triacontiditeron ... 64, 360, 592, 352, 58
naquitant penteractiquasitruncated penteractitriacontaditeron 1.354911 640, 1600, 1280, 440, 52
nottant penteractitruncated penteractitriacontaditeron 2.159679 640, 1600, 1280, 440, 52
gaqrin great quasirhombated penteract 1.673396 640, 1600, 1520, 680, 122
girn great rhombated penteract, cantitruncated penteract 3.563671 640, 1600, 1520, 680, 122
getitdin great tesseractitriacontidiadispenteract 1.276197 640, 2240, 2160, 760, 92
setitdin small tesseractitriacontidiadispenteract 2.423081 640, 2240, 2160, 760, 92
gancpan great spinocelliprismated penteract 1.276197 640, 2240, 2640, 1080, 132
cappin celliprismated penteract, steritruncated pentacross 2.423081 640, 2240, 2880, 1520, 242
caquapin celliquasiprismated penteract 1.276197 640, 2240, 2880, 1520, 242
capt celliprismated triacontiditeron, steritruncated penteract 2.878460 640, 2240, 2960, 1600, 242
quacpot quasicelliprismated triacontiditeron 1.102028 640, 2240, 2960, 1600, 242
gektabcadont (old: giktabacadint) great skewtrigonary biprismatocellidispenteractitriacontiditeron 1.5 640, 2880, 3920, 1920, 172
skatbacadint small skewtrigonary biprismatocellidispenteractitriacontiditeron 1.5 640, 2880, 3920, 1920, 172
... truncation of icoap 2.816377 672, 2640, 3744, 2064, 290
3,n-dippip triangle - n-gon duoprismatic prism sqrt[7/12+1/(4 sin2(π/n))] 6n, 15n, 14n+6, 6n+9, n+5
n,oct-dip n-gon - octahedron duoprism sqrt[1/2+1/(4 sin2(π/n))] 6n, 18n, 20n+6, 9n+12, n+8
squete square-pyramidal pyramid pyramid, square-tettene, triangular-square disphenoid, half of the triacontiditeron 0.707107 7, 19, 26, 19, 7
penit (old: pendpy) pentachoral (line-)tegum, pentachoral dipyramid 7, 20, 30, 25, 10
rapalprip, rap || inv prip (degenerate) rap atop inverted prip ∞   i.e. flat in euclidean space 70, 240, 300, 160, 32
idadope icosidodecahedron atop dodecahedron-prism 1.618034 70, 260, 326, 169, 35
spidasripu (spid,srip)-based ursateron 1.331369 70, 260, 350, 195, 37
hahip (old: hiddippip) hexagon hexagonal-prism duoprism, hexagon-hexagon duoprismatic prism 1.5 72, 180, 168, 72, 14
hatut (old: hittut) hexagon truncatet-tetrahedron duoprism 1.541104 72, 180, 168, 72, 14
traquith triangle quasitruncated-cube duoprism 0.817997 72, 180, 174, 81, 17
tratic triangle truncated-cube duoprism 1.870173 72, 180, 174, 81, 17
tratoe (alt.: totoe totric) triangle truncated-octahedron duoprism, (toe,toe,toe)-trigonic 1.683251 72, 180, 174, 81, 17
tuttipa tope tuttip atop tope, tutatoe-prism, tuttip-first cap of prippip 1.688194 72, 192, 194, 90, 18
copatope cope atop tope, coatoe prism, cope-first monostratic cap of ricope 1.802776 72, 204, 212, 96, 18
copeatope cope atop tope, coatoe-prism 1.802776 72, 204, 212, 96, 18
tragocco triangle - great-cubicuboctahedron duoprism 0.936070 72, 216, 228, 111, 23
trasocco triangle - small-cubicuboctahedron duoprism 1.513420 72, 216, 228, 111, 23
haco (old: hicco) hexagon cuboctahedron duoprism 1.414214 72, 216, 240, 114, 20
trasirco triangle small-rhombicuboctahedron duoprism 1.513420 72, 216, 246, 129, 29
sircoa ticcup small-rhombicuboctahedron atop truncated-cube-prism 2.207107 72, 240, 282, 141, 29
ticca sircope truncated-cube atop small-rhombicuboctahedron-prism 1.914214 72, 252, 306, 153, 29
toa sircope truncated-octahedron atop small-rhombicuboctahedron-prism 1.583946 72, 252, 306, 153, 29
hike hexagon icosahedron duoprism 1.380039 72, 252, 312, 156, 26
trasnic triangle - snub-cube duoprism 1.462497 72, 252, 318, 177, 41
icathex ico atop thex, ico-first segment of sart 1.732051 72, 264, 312, 144, 26
hexasidpith (degenerate) hex atop sidpith ∞   i.e. flat in euclidean space 72, 280 ,432, 304, 82
odnit octadiminished penteractitriacontiditeron 1.224745 72, 384, 556, 292, 50
gocad (old: gohad) great cellated dodecateron (great hedrated dodecateron), omnitruncated hexateron, Voronoi cell of lattice A5*, permutoteron of 6 elements 2.958040 720, 1800, 1560, 560, 62
hagrid hexagon - great-rhombicosidodecahedron duoprism 3.931692 720, 1800, 1572, 558, 68
gogishiagax great grand stellated hecatonicosachoron antiprism, grand hexacosachoron antiprism, taller great grand stellated hecatonicosachoron atop grand hexacosachoron 0.667731 720, 4320, 9120, 8160, 2642
gogishiragax great grand stellated hecatonicosachoron retroprism, grand hexacosachoron retroprism, narrower great grand stellated hecatonicosachoron atop grand hexacosachoron 0.636010 720, 4320, 91420, 8160, 2642
xhip hexacosihecatonicosachoron prism, bitruncated-hecatonicosachoron prism, bitruncated-hexacosachoron prism 7.596108 7200, 18000, 15840, 5760, 722
sirgaship small-rhombated-grand-stellated-hecatonicosachoron prism 1.666693 7200, 25200, 25200, 9120, 962
sirghipe small-rhombated-great-hecatonicosachoron prism 3.423760 7200, 25200, 25200, 9120, 962
..., srahi || xhi (degenerate) srahi atop xhi ∞   i.e. flat in euclidean space 7200, 25200, 27840, 11760, 1922
srixip small-rhombated-hexacosachoron prism, cantellated-hexacosachoron prism 6.094140 7200, 25200, 28080, 11520, 1442
srahip (old: srahipe) small-rhombated-hecatonicosachoron prism 6.753568 7200, 25200, 29040, 12960, 1922
wavhiddixa sphenoverted hecatonicosadishexacosachoron alterprism 5.345177 7200, 28800, 30240, 10560, 1322
sirgashia small rhombated grand stellated hecatonicosachoron alterprism 1.618034 7200, 36000, 43200, 17040, 1682
sirghia small rhombated great hecatonicosachoron alterprism 3.404434 7200, 36000, 43200, 17040, 1682
srixasrahi (degenerate) srix atop srahi ∞   i.e. flat in euclidean space 7200, 36000, 46560, 20400, 2642
gaquidpothip great-quasidisprismatotesseractihexadecachoric prism, great-quasiprismated-tesseract prism 2.001839 768, 1920, 1696, 624, 82
gidpithip great-disprismatotesseractihexadecachoric prism, great-prismated-tesseract prism, central segment of cogart 3.534493 768, 1920, 1696, 624, 82
..., tico || gyro prico (degenerate) tico atop gyrated prico ∞   i.e. flat in euclidean space 768, 2400, 2784, 1392, 242
paccarnit partially contracted cellirhombated penteractitriacontiditeron ... 768, 3168, 3920, 1712, 194
trippasc triangular-prismatic scalene, triangular-prismatic-pyramid pyramid, line atop fully orthogonal triangular-prism 0.790569 8, 22, 29, 20, 7
state stellar tettene, pentagrammic tettene, pentagram-pyramidal pyramid pyramid, triangle atop fully orthogonal pentagram 0.636010 8, 23, 32, 23, 8
..., {4} || perp {4} (degenerate) square atop fully orthogonal square, square disphenoid ∞   i.e. flat in euclidean space 8, 24, 34, 24, 8
octasc octahedral scalene, octahedron-pyramid pyramid, line atop fully orthogonal octahedron, 1/4-lune of triacontiditeron 0.707107 8, 25, 38, 29, 10
squadoe square-dodecahedron duoprism 1.569562 80, 200, 188, 82, 16
raptum rap-first bistratic cap of thin, rap-based tutsatope, rap-based tutism 1.903943 80, 220, 230, 110, 22
tipagrip tip atop grip 2.150581 80, 220, 230, 110, 22
tipalprip tip atop inverted prip 1.632993 80, 250, 300, 160, 32
spidaprip spid atop prip, spid-first monostratic cap of spat 1.870829 80, 270, 340, 180, 32
tot truncated triacontiditeron, truncated pentacross 1.581139 80, 280, 400, 240, 42
doa iddip dodecahedron atop icosidodecahedron-prism 1.738546 80, 300, 376, 189, 35
tipaprip, tip || prip (degenerate) tip atop prip ∞   i.e. flat in euclidean space 80, 310, 390, 190, 32
ritag thex rit atop gyrated thex, rit-first cap of sirhin 1.620185 80, 312, 376, 168, 26
rin rectified penteract 1.414214 80, 320, 400, 200, 42
tin triacontadipenteract 1.414214 80, 320, 480, 320, 42
firn facetorectified penteract 1.414214 80, 320, 480, 320, 80
fenandoh facetospinopenteractidishexadecateron 1.274755 80, 400, 620, 280, 42
pabgysiphin parabigyrated small-prismated-hemipenteract 1.274755 80, 400, 720, 480, 82
siphin small prismated hemipenteract, runcinated demipenteract, steric penteract 1.274755 80, 400, 720, 480, 82
fidoh facetoinverted decahexadecateron 1.274755 80, 400, 940, 320, 26
ritathex (degenerate) rit atop thex ∞   i.e. flat in euclidean space 80, 408, 568, 288, 50
irohlohn invertiretrohexadecalepidohemipenteract 1.224745 80, 480, 1120, 640, 69
nat spinotriacontaditeron 1.224745 80, 480, 640, 240, 32
nit penteractitriacontiditeron, birectified penteract, birectified triacontiditeron, birectified pentacross, Gosset polytope 02,1,1 1.224745 80, 480, 640, 280, 42
irl invertiretrolepidoteron 1.224745 80, 480, 880, 400, 48
raccoth retrocellitriacontadiahexadecateron 1.224745 80, 480, 960, 640, 88
..., cont || grico (degenerate) cont atop grico ∞   i.e. flat in euclidean space 864, 2304, 2208, 912, 146
..., srico || prico (degenerate) srico atop prico ∞   i.e. flat in euclidean space 864, 2880, 3264, 1488, 242
ica sidpith, ico || sidpith icositetrachoron atop small disprismatotesseractihexadecachoron 1.847759 88, 480, 784, 472, 82
n,cube-dip n-gon - cube duoprism sqrt[3/4+1/(4 sin2(π/n))] 8n, 20n, 18n+8, 7n+12, n+6
... tetrahedral - n-prismantiprismoid ... 8n, 44n, 80n+8, 54n+12, 10n+6
tepepy tetrahedral-prismatic pyramid, vertex pyramid of rectified hexateron 0.816497 9, 24, 30, 20, 7
bidrappy bidrap pyramid 0.790569 9, 26, 35, 24, 8
sistadow (square,pentagram)-disphenoid, square atop fully orthogonal pentagram 0.707107 9, 29, 42, 29, 9
hexpy hexadecachoral pyramid, vertex-first rotunda of triacontiditeron 0.707107 9, 32, 56, 48, 17
deca agrip deca atop grip, deca-first cap of pirx 1.914854 90, 240, 240, 110, 22
sripagrip srip atop grip, srip-first cap of sibrant 2.236068 90, 270, 280, 120, 22
trid triangle - icosidodecahedron duoprism 1.717954 90, 270, 306, 159, 35
sripadecu (srip,deca)-based ursateron 1.514954 90, 300, 340, 155, 27
sripaprip srip atop prip, srip-first cap of card 1.658312 90, 300, 350, 170, 32
deca aprip deca atop prip 1.620185 90, 330, 400, 190, 32
sripalgrip, srip || inv grip (degenerate) srip atop inverted grip ∞   i.e. flat in euclidean space 90, 330, 400, 190, 32
rabird retrobirhombidodecateron 1.414214 90, 360, 360, 120, 18
... isomorph of small birhombated dodecateron 0.816497 90, 360, 420, 180, 32
sibrid (old: sadrid) small birhombated dodecateron, bicantellated hexateron 1.414214 90, 360, 420, 180, 32
sripalprip srip atop inverted prip, srip-first cap of sart 1.732051 90, 360, 440, 200, 32
hodidgyt hollow dodecadodecahedral gyrotrigonism 1.098185 90, 540, 696, 288, 39
otut octagon - truncated-tetrahedron duoprism 1.755593 96, 240, 220, 90, 16
squatic square - truncated-cube duoprism 1.914214 96, 240, 224, 96, 18
squatoe (old: squato) square - truncated-octahedron duoprism 1.732051 96, 240, 224, 96, 18
twacube dodecagon - cube duoprism 2.117085 96, 240, 224, 96, 18
..., rit || tat (degenerate) rit atop tat ∞   i.e. flat in euclidean space 96, 288, 304, 136, 26
thexip truncated-hexadecachoron prism 1.658312 96, 288, 312, 144, 26
oco (old: occo) octagon cuboctahedron duoprism 1.645329 96, 288, 316, 144, 22
squasirco square - small-rhombicuboctahedron duoprism 1.567516 96, 288, 320, 156, 30
thexa (old: thexag thex), thex || gyro thex thex alterprism, thex atop gyro thex, equatorial segment of sirhin 1.620185 96, 336, 384, 168, 26
oike octagon-icosahedron duoprism 1.616049 96, 336, 412, 198, 28
squasnic square - snub-cube duoprism 1.518409 96, 336, 416, 216, 42
pac scant partially contracted small cellated penteractitriacontiditeron ... 96, 384, 640, 512, 162
rita sidpith, rit || sidpith rectified-tesseract atop small-disprismated-tesseractihexadecachoron 1.502958 96, 480, 776, 472, 82
danbitot dispenteractibitruncated triacontaditeron 1.802776 960, 2400, 1760, 480, 52
ogrid octagon - great-rhombicosidodecahedron duoprism 4.020611 960, 2400, 2056, 684, 70
giphin great prismated hemipenteract, steriruncicantic penteract 3.259601 960, 2400, 2080, 720, 82
gibrant great birhombated penteractitriacontiditeron, bicantitruncated penteract 3.391165 960, 2400, 2160, 840, 122
gibtadin great biprismatotriacontadiadispenteract 1.488108 960, 2880, 2720, 1000, 132
sibtadin small biprismatotriacontadiadispenteract 3.047217 960, 2880, 2720, 1000, 132
repirt retroprismatorhombated triacontiditeron 3 960, 2880, 2800, 1040, 132
pirt prismatorhombated triacontiditeron, runcicantellated pentacross 3 960, 2880, 2960, 1200, 162
prin prismatorhombated penteract, runcicantellated penteract 3.047217 960, 2880, 2960, 1240, 202
quiprin quasiprismatorhombated penteract 1.488108 960, 2880, 2960, 1240, 202
gloptin great lapidoprismatotruncated penteract 1.416813 960, 3260, 3440, 1280, 132
sroptin small retroprismatotruncated penteract 3.239235 960, 3360, 3440, 1240, 132
pattit prismatotruncated triacontiditeron, runcitruncated pentacross 2.738613 960, 3360, 3680, 1440, 162
pattin prismatotruncated penteract, runcitruncated penteract 3.239235 960, 3360, 3760, 1560, 202
quiptin quasiprismatotruncated penteract 1.416813 960, 3360, 3760, 1560, 202
garcornit great retrocellirhombated penteractitriacontaditeron 1.192297 960, 3840, 3920, 1280, 142
rawcbinant (old: recarnit) retrosphenary cellibiprismatopenteractipenteractitriacontaditeron, retrocellirhombated penteractitriacontaditeron 2.660531 960, 3840, 4240, 1600, 172
wacbinant sphenary cellibiprismatopenteractipenteractitriacontaditeron 1.192297 960, 3840, 4240, 1600, 172
gadencorn great dispinocellirhombated penteract 1.192297 960, 3840, 4480, 1600, 132
carnit (old: scarnit) (small) cellirhombated penteractitriacontiditeron, stericantellated penteract, stericantellated pentacross 2.660531 960, 3840, 4720, 2080, 242
quacrant quasicellirhombipenteractitriacontiditeron 1.192297 960, 3840, 4720, 2080, 242
gofixu gax-based ursateron 1.008123 960, 5880, 8160, 3000, 242
exu (degenerate) ex-based ursateron ∞   i.e. flat in euclidean space 960, 5880, 9120, 4920, 722
gaxu gax-based ursateron 1.008123 960, 5880, 9120, 4920, 722
snippit (old: spitac, alt.: snahin) snub prismatotriacontaditeron (snub demipenteract), alternation of great prismated triacontaditeron ... 960, 6720, 10880, 6240, 1122

Count of actually available polytopes: 687


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 6D
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Acronym Name Circumradius Face vector
tepasc tetrahedral-prismatic scalene, tetrahedron-prism-pyramid pyramid, line atop fully orthogonal tetrahedron prism 0.866025 10, 33, 54, 50, 27, 8
hexasc hexadecachoric scalene, hexadecachoron-pyramid pyramid, line atop fully orthogonal hexadecachoron, 1/4-lune of hexacontatetrapeton 0.707107 10, 41, 88, 104, 65, 18
batal bitruncated heptapeton 1.647509 105, 315, 385, 245, 84, 14
sril small rhombated heptapeton, cantellated heptapeton 1.362770 105, 525, 805, 560, 210, 35
scal small cellated heptapeton, stericated heptapeton 1.195229 105, 630, 1400, 1470, 700, 105
harjak (old: trojak) demirectified icosiheptaheptacontidipeton (trirectified icosiheptaheptacontidipeton) 2.160247 1080, 6480, 10080, 6120, 1566, 126
shopjak small demiprismated icosiheptaheptacontidipeton 1.914854 1080, 8640, 19440, 16200, 4662, 342
n,rap-dip n-gon - rectified-pentachoron duoprism 10n, 40n, 60n+10, 40n+30, 11n+30, n+10
penppy penp pyramid, vertex-pyramid of ril 0.845154 11, 35, 55, 50, 27, 8
triddipasc triangle-duoprismatic scalene, triangle-duoprism-pyramid pyramid, line atop fully orthogonal triangle duoprism 1 11, 37, 60, 54, 28, 8
tacpy triacontaditeric pyramid, vertex-first rotunda of gee 0.707107 11, 50, 120, 160, 112, 33
dottasibrid dot atop sibrid, dot-first cap of ram 1.732051 110, 630, 990, 660, 224, 34
pentarin tesseract atop rectified tesseract 1.418705 112, 560, 880, 640, 252, 44
hinu hin-based ursapeton 1.287166 112, 736, 1360, 1040, 348, 44
pentanit pent atop nit 1.228783 112, 880, 2000, 1840, 732, 124
hatico hexagon - truncated-icositetrachoron duoprism 2.828427 1152, 3456, 3936, 2112, 534, 54
big dispox bi-hexacontatetra (= g)-diminished small-prismated-hexeract 2.263033 1152, 6336, 12000, 9792, 3404, 428
captog celliprismatotruncated hexacontitetrapeton, steriruncitruncated hexacross 4.123106 11520, 40320, 50880, 28320, 6446, 536
coprag celliprismatorhombated hexacontitetrapeton, steriruncicantellated hexacross 4.415880 11520, 40320, 52800, 31200, 7736, 536
coprix (small) celliprismatorhombated hexeract, steriruncicantellated hexeract 4.400450 11520, 40320, 52800, 31680, 8348, 668
cagorg (old: gacorg) celligreatorhombihexacontitetrapeton, (old: great cellirhombated hexacontatetrapeton), stericantitruncated hexacontatetrapeton 3.937004 11520, 46080, 63360, 36480, 8216, 536
tocrax (old: stocrax) (small) tericellirhombated hexeract, pentiruncitruncated hexacontitetrapeton 3.734936 11520, 51840, 77760, 48480, 11768, 728
hixip hexateron prism, vertex figure of roc 0.816497 12, 36, 55, 50, 27, 8
tratriddipdit (triangle,triangular duoprism)-duotegum, tegum product of triangle and triangular duoprism 12, 48, 96, 105, 63, 18
rapesc rectified-pentachoric scalene, rectified-pentachoron-pyramid pyramid, line atop fully orthogonal rectified pentachoron 0.816497 12, 51, 100, 100, 51, 12
thox (old: thod) triacontidiahemihexeract, triacontidihemidodecapenton, cytohemiectid, vertex figure of guhsa 0.707107 12, 60, 160, 240, 192, 38
gee (old: xic) hexacontitetrapeton, hexacross (β6), aeroex(id), hexateral antiprism, triacontaditeric bipyramid, octahedral duotegum, square triotegum, vertex figure of zee, Gosset polytope 31,1, lattice C6 contact polytope (span of its small roots) 0.707107 12, 60, 160, 240, 192, 64
tradope triangle-dodecahedron duoprismatic prism 1.595888 120, 360, 442, 284, 99, 17
gisdiddit (gisdid,gisdid)-duotegum, gisdid duotegum, tegum product of 2 great snub dodekicosidodecahedra 0.707107 120, 3960, 21808, 44880, 37440, 10816
octdoe octahedron-dodecahedron duoprism 1.569562 120, 420, 592, 410, 138, 20
tetid tetrahedron-icosidodecahedron duoprism 1.730039 120, 420, 608, 466, 194, 36
bittixa (old: bittixalbittix) bitruncated-hexateron alterprism, bitruncated-hexateron atop inverted bitruncated-hexateron, equatorial segment of rectified hexeract 1.581139 120, 480, 730, 540, 204, 34
tag truncated hexacontitetrapeton 1.581139 120, 540, 1120, 1200, 576, 76
sarxip small-rhombated-hexateron prism 1.384437 120, 540, 820, 560, 189, 29
spixip small-prismated-hexateron prism 1.290994 120, 600, 1110, 930, 349, 49
spixalsarx spix atop inverted sarx 1.290994 120, 870, 1790, 1530, 554, 64
spixa (old: spixalspix) small prismated hexateron alterprism, small prismated hexateron atop inverted small prismated hexateron, medial segment of dot-first birectified hexacontitetrapeton 1.224745 120, 900, 1920, 1620, 544, 64
ratanit rectified triacontaditeron atop penteractitriacontiditeron, rat-first rotunda of brag 1.224745 120, 960, 1760, 1240, 364, 44
ratasiphin rat atop siphin, rat-first cap of rojak 1.290994 120, 960, 2240, 2000, 684, 84
n,rahi-dip n-gon - rectified-hecatonicosachoron duoprism 1200n, 4800n, 6720n+1200, 3840n+3600, 721n+3120, n+720
n,ex-dip n-gon - hexacosachoron duoprism 120n, 740n, 1920n+120, 1800n+720, 601n+1200, n+600
pettip pentagon-pentagon-pentagon-triprism 1.473370 125, 375, 450, 275, 90, 15
gibpof great biprismated tetradecapeton, biruncicantitruncated heptapeton 3 1260, 3780, 4410, 2520, 714, 84
captal celliprismatotruncated heptapeton, steriruncitruncated heptapeton 2.591194 1260, 4410, 5670, 3360, 945, 105
copril celliprismatorhombated heptapeton, steriruncicantellated heptapeton 2.725541 1260, 4410, 5880, 3675, 1050, 105
cagral (old: gacral) celligreatorhombated heptapeton, stericantitruncated heptapeton 2.618615 1260, 5040, 7140, 4410, 1155, 105
taporf (old: staporf) teriprismatorhombitetradecapeton, pentiruncicantellated heptapeton 2.449490 1260, 5040, 7560, 5250, 1596, 126
tocral (old: stocral) tericellirhombated heptapeton, pentiruncitruncated heptapeton 2.329929 1260, 5670, 8610, 5565, 1491, 126
squarit square - rectified-tesseract duoprism 1.414214 128, 512, 768, 544, 188, 28
ritas rit altersquarism, cyclotetra-diminished sochax, medial segment of siphina, partial Stott expansion of hax 1.322876 128, 832, 1984, 1984, 804, 100
quapox quasiprismated hexeract 0.937379 1280, 7680, 14400, 11200, 3708, 508
spox small prismated hexeract, runcinated hexeract 2.263033 1280, 7680, 14400, 11200, 3708, 508
gram (old: gakbram) great rhombated pentacontitetrapeton, (old: great heptacontiduo-birhombated pentacontitetrapeton), cantitruncated pentacontitetrapeton 5 12960, 38880, 45360, 25920, 7326, 846
patom (old: kaprom) prismatotruncated pentacontitetrapeton, runcitruncated pentacontitetrapeton, (heptacontidiprismatorhombated pentacontitetrapeton) 3.872983 12960, 58320, 86400, 54000, 14238, 1278
n,oct-dippip n-gon - octahedron duoprismatic prism 12n, 42n, 58n+12, 38n+30, 11n+28, n+10
tratetpy (triangle,tetrahedron)-duoprism pyramid, vertex-pyramid of bril 0.925820 13, 42, 64, 55, 28, 8
dotu dot-based ursapeton 1.432173 130, 650, 990, 660, 224, 34
hixacube hix atop edge-parallel cube 0.866025 14, 51, 86, 78, 39, 10
... tetradecapeton dual 0.774597 14, 84, 280, 490, 420, 140
fe tetradecapeton, tritruncated heptapeton, equatorial cross-section of (vertex first) q-hept 1.732051 140, 420, 490, 280, 84, 14
spil small prismated heptapeton, runcinated heptapeton 1.309307 140, 840, 1610, 1295, 455, 70
hidbrag hexadeca-diminished brag, tegum sum of 2 antialigned octcoes 1.224745 144, 1152, 2592, 2280, 788, 92
shihtip square-hexagon-hexagon triprism 1.581139 144, 432, 516, 312, 100, 16
tutdip truncated-tetrahedron duoprism 1.658312 144, 432, 516, 312, 100, 16
codip cuboctahedron-cuboctahedron duoprism 1.414214 144, 576, 912, 696, 244, 28
thexgyt (alt.: pex tedjak) truncated-hexadecachoral gyrotrigonism, partially expanded tridiminished icosiheptaheptacontidipeton, partially expanded tridiminished 21,2 1.632993 144, 648, 1056, 816, 315, 51
coike cuboctahedron-icosahedron duoprism 1.380039 144, 648, 1128, 924, 334, 34
ikedip icosahedron-icosahedron duoprism 1.344997 144, 720, 1380, 1224, 460, 40
gocadip great-cellated-hexateron prism 3 1440, 4320, 4920, 2640, 664, 64
tim truncated pentacontitetrapeton 2.645751 1440, 7200, 10800, 6480, 1566, 126
siborg small birhombated hexacontitetrapeton, bicantellated hexacross, rectified birectified-hexacontitetrapeton 2.236068 1440, 8640, 13440, 8400, 2396, 236
trapen triangle - pentachoron duoprism, vertex figure of broc 0.856349 15, 45, 65, 55, 28, 8
trial tratet triangle atop dual tratet, triangle-first cap of ril 0.845154 15, 57, 95, 85, 43, 11
tripal triddip trip atop gyro-perp triddip 0.816497 15, 63, 110, 97, 46, 11
penaf (old: penalpenp) pentachoron antifastegium, pentachoron atop inverted pentachoral-prism, pen-first cap of jak 0.816497 15, 75, 180, 225, 138, 33
sarxasibrid small rhombated hexateron atop small birhombated dodecateron, rix-first subsegment of brox 1.414214 150, 960, 1610, 1125, 374, 49
tetdip tetrahedron-tetrahedron duoprism, vertex figure of he 0.866025 16, 48, 68, 56, 28, 8
pedril (alt.: squatratet) pentadiminished rectified heptapeton, square atop tratet 0.845154 16, 58, 95, 83, 40, 10
tetal tratet tetrahedron atop alternate triangle,tetrahedron-duoprism 0.866025 16, 72, 146, 148, 76, 18
rixpy rectified-hexateronal pyramid, vertex pyramid of demihexeract 0.866025 16, 75, 140, 125, 57, 13
nitip penteractitriacontiditeron prism 1.322876 160, 1040, 1760, 1200, 364, 44
nitarin nit atop rin, nit-first rotunda of brox 1.414214 160, 1120, 1840, 1200, 364, 44
siphina siphin alterprism, medial segment of sochax 1.322876 160, 1120, 2880, 3120, 1364, 164
nitasiphin nit atop siphin, hin-first medial segment of rojak 1.290994 160, 1360, 3040, 2600, 844, 84
brag (old: dric) birectified hexacontitetrapeton, Voronoi cell of lattice D6* 1.224745 160, 1440, 2880, 2160, 636, 76
cubedoe cube-dodecahedron duoprism 1.647278 160, 480, 576, 352, 114, 18
rinnip rectified-penteract prism 1.5 160, 720, 1120, 800, 284, 44
siphinnip small-prismated-hemipenteractic prism 1.369306 160, 880, 1840, 1680, 644, 84
medrojak (alt.: tritith) pentacontitetra-diminished rojak, tri - (triangle,triangle,hexagon)-trioprism 1.290994 162, 1134, 2754, 3078, 1638, 342
rettidjak rectification of tridiminished icosiheptaheptacontidipeton 1.632993 168, 1440, 2880, 2256, 723, 75
n,tes-dip n-gon - tesseract duoprism 16n, 48n, 56n+16, 32n+32, 9n+24, n+8
hexippy hexip pyramid, vertex pyramid of rag 1 17, 72, 144, 152, 82, 19
dedjak decadiminished icosiheptaheptacontidipeton 0.816497 17, 86, 205, 255, 158, 39
stasissiddow (pentagramm,sissid)-disphenoid, pentagram atop fully orthogonal small stellated doedcahedron 0.639240 17, 95, 223, 223, 95, 17
hinpy demipenteractic pyramid, vertex pyramid of jak 0.816497 17, 96, 240, 280, 146, 27
hint demipenteractic (line-)tegum, demipenteractic dipyramid ... 18, 112, 320, 440, 266, 52
tepepyp tetrahedral-prismatic pyramid prism, prism of tepepy 0.957427 18, 57, 84, 70, 34, 9
tidril tridiminished rectified heptapeton, (pen,pen,bidrap)-trigonic 0.845154 18, 75, 127, 107, 48, 11
octa tratet oct atop tratet, oct-first cap of ril 0.845154 18, 78, 132, 112, 52, 12
endjak ennea-diminished jak 0.816497 18, 90, 192, 213, 126, 33
tragrip triangle - great-rhombated-pentachoron duoprism 1.932184 180, 540, 660, 420, 143, 23
tridep triangle-icosidodecahedron duoprismatic prism 1.789237 180, 630, 882, 624, 229, 37
octid octahedron-icosidodecahedron duoprism 1.765796 180, 720, 1152, 900, 328, 40
trahi triangle - hecatonicosachoron duoprism 3.747204 1800, 5400, 6360, 3720, 1083, 123
troctpy troct pyramid, vertex pyramid of brag 1.224745 19, 72, 120, 105, 50, 12
codibrox tetracontaocta-diminished birectified hexeract 1.414214 192, 1152, 2336, 2080, 828, 124
sochax small cellated hemihexeract, stericated demihexeract, pentic hexaract 1.322876 192, 1440, 4000, 4800, 2344, 296
cubesirco cube-small-rhombicuboctahedron duoprism 1.645329 192, 672, 928, 632, 216, 32
tragittith (triangle,gittith)-duoprism 1.061238 192, 768, 1048, 696, 235, 35
trasteth (triangle,steth)-duoprism 1.593876 192, 768, 1048, 696, 235, 35
rax rectified hexeract, rectified dodecapeton 1.581139 192, 960, 1520, 1120, 444, 76
forx facetorectified hexeract 1.581139 192, 960, 1920, 1920, 960, 192
crohax (old: scrohax) (small) cellirhombated hemihexeract, pentiruncinated demihexeract, pentiruncic hexeract 2.397916 1920, 10560, 16960, 11040, 3016, 296
sobpoxog small biprismated hexeractihexacontatetrapeton, biruncinated hexeract, biruncinated hexacross 2.345208 1920, 11520, 22560, 17760, 5276, 476
cakix celliskewed hexeract 1.581139 1920, 11520, 23040, 21120, 8048, 548
rackix retrocelliskewed hexeract 1.581139 1920, 11520, 23040, 21120, 8048, 548
girhax great rhombated hemihexeract, cantitruncated demihexeract, runcicantic hexeract 3.278719 1920, 5760, 6560, 3520, 876, 76
gaqrox great quasirhombihexeract 1.906840 1920, 5760, 7280, 4960
grox great rhombihexeract, cantitruncated hexeract 4.045239 1920, 5760, 7280, 4960, 1788, 268
prohax prismatorhombated hemihexeract, runcicantellated demihexeract, steriruncic hexeract 2.783882 1920, 7680, 10720, 6720, 1996, 236
tacox tericellated hexeract, pentitruncated hexacross 2.474130 1920, 8640, 15680, 13920, 5688, 728
quotacog quasitericellated hexacontatetrapeton 1.121320 1920, 8640, 16320, 15360, 6488, 728
tacog tericellated hexacontitetrapeton, pentitruncated hexeract 3.121320 1920, 8640, 16320, 15360, 6488, 728
saborx small birhombated hexeract, bicantellated hexeract 2.645751 1920, 9600, 13760, 8320, 2556, 316
cathix cellitruncated hemihexeract, steritruncated demihexeract, penticantic hexeract 2.598076 1920, 9600, 16800, 12480, 3656, 296
rapalpenp rap atop inverted penp, pen-first medial subsegment of jak 0.816497 20, 115, 270, 280, 128, 23
hedjak heptadiminished jak, square || hin 0.816497 20, 116, 289, 328, 166, 31
starpglassdit pentagrammic-retroprismatic-hourglass duotegum 0.707107 20, 120, 229, 190, 75, 14
squapen square-pentachoron duoprism, vertex figure of bersa 0.948683 20, 60, 85, 70, 34, 9
... (mono) tetal tratet augmented tetdip 0.866025 20, 90, 180, 183, 97, 24
taccup triacontiditeron prism, vertex figure of rez 0.866025 20, 90, 200, 240, 144, 34
rapa penp rap atop penp, rap-first cap of ril 0.845154 20, 95, 160, 130, 58, 13
ril (old: riss) rectified heptapeton, vertex figure of hesa, Gosset polytope 04,1 0.845154 21, 105, 175, 140, 63, 14
firl facetorectified heptapeton 0.845154 21, 105, 245, 315, 217, 63
dotpy dodecateron pyramid, vertex pyramid of mo 1 21, 110, 210, 180, 72, 13
hixalrix hexateron atop inverted rectified hexateron, hix-first rotunda of jak 0.816497 21, 135, 370, 480, 273, 49
tatraffip triangle atop traffip 0.925820 21, 84, 139, 117, 53, 12
sabril small birhombated heptapeton, bicantellated heptapeton 1.558387 210, 1050, 1540, 980, 329, 49
sibpof small biprismated tetradecapeton, biruncinated heptapeton 1.414214 210, 1260, 2520, 2100, 716, 84
restaf rectified staf 1.732051 210, 1680, 3850, 3990, 1778, 168
gril great rhombated heptapeton, cantitruncated heptapeton 2.104417 210, 630, 805, 560, 210, 35
tocal teracellated heptapeton, pentitruncated heptapeton 1.647509 210, 945, 1820, 1785, 826, 126
rojak rectified icosiheptaheptacontidipeton 1.290994 216, 2160, 5040, 4320, 1350, 126
hittip hexagon-hexagon-hexagon-triprism 1.732051 216, 648, 756, 432, 126, 18
catjak (old: detidjik) cellitruncated icosiheptapeton (disteridisicosiheptaheptacontidipeton) 2.581989 2160, 11880, 23760, 19440, 5958, 558
... isomorph of birectified pentacontitetrapeton 0.816497 2160, 12960, 19440, 10800, 2286, 126
barm (old: scram, bram, remak, kram) birectified pentacontitetrapeton, (small centrorhombated pentacontitetrapeton) 2.449490 2160, 12960, 19440, 10800, 2286, 126
trarox triangle - rectified-hexacosachoron duoprism 3.131369 2160, 12960, 22320, 16560, 5763, 723
sirjak small rhombated icosiheptaheptacontidipeton 2.380476 2160, 15120, 24480, 15120, 3942, 342
spam (old: skopam) small prismated pentacontitetrapeton, (small hebdomecontadiaprismated pentacontitetrapeton) 2.236068 2160, 15120, 36720, 36720, 14238, 1278
botajik bitruncated icosiheptaheptacontidipeton 2.943920 2160, 8640, 11520, 6480, 1566, 126
hotjak demitruncated icosiheptapeton 2.828427 2160, 9720, 14400, 9360, 2862, 342
dotet (line,)dodecateron-tegum, dodecateron dipyramid 22, 130, 300, 300, 132, 24
dotum dot-first bistratic cap of tim, dot-based tutsatope, dot-based tutism 2.645751 220, 740, 990, 660, 224, 34
gocog great cellated hexacontitetrapeton, steriruncicantitruncated hemihexeract, omnitruncated hemihexeract 5.244044 23040, 69120, 76800, 38400, 8216, 536
tisdip altratet tisdip atop gyrated tratet 0.925820 24, 102, 173, 144, 62, 13
tetafip prism of tetrahedral antifastegium, tetaf prism, tepe atop inverted squatet, half of hinnip 0.935414 24, 104, 202, 196, 93, 19
tetaco altepetric (tetaco,tepe)-disphenoid, (tet,co,inv tepe)-trigonic 1 24, 106, 200, 186, 86, 18
tratetdafup triangular-tetrahedral duoantifastegiaprism, tratet atop bidual tratet 0.866025 24, 132, 284, 282, 128, 22
odhax octadiminished hemihexeract 0.866025 24, 132, 310, 336, 162, 28
hexaf, hex || gyro hexip hexadecachoral alterfastegium, hex atop gyrated hexip, hex-first rotunda of hax 0.866025 24, 144, 344, 352, 155, 27
tedjak (alt.: hexgyt, hexalhin) tridiminished icosiheptaheptacontidipeton, tridiminished 22,1, hexadecachoral gyrotrigonism 0.816497 24, 168, 480, 600, 315, 51
tratepe triangle-tetrahedron-duoprism prism, vertex figure of lanq 0.978945 24, 72, 98, 76, 35, 9
tetoct tetrahedron-octahedron duoprism, vertex figure of sez 0.935414 24, 84, 128, 106, 50, 12
trahex triangle - hexadecachoron duoprism, vertex figure of barz 0.912871 24, 96, 176, 168, 83, 19
rinathin rectified penteract atop truncated demipenteract, rectified demipenteract-first cap of demirectified icosiheptaheptacontidipeton 2.160247 240, 1200, 1840, 1200, 364, 44
cappixa (old: cappixalcappix) cappix alterprism, cappix atop alternate cappix 1.658312 240, 1200, 2220, 1770, 574, 64
nitasirhin nit atop sirhin, nit-first cap of ram 1.732051 240, 1680, 2720, 1680, 444, 44
brox (old: drax) birectified hexeract, Gosset polytope 03,1,1 1.414214 240, 1920, 3200, 2080, 636, 76
codoe cuboctahedron-dodecahedron duoprism 1.721489 240, 840, 1144, 740, 222, 26
cubid cube-icosidodecahedron duoprism 1.835220 240, 840, 1156, 782, 264, 38
ikedoe icosahedron-dodecahedron duoprism 1.693527 240, 960, 1444, 992, 300, 32
squahi square-hecatonicosachoron duoprism 3.769377 2400, 7200, 8280, 4560, 1204, 124
n,ico-dip n-gon - icositetrachoron duoprism 24n, 120n, 192n+24, 120n+96, 25n+96, n+24
n,co-dippip n-gon - cuboctahedron duoprismatic prism 24n, 84n, 112n+24, 68n+60, 17n+52, n+16
n,ike-dippip n-gon - icosahedron duoprismatic prism 24n, 96n, 142n+24, 92n+72, 23n+70, n+22
penarappip pen-first cap of birectified heptapeton 0.925820 25, 120, 200, 155, 63, 13
gacal great cellated heptapeton, steriruncicantitruncated heptapeton 3.380617 2520, 7560, 8610, 4620, 1155, 105
tacogral (old: gatocral) tericelligreatorhombated heptapeton, pentistericantitruncated heptapeton 2.976095 2520, 8820, 11340, 6510, 1596, 126
tagopal (old: gatopal) terigreatoprismated heptapeton, pentiruncicantitruncated heptapeton 3.116775 2520, 8820, 11550, 6825, 1701, 126
gabrim (old: prarm, older: girmak, oldest: gokorm) great birhombated pentacontitetrapeton (prismatorhombated rectified pentacontitetrapeton), bicantitruncated pentacontitetrapeton 5.385165 25920, 77760, 86400, 43200, 9198, 558
prom (old: kaptom) prismatorhombated pentacontitetrapeton, (heptacontidiprismatotruncated pentacontitetrapeton) 4.582576 25960, 103680, 140400, 79920, 18558, 1278
hixadot hexateron atop dodecateron, hix-first half of hax 0.866025 26, 165, 380, 365, 153, 29
dijak (alt.: taccahin) (mono-)diminished icosiheptaheptacontidipeton, tac atop hin 0.816497 26, 200, 640, 920, 538, 84
hixu hexateral-based ursapeton ofx3xoo3ooo3ooo3ooo&#xt, hix-based ursulate 1.048383 27, 111, 175, 140, 63, 14
triddippa tridafup triddip atop tridafup 0.925820 27, 126, 225, 192, 81, 15
triddipabl tratrip triddip atop bidual tratrip 1 27, 135, 243, 201, 81, 15
kaje heptacontidiaicosiheptapeton, vertex figure of quil 0.816497 27, 216, 720, 1080, 567, 99
jak (old: yaz) icosiheptaheptacontidipeton, argyropeton, sideropeton, Gosset polypeton 22,1, vertex figure of naq, Delone cell of lattice E6 0.816497 27, 216, 720, 1080, 648, 99
daj (old: dije) disicosiheptapeton, vertex figure of nal 0.816497 27, 216, 720, 1080, 783, 54
gaje (old: gaj, older: gij) great icosiheptaheptacontidipeton 0.816497 27, 216, 990, 990, 216, 27
trittip triangle-triangle-triangle-triprism, vertex figure of ramoh 1 27, 81, 108, 81, 36, 9
titraf triangle-traf duoprism 0.966092 27, 99, 153, 123, 54, 12
sibridacard sibrid atop card, first subsegment of dot-first ram 1.732051 270, 1800, 3120, 2160, 634, 64
trim (old: cacam, tram, mak) trirectified pentacontitetrapeton, (centrocellated pentacontitetrapeton, pentacontitetraheptacontidipeton) 1.414214 270, 2160, 6480, 8640, 4608, 558
ladbril heptadiminished birectified heptapeton 0.925820 28, 126, 245, 238, 112, 21
hexipaco hexip atop co 1 28, 128, 246, 229, 102, 19
hinaco hemipenteract atop cuboctahedron 1 28, 152, 342, 345, 154, 27
cotoe cuboctahedron - truncated-octahedron duoprism 1.870829 288, 1008, 1368, 876, 256, 28
trarico triangle - rectified-icositetrachoron duoprism 1.825742 288, 1152, 1680, 1152, 387, 51
tahgyt tesseractihexadecachoric gyrotrigonism 2.160247 288, 1152, 1704, 1176, 387, 51
pabex hax partially biexpanded hemihexeract, truncated tetrahedral duoalterprism 1.658312 288, 1440, 2688, 2208, 756, 84
hatope hexagon - truncated-octahedron duoprismatic prism 1.936492 288, 864, 1008, 576, 166, 22
tratah triangle - tesseractihexadecachoron duoprism 2.198484 288, 864, 1032, 624, 195, 27
gaborg great birhombihexacontitetrapeton, bicantitruncated hexacross 3.391165 2880, 10080, 13440, 8400, 2396, 236
prog prismatorhombated hexacontitetrapeton, runcicantellated hexacross 3 2880, 11520, 16800, 11280, 3416, 296
pithax prismatotruncated hemihexeract, runcitruncated demihexeract, stericantic hexeract 2.958040 2880, 12960, 18240, 10560, 2636, 236
potag prismatotruncated hexacontitetrapeton, runcitruncated hexacross 2.738613 2880, 15840, 24960, 15600, 3896, 296
squarox square - rectified-hexacosachoron duoprism 3.157869 2880, 17280, 29520, 20880, 6484, 724
trarap triangle - rectified-pentachoron duoprism, vertex figure of branq 0.966092 30, 120, 190, 150, 63, 13
spidapenp spid atop penp, wedge of staf 1 30, 125, 240, 250, 138, 33
rixip rectified-hexateron prism, vertex figure of rolaq 0.957427 30, 135, 220, 170, 69, 14
tratet altroct triangle-tetrahedron duoprism atop gyrated triangle-octahedron duoprism, vertex-first medial segment of birectified heptapeton 0.925820 30, 156, 280, 228, 90, 16
rixa (alt.: pabdihax, old: rixalrix) rectified hexateron alterprism, parabidiminished demihexeract, rectified hexateron atop inverted rectified hexateron 0.866025 30, 210, 520, 510, 204, 34
squahex square-hexadecachoron duoprism, vertex figure of braxh 1 32, 128, 232, 216, 100, 20
hexcopedaw (alt.: hexorcope) (hex,cope)-disphenoid, tetrahedral antiprism atop axis-orthogonal cuboctahedron prism 1.224745 32, 132, 228, 196, 86, 18
hinnip hemipenteractic prism, vertex figure of ranq 0.935414 32, 176, 400, 400, 172, 28
hax hemihexeract, vertex figure of laq, Gosset polytope 13,1 0.866025 32, 240, 640, 640, 252, 44
tetcube tetrahedron - cube duoprism 1.060660 32, 96, 128, 96, 42, 10
ginnontip ginnont prism 1.137055 320, 1440, 1920, 1200, 384, 54
sinnontip sinnont prism 1.645329 320, 1440, 1920, 1200, 384, 54
sirhina sirhin alterprism, medial segment of sophax 1.658312 320, 1920, 3680, 2880, 924, 124
n,rit-dip n-gon - rectified-tesseract duoprism 32n, 128n, 184n+32, 112n+96, 25n+88, n+24
tettidjak truncation of tridiminished icosiheptaheptacontidipeton 2.449490 336, 1608, 2880, 2256, 723, 75
bril (old: driss) birectified heptapeton, vertex figure of lin, Gosset polytope 03,2 0.925820 35, 210, 350, 245, 84, 14
titstip triangle-triangle-square triprism 1.080123 36, 108, 141, 102, 43, 10
trope (old: troctip) triangle-octahedron duoprismatic prism 1.040833 36, 126, 186, 144, 61, 13
octdip octahedron-octahedron duoprism, dual of Delone cell of lattice D6*, vertex figure of traxh 1 36, 144, 240, 204, 88, 16
tridafupip tridafup prism 1 36, 162, 276, 222, 88, 16
hixascad hexateron atop small cellated decateron, hix-first rotunda of small terated tetradecapeton 1 36, 165, 350, 405, 248, 64
coid cuboctahedron-icosidodecahedron duoprism 1.902113 360, 1440, 2244, 1650, 532, 46
cardip cellirhombated-dodecateron prism 1.732051 360, 1620, 2520, 1740, 544, 64
ikid icosahedron-icosidodecahedron duoprism 1.876844 360, 1620, 2784, 2202, 730, 52
trex triangle - hexacosachoron duoprism 1.717954 360, 2520, 5880, 6120, 3003, 603
trarahi triangle - rectified-hecatonicosachoron duoprism 4.571175 3600, 14400, 21360, 15120, 5283, 723
quotox quasitruncated hexeract 0.681517 384, 1152, 1520, 1120, 444, 76
tox truncated hexeract 2.745093 384, 1152, 1520, 1120, 444, 76
squarico square - rectified-icositetrachoron duoprism 1.870829 384, 1536, 2208, 1440, 436, 52
goxaxog great hexeractihexeractihexacontitetrapeton 1.137055 384, 1920, 2480, 1600, 564, 88
soxaxog small hexeractihexeractihexacontitetrapeton 1.645329 384, 1920, 2480, 1600, 564, 88
quitoxog quasiterated hexeractihexacontatetrapeton 1.137055 384, 1920, 4160, 4800, 2904, 728
stoxog small terated hexeractihexacontatetrapeton, pentellated hexeract, pentellated hexacross 1.645329 384, 1920, 4160, 4800, 2904, 728
gippitip great-prismated-triacontiditeron prism 3.905125 3840, 11520, 13120, 7040, 1764, 164
gaborx great birhombated hexeract, bicantitruncated hexeract 4 3840, 11520, 13760, 8320, 2556, 316
prox prismatorhombated hexeract, runcicantellated hexeract 3.598576 3840, 13440, 17600, 11200, 3708, 508
caprohax small celliprismatorhombated hemihexeract, steriruncicantellated demihexeract, pentisteriruncic hexeract 3.278719 3840, 15360, 21760, 13440, 3496, 296
copox celliprismated hexeract, steriruncinated hexeract 3.087966 3840, 15360, 23360, 16320, 5148, 668
copog celliprismated hexacontitetrapeton, steriruncinated hexacross 3.316625 3840, 15360, 24000, 17280, 5336, 536
potax prismatotruncated hexeract, runcitruncated hexeract 3.762560 3840, 17280, 25280, 16000, 4668, 508
quoptax quasiprismatotruncated hexeract 1.686163 3840, 17280, 25280, 16000, 4668, 508
catog cellitruncated hexacontitetrapeton, steritruncated hexacross 2.828427 3840, 19200, 33600, 24480, 6776, 536
catax cellitruncated hexeract 3.456841 3840, 19200, 34080, 25440, 7388, 668
quactix quasicellitruncated hexeract 1.431870 3840, 19200, 34080, 25440, 7388, 668
tapox (old: stapox) teriprismated hexeract, penticantellated hexacross 2.707107 3840, 21120, 38720, 30240, 9528, 728
topag (old: stopag) teriprismated hexacontitetrapeton, penticantellated hexeract 2.921564 3840, 21120, 39360, 31680, 10328, 728
open octagon-pentachoron duoprism 1.451588 40, 120, 165, 130, 58, 13
stopen octagram-pentachoron duoprism 1.092197 40, 120, 165, 130, 58, 13
squarap square - rectified-pentachoron duoprism 1.048809 40, 160, 250, 190, 74, 14
dotip dodecateron prism 1 40, 200, 330, 240, 84, 14
hexipaico hexip atop ico, diminished 1/4-lune of rag 1 40, 248, 472, 400, 163, 27
spida rappip spid || rappip, (rap,rap,spid)-trigonic 1 40, 250, 520, 470, 193, 33
dodoe dodecahedron-dodecahedron duoprism (or simply: dodecahedral duoprism) 1.981679 400, 1200, 1380, 760, 204, 24
sirhinasart sirhin atop sart, nit-first subsegment of ram 1.732051 400, 2880, 4800, 3080, 844, 84
n,doe-dippip n-gon - dodecahedron duoprismatic prism 40n, 120n, 134n+40, 68n+80, 15n+54, n+14
til truncated heptapeton 1.362771 42, 126, 175, 140, 63, 14
fohaf tetradecahemitetradecapeton 1 42, 210, 315, 245, 105, 21
staf (interim: stef) small terated tetradecapeton, pentellated heptapeton, expanded heptapeton, lattice A6 contact polytope (span of its roots) 1 42, 210, 490, 630, 434, 126
gabril great birhombated heptapeton, bicantitruncated heptapeton 2.390457 420, 1260, 1540, 960, 329, 49
pril prismatorhombated heptapeton, runcicantellated heptapeton 2.104417 420, 1470, 1960, 1295, 455, 70
copal celliprismated heptapeton, steriruncinated heptapeton 1.963961 420, 1680, 2660, 1995, 700, 105
patal prismatotruncated heptapeton, runcitruncated heptapeton 2 420, 1890, 2800, 1820, 560, 70
catal cellitruncated heptapeton, steritruncated heptapeton 1.851640 420, 2100, 3780, 2940, 945, 105
topal (old: stopal) teriprismated heptapeton, penticantellated heptapeton 1.690309 420, 2310, 4340, 3570, 1246, 126
tojak truncated icosiheptaheptacontidipeton 2 432, 2376, 5040, 4320, 1350, 126
hejak demified icosiheptaheptacontidipeton 1.632993 432, 3240, 7920, 7200, 2430, 342
titajak (old: totajik, oldest: hibtajak) tritruncated icosiheptaheptacontidipeton, (demibitruncated icosiheptaheptacontidipeton) 3.829708 4320, 12960, 14400, 7200, 1566, 126
girjak great rhombated icosiheptaheptacontidipeton 3.605551 4320, 17280, 24480, 15120, 3942, 342
shorjak small demirhombated icosiheptaheptacontidipeton 3.265986 4320, 19440, 27360, 15840, 3942, 342
hopitjak (old: hoptijak) demiprismatotruncated icosiheptaheptacontidipeton 3.109126 4320, 21600, 32400, 19440, 4662, 342
spojak small prismated icosiheptapeton 2.768875 4320, 25920, 47520, 34560, 9702, 1062
rixascad rectified hexateron atop small cellated dodecateron, half of rectified hexacontitetrapeton (its rix-first rotunda) 1 45, 300, 710, 795, 404, 64
gaquitxog great quasiterated hexeractihexacontatetrapeton 4.288753 46080, 138240, 151680, 72960, 14168, 728
gotaxog great terated hexeractihexacontatetrapeton 6.293378 46080, 138240, 151680, 72960, 14168, 728
tratess triangle - tesseract duoprism 1.154701 48, 144, 184, 128, 51, 11
tettut (tetrahedron,truncated-tetrahedron)-duoprism 1.322876 48, 144, 188, 136, 56, 12
octcube octahedron-cube duoprism 1.118034 48, 168, 244, 182, 72, 14
tetco tetrahedron-cuboctahedron duoprism 1.172604 48, 168, 248, 196, 86, 18
tetike tetrahedron-icosahedron duoprism 1.131154 48, 192, 308, 256, 116, 24
xedrag hexeractidiminished rectified hexacontatetrapeton, square cuboctahedroltriate, scaliform dodecadiminished rectified hexacontatetrapeton 1 48, 288, 688, 768, 396, 76
raddirag rhombidodecahedraly-diminished rectified hexacontatetrapeton 1 48, 312, 758, 906, 532, 120
squagippid square - great-prismated-pentachoron duoprism 2.345208 480, 1440, 1680, 960, 274, 34
sarxa gippixtum sarx-first bistratic cap of shorjak, sarx-based tutsatope, sarx-based tutism 3.265986 480, 1620, 2080, 1280, 389, 49
botag bitruncated hexacontitetrapeton, bitruncated hexacross 2.121320 480, 1920, 3040, 2160, 636, 76
thax truncated hemihexeract, cantic hexeract 2.179449 480, 2160, 3200, 2080, 636, 76
sartabittit small rhombated triacontadipeton atop bitruncated triacontadipeton, sart-first cap of small birhombated hexacontitetrapeton 2.236068 480, 2400, 3680, 2440, 764, 84
srog small rhombihexacontitetrapeton, cantellated hexacross 1.732051 480, 3360, 6400, 5040, 1656, 136
sophax small prismated hemihexeract, runcinated demihexeract, steric hexeract 1.658312 480, 3360, 7360, 6240, 1996, 236
squex square-hexacosachoron duoprism 1.765796 480, 3360, 7800, 7920, 3604, 604
squarahi square - rectified-hecatonicosachoron duoprism 4.589369 4800, 19200, 28080, 18960, 6004, 724
4,n,n-tip square - n-gon - n-gon - triprism sqrt[1/2+1/(2 sin2(π/n))] 4n2, 12n2, 13n2+8n, 6n2+16n, n2+10n+4, 2n+4
4,n,m-tip square - n-gon - m-gon - triprism sqrt[1/2+1/(4 sin2(π/n))+1/(4 sin2(π/m))] 4nm, 12nm, 13nm+4n+4m, 6nm+8n+8m, nm+5n+5m+4, n+m+4
taccarat triacontaditeron atop rectified triacontaditeron, tac-first rotunda of rectified hexacontitetrapeton, rectified triacontaditeron-pyramid 1 50, 360, 760, 720, 314, 44
dottascad dodecateron atop small cellated dodecateron 1 50, 390, 1050, 1140, 494, 64
gotaf great terated tetradecapeton, omnitruncated heptapeton, Voronoi cell of lattice A6*, permutopeton of 7 elements 3.741657 5040, 15120, 16800, 8400, 1806, 126
gopam (old: gakpam) great prismated pentacontitetrapeton, (great heptaheptacontidiprismated pentacontitetrapeton), omnitruncated pentacontitetrapeton, omnitruncated icosiheptaheptacontidipeton 6.244998 51840, 155520, 172800, 86400, 18558, 1278
tithtip triangle-triangle-hexagon triprism 1.290994 54, 162, 207, 144, 57, 12
oddimo (alt.: bittip) octadeca-diminished mo, bitriangular trioprism, triangular trioalterprism 1 54, 378, 864, 864, 396, 72
... bidodecateric heptacontadipeton, pentacontitetrapeton dual, convex hull of madek 0.816497 54, 702, 2160, 2160, 720, 72
hinro (alt.: hinarat) demipenteractic rotunda, hin-first half of mo, hin atop rat 1 56, 480, 1280, 1240, 428, 44
toedip truncated-octahedron - truncated-octahedron duoprism 2.236068 576, 1728, 1968, 1056, 268, 28
sircotic small-rhombicuboctahedron - truncated-cube duoprism 2.263033 576, 2016, 2688, 1656, 448, 40
bicotoe bi - (cuboctahedron, truncated octahedron)-duoprism 1.870829 576, 2592, 4464, 3696, 1472, 224
gophax great prismated demihexeract, steriruncicantic hexeract 4.092676 5760, 17280, 19680, 10560, 2636, 236
gopog great prismated hexacontitetrapeton, runcicantitruncated hexacross 3.872983 5760, 20160, 26400, 15600, 3896, 296
capthix small celliprismatotruncated hemihexeract, steriruncitruncated demihexeract, pentistericantic hexeract 3.278719 5760, 23040, 31200, 17760, 4136, 296
boprax biprismatorhombated hexeract, biruncitruncated hexacross 3.464102 5760, 23040, 31680, 19200, 5276, 476
boprag biprismatorhombated hexacontitetrapeton, biruncitruncated hexeract 3.674235 5760, 23040, 32160, 19680, 5276, 476
crag (old: scrag) cellirhombated hexacontitetrapeton, stericantellated hexacross 3.082207 5760, 28800, 45120, 29280, 7736, 536
crax (old: scrax) (small) cellirhombated hexeract, stericantellated hexeract 3.277597 5760, 28800, 45600, 30240, 8348, 668
n,pen-dip n-gon - pentachoron duoprism sqrt[1/(4 sin2(π d/n))+2/5] 5n, 15n, 20n+5, 15n+10, 6n+10, n+5
tixip truncated-hexateron prism 1.414214 60, 180, 235, 170, 69, 14
traspid triangle - small-prismated-pentachoron duoprism 1.154701 60, 240, 410, 360, 163, 33
scadip small-cellated-dodecateric prism 1.118034 60, 270, 540, 570, 304, 64
tacu tac-based ursapeton 1.144123 60, 370, 760, 720, 314, 44
rag (old: ric) rectified hexacontitetrapeton, lattice B6 contact polytope (span of its small roots), lattice D6 contact polytope (span of its roots) 1 60, 480, 1120, 1200, 576, 76
iddoe icosidodecahedron-dodecahedron duoprism 2.140458 600, 2100, 2800, 1730, 474, 44
n,hi-dip n-gon - hecatonicosachoron duoprism 600n, 1800n, 1920n+600, 840n+1200, 121n+720, n+120
n,id-dippip n-gon - icosidodecahedron duoprismatic prism 60n, 210n, 274n+60, 158n+150, 35n+124, n+34
bapril biprismatorhombated heptapeton, biruncitruncated heptapeton 2.203893 630, 2520, 3570, 2310, 714, 84
cral (old: scral) cellirhombated heptapeton, stericantellated heptapeton 1.927248 630, 3150, 5040, 3465, 1050, 105
ax (old: hexe) hexeract, dodecapeton, 6D measure-polytope (γ6), geoex(id) 1.224745 64, 192, 240, 160, 60, 12
sirhax small rhombated hemihexeract, cantellated demihexeract, runcic hexeract 1.936492 640, 3840, 5920, 3520, 876, 76
bitem (old: gacram, botam, kobtam) bitruncated pentacontitetrapeton, (great centrorhombated pentacontitetrapeton, heptacontidia-bitruncated pentacontitetrapeton) 4.123106 6480, 19440, 21600, 10800, 2286, 126
haprojak demiprismatorhombated icosiheptapeton 3.559026 6480, 25920, 34560, 19440, 4662, 342
sram (old: skobram, skabram) small rhombated pentacontitetrapeton, (small hebdomecontadiabirhombated pentacontitetrapeton) 3.316625 6480, 32400, 45360, 25920, 7326, 846
sabrim (old: pirm, sirmak, skorm) small birhombated pentacontitetrapeton, (prismatorectified pentacontitetrapeton, small rhombated pentacontitetraheptacontidipeton, small heptacontidirhombated pentacontitetrapeton) 3 6480, 38880, 62640, 38880, 9198, 558
hop (old: hep) heptapeton, 6D simplex (α6), pyroex(id), hexateral pyramid, vertex figure of oca, Gosset polytope 05 0.654654 7, 21, 35, 35, 21, 7
pabdimo, dot||scad||dot parabidiminished mo, dodecateron atop pseudo small cellated dodecateron atop dodecateron 1 70, 680, 1980, 1980, 666, 56
tracope triangle-cuboctahedron duoprismatic prism 1.258306 72, 252, 360, 264, 103, 19
trikep triangle-icosahedron duoprismatic prism 1.219771 72, 288, 450, 348, 139, 25
octco octahedron-cuboctahedron duoprism 1.224745 72, 288, 468, 378, 148, 22
octike octahedron-icosahedron duoprism 1.185120 72, 324, 576, 498, 202, 28
trico triangle - icositetrachoron duoprism 1.154701 72, 360, 600, 456, 171, 27
icaf (alt.: icalicope) icositetrachoron antifastegium, icositetrachoron atop inverted icositetrachoral-prism 1.123033 72, 600, 1680, 2088, 1179, 243
mo pentacontitetrapeton, chrysopeton, Gosset polypeton 12,2, vertex figure of jakoh, lattice E6 contact polytope (span of its roots) 1 72, 720, 2160, 2160, 702, 54
hagippid hexagon - great-prismated-decachoron duoprism 2.449490 720, 2160, 2460, 1320, 336, 36
cograxa (old: cograxalcograx) cograx alterprism, cograx atop alternate cograx 2.345208 720, 2880, 4080, 2520, 664, 64
bittita sibrant bitruncated triacontadipeton atop small birhombated penteractitriacontiditeron, sart-first subsegment of small birhombated hexacontitetrapeton 2.236068 720, 3600, 5280, 3280, 1004, 124
ram rectified pentacontitetrapeton, Gosset polypeton 02,2,1, Voronoi cell of lattice E6* 1.732051 720, 6480, 10800, 6480, 1566, 126
n,rox-dip n-gon - rectified-hexacosachoron duoprism 720n, 4320n, 7200n+720, 4320n+3600, 721n+3600, n+720
rixalspix rectified hexateron atop small prismated hexateron, rix-first cap of scal 1.195229 75, 390, 770, 720, 314, 49
rixasarx rectified hexateron atop small rhombated hexateron, rix-first cap of brox 1.414214 75, 420, 670, 470, 174, 29
rixaspix rectified hexateron atop small prismated hexateron, rix-first cap of rojak 1.290994 75, 510, 1130, 1020, 374, 49
redscox (alt.: trisoo) hecatonenenecontadia-diminished small cellihexeract, partially triexpanded xedrag, tri - (4,8,8)-trioprism 1.978437 768, 3840, 7616, 7296, 3288, 536
togrig (old: gotrig) terigreatorhombihexacontitetrapeton, (old: great terirhombated hexacontatetrapeton), penticantitruncated hexacontitetrapeton 3.569684 7680, 30720, 47360, 33600, 10008, 728
squepe square pennene 0.707107 8, 26, 45, 45, 26, 8
hixit hexateral (line-)tegum, hexateral dipyramid 8, 27, 50, 55, 36, 12
tetdoe tetrahedron-dodecahedron duoprism 1.529224 80, 240, 308, 216, 84, 16
ratip rectified-triacontiditeron prism 1.118034 80, 520, 1040, 880, 324, 44
dottaspix dodecateron atop small prismated hexateron, dot-first cap of birectified hexacontitetrapeton 1.224745 80, 540, 1080, 885, 314, 49
gapil great prismated heptapeton, runcicantitruncated heptapeton 2.803060 840, 2520, 3010, 1820, 560, 70
tactaf tericellitruncated tetradecapeton, pentisteritruncated heptapeton 2.236068 840, 3360, 5250, 3780, 1176, 126
togral (old: gotral) terigreatorhombated heptapeton, penticantitruncated heptapeton 2.390457 840, 3360, 5390, 4096, 1351, 126
titam (old: cacram, totam, tomak, katom) tritruncated pentacontitetrapeton, (centrocellirhombated pentacontitetrapeton, trunkated pentacontitetraheptacontidipeton, heptacontiditruncated pentacontitetrapeton) 3.741657 8640, 34560, 47520, 28080, 7038, 558
n,tet-dippip n-gon - tetrahedron duoprismatic prism 8n, 24n, 30n+8, 20n+16, 7n+14, n+6
n,hex-dip n-gon - hexadecachoron duoprism sqrt[2+1/sin2(π/n)] 8n, 32n, 56n+8, 48n+24, 17n+32, n+16
trippete trip tettene, {3}-first cap of jak 0.816497 9, 30, 51, 49, 27, 8
octete octahedral tettene, octahedral-pyramid pyramid pyramid, triangle atop fully orthogonal octahedron 0.707107 9, 33, 63, 67, 39, 11
trasrip (triangle,small rhombated pentachoron)-duoprism 1.316561 90, 360, 540, 390, 143, 23
scadaspix small cellated dodecateron atop small prismated hexateron, scad-first cap of scal 1.195229 90, 510, 1050, 1005, 439, 64
idodip icosidodecahedron-icosidodecahedron duoprism 2.288246 900, 3600, 5520, 3900, 1144, 64
tetgocco (tet,gocco)-duoprism 0.958067 96, 336, 464, 340, 134, 24
tetsocco (tet,socco)-duoprism 1.527124 96, 336, 464, 340, 134, 24
cocube cuboctahedron-cube duoprism 1.322876 96, 336, 482, 332, 120, 20
trarit triangle - rectified-tesseract duoprism 1.354006 96, 384, 584, 432, 163, 27
cubike cube-icosahedron duoprism 1.286277 96, 384, 592, 440, 162, 26
bitettut (alt.: pabex gee) bi - (tetrahedron, truncated tetrahedron)-duoprism, partially bi-expanded hexacontitetrapeton 1.322876 96, 432, 808, 780, 388, 80
squico square-icositetrachoron duoprism 1.224745 96, 480, 792, 576, 196, 28
hinarin demipenteract atop rectified penteract, demipenteract-first cap of demified icosiheptaheptacontidipeton 1.632993 96, 480, 880, 720, 268, 44
hinasiphin hin atop siphin, hin-first cap of sochax 1.322876 96, 560, 1280, 1320, 588, 84
ritgyt rectified-tesseractic gyrotrigonism 1.290994 96, 576, 1224, 1080, 387, 51
pexhax partially expanded hemihexeract 1.322876 96, 576, 1312, 1256, 488, 64
hinanit hin atop nit, hin-first cap of rojak 1.290994 96, 720, 1360, 1040, 348, 44
botox bitruncated hexeract 2.915476 960, 2880, 3440, 2080, 636, 76
xog hexeractihexacontatetrapeton, tritruncated hexeract, tritruncated hexacross 2.549510 960, 3360, 4160, 2320, 636, 76
grog great rhombihexacontitetrapeton, cantitruncated hexacross 2.645751 960, 3840, 6400, 5040, 1656, 136
qrax quasirhombated hexeract 0.819496 960, 4800, 7280, 4960, 1788, 268
rerax rectified rectified-hexeract, variation of small rhombated hexeract 2.645751 960, 4800, 7280, 4960, 1788, 268
srox small rhombated hexeract, cantellated hexeract 2.515637 960, 4800, 7280, 4960, 1788, 268
cophix small celliprismated hemihexeract, steriruncinated demihexeract, pentisteric hexeract 2.179449 960, 5280, 10720, 9120, 3016, 296
quacox quasicellihexeract 1.042011 960, 5760, 12320, 12000, 5148, 668
scox small cellihexeract, stericated hexeract 1.978437 960, 5760, 12320, 12000, 5148, 668
scag small cellihexacontitetrapeton, stericated hexacross 2 960, 5760, 12480, 12480, 5336, 536
spog small prismatohexacontitetrapeton, runcinated hexacross 1.870829 960, 7200, 14400, 11280, 3416, 296
n,rico-dip n-gon - rectified-icositetrachoron duoprism 96n, 384n, 576n+96, 264n+288, 49n+216, n+48
n,n,k-tip n-gon - n-gon - k-gon - triprism sqrt[1/(2 sin2(π/n))+1/(4 sin2(π/k))] n2k, 3n2k, 3n2k+n2+2nk, n2k+2n2+4nk, n2+2nk+2n+k, 2n+k
n,n,n-tip n-gon - n-gon - n-gon - triprism sqrt[3/(4 sin2(π/n))] n3, 3n3, 3n3+3n2, n3+6n2, 3n2+3n, 3n
n,m,k-tip n-gon - m-gon - k-gon - triprism sqrt[1/(4 sin2(π/n))+1/(4 sin2(π/m))+1/(4 sin2(π/k))] nmk, 3nmk, 3nmk+nm+nk+mk, nmk+2nm+2nk+2mk, nm+nk+mk+n+m+k,n+m+k

Count of actually available polytopes: 398


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 7D
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Acronym Name Circumradius Face vector
octepe octahedral pennene 0.707107 10, 42, 96, 130, 106, 50, 12
lanq (inbetween: rolin) pentacontihexa-hecatonicosihexa-pentacosiheptacontihexa-exon, rectified pentacontihexahecatonicosihexaexon, Gosset polytope 03,2,1 2.449490 10080, 120960, 241920, 191520, 72072, 12348, 758
gotafip great-terated-tetradecapeton prism 3.774917 10080, 35280, 48720, 33600, 12012, 2058, 128
gabach great bicellihexadecaexon 3.872983 10080, 35280, 49560, 35700, 13832, 2688, 198
gopamp great-prismated-pentacontitetrapeton prism 6.264982 103680, 362880, 501120, 345600, 123516, 21114, 1280
hexete hexadecachoric tettene, hexadecachoron-pyramid pyramid-pyramid, triangle atop fully orthogonal hexadecachoron 0.707107 11, 51, 129, 192, 169, 83, 19
sadlaq hepteract-diminished pentacontihexapentacosiheptacontihexaexon 1 112, 1568, 6720, 11200, 7924, 2184, 198
puph petaprismated hexadecaexon 1.732051 1120, 8400, 21560, 25760, 15288, 4060, 254
hagippit hexagon - great-prismated-triacontiditeron duoprism 4 11520, 40320, 55680, 38400, 13772, 2418, 168
penpasc pentachoron-prismatic scalene, pentachoron-prism-pyramid pyramid, line atop fully orthogonal pentachoron prism 0.935414 12, 46, 90, 105, 77, 35, 9
taccasc triacontiditeron scalene 0.707107 12, 61, 170, 280, 272, 145, 34
ragip rectified-hexacontitetrapeton prism 1.118034 120, 1020, 2720, 3520, 2352, 728, 78
goccopen (gocco,pen)-duoprism 0.971027 120, 480, 820, 805, 474, 158, 25
soccopen (socco,pen)-duoprism 1.535287 120, 480, 820, 805, 474, 158, 25
tetsrip tetrahedron - small-rhombated-pentachoron duoprism 0.987421 120, 540, 980, 950, 534, 166, 24
sranq small rhombated hecatonicosihexapentacosiheptacontihexaexon 2.645751 12096, 133056, 346752, 372960, 178416, 32760, 1514
botnaq truncated hecatonicosihexapentacosiheptacontihexaexon 3.278719 12096, 72576, 165312, 161280, 68040, 12348, 758
laq pentacontihexapentacosiheptacontihexaexon, argyroexon, Gosset polyexon 21,3, vertex figure of naquoh, lattice E7 contact polytope (span of its roots) 1 126, 2016, 10080, 20160, 16128, 4788, 632
hept hepteract, tetradecaexon, 7D measure-polytope (γ7), geozett(id) 1.322876 128, 448, 672, 560, 280, 84, 14
tetrit tetrahedron - rectified-tesseract duoprism 1.369306 128, 576, 1056, 1040, 596, 190, 28
hixippy hexateron prism pyramid, vertex-pyramid of roc 0.866025 13, 48, 91, 105, 77, 35, 9
rapete rap tettene 0.866025 13, 63, 151, 200, 151, 63, 13
geepy hexacontitetrapeton pyramid, vertex-first rotunda of gee 0.707107 13, 72, 220, 400, 432, 256, 64
thesa truncated demihepteract, cantic hepteract 2.423840 1344, 7392, 13440, 11760, 5656, 1428, 142
hopip heptapeton prism, vertex figure of rene 0.823754 14, 49, 91, 105, 77, 35, 9
zee (old: hio) hecatonicosoctaexon, heptacross (β7), aerozett(id), heptapetal antiprism, vertex figure of ek, Gosset polytope 41,1, lattice C7 contact polytope (span of its small roots) 0.707107 14, 84, 280, 560, 672, 448, 128
guhsa (old: xhaf) hexacontitetrahemihepteract, hexacontitetrahemitetradecaexon 0.707107 14, 84, 280, 560, 672, 448, 71
octico octahedron - icositetrachoron duoprism 1.224745 144, 864, 1920, 2088, 1158, 300, 32
hagippiddip hexagon - great-prismated-pentachoron duoprism prism 2.5 1440, 5040, 7080, 5100, 1992, 408, 38
tanq truncated hecatonicosihexapentacosiheptacontihexaexon 2.179449 1512, 12852, 44352, 70560, 48384, 11592, 758
stanq small terated hecatonicosihexapentacosiheptacontihexaexon 1.658312 1512, 19656, 90720, 191520, 191520, 80136, 7562
squarat square rectified-triacontiditeron duoprism 1.224745 160, 1120, 2600, 2800, 1528, 412, 46
saro small rhombated octaexon, cantellated octaexon 1.414214 168, 1008, 1876, 1750, 980, 308, 44
seto small terated octaexon, pentellated octaexon 1.198958 168, 1260, 3640, 5460, 4452, 1764, 226
bittoc bitruncated octaexon 1.713914 168, 588, 896, 770, 392, 112, 16
taz truncated hecatonicosoctaexon, truncated heptacross 1.581139 168, 924, 2520, 3920, 3360, 1344, 142
tetdippy tetdip pyramid, vertex pyramid of he 1 17, 64, 116, 124, 84, 36, 9
rixasc rectified-hexateronal scalene, rectified-hexateronal-pyramid pyramid, line atop fully orthogonal rectified-hexateron 1 17, 91, 215, 265, 182, 70, 14
brilalspil bril atop inverted spil 1.322876 175, 1190 2800, 3150, 1834, 539, 72
trarixdit (triangle,rix)-duotegum, tegum product of triangle and rectified hexateron 18, 108, 305, 465, 387, 171, 36
hixaf hexateron antifastegium, hix atop inverted hixip, hix-first cap of naq 0.866025 18, 111, 345, 605, 603, 313, 65
hinsc demipenteractic scalene, demipenteractic-pyramid pyramid, line atop fully orthogonal demipenteract 0.866025 18, 113, 336, 520, 426, 173, 28
trahix triangle - hexateron duoprism, vertex figure of brene 0.866025 18, 63, 111, 120, 83, 36, 9
trial trapen triangle atop inverted triangle-pentachoron duoprism, triangle-first cap of roc 0.866025 18, 78, 156, 180, 128, 54, 12
trasarx triangle-rsarxix duoprism 1.414214 180, 900, 1650, 1515, 776, 219, 30
ritgyo rectified-tesseract gyro-octahedronism, 384-diminished pentacontihexahecatonicosihexaexon 1.322876 192, 1824, 5904, 7920, 4758, 1188, 80
haxabrag hax-first monostratic cap of lin, hax atop brag 1.322876 192, 2320, 7360, 8720, 4408, 996, 78
tetal tetdip tet atop dual tetdip 0.935414 20, 102, 240, 305, 224, 94, 19
tetpen tetrahedron-pentachoron duoprism, vertex figure of trene 0.880341 20, 70, 120, 125, 84, 36, 9
rolaq rectified pentacontihexapentacosiheptacontihexaexon 1.732051 2016, 30240, 90720, 100800, 47880, 10332, 758
tolin truncated pentacontihexahecatonicosihexaexon 3.708099 20160, 131040, 241920, 191520, 72072, 12348, 758
taccuppy triancontaditeron-prism pyramid, vertex pyramid of rectified hecatonicosoctaexon 1 21, 110, 290, 440, 384, 178, 35
srillip small-rhombated-heptapeton prism 1.451600 210, 1155, 2135, 1925, 980, 280, 37
scala (old: scalal scal) small cellated heptapeton alterprism, small cellated heptapeton atop inverted small cellated heptapeton, medial segment of barz 1.224745 210, 210, 6160, 8190, 5180, 1406, 148
octatetdip oct atop tetdip, oct-first half of roc 0.866025 22, 108, 220, 245, 164, 64, 13
tacpyp triacontaditeric-pyramid prism, edge-first rotunda of geep 0.866025 22, 111, 290, 440, 384, 178, 35
rilpy rectified-heptapetonal pyramid, vertex pyramid of demihepteract 0.935414 22, 126, 280, 315, 203, 77, 15
ragabrag rag atop brag, rag-first rotunda of barz 1.224745 220, 2400, 5920, 6400, 3372, 788, 78
totaz tritruncated hecatonicosoctaexon, Voronoi cell of lattice D7* 2.549510 2240, 10080, 17920, 15120, 6328, 1428, 142
sirhesa small rhombated hemihepteract, cantellated demihepteract 2.207940 2240, 16800, 31360, 25200, 10360, 2100, 142
spaz small prismated hecatonicosoctaexon, runcinated heptacross 1.870829 2240, 23520, 62720, 71120, 38696, 9520, 506
tedroc tetradiminished rectified octaexon, (hix,hix,tedrix)-trigonic 0.866025 24, 120, 246, 264, 164, 60, 12
geep hexacontitetrapeton prism, hexacross prism, vertex figure of rek 0.866025 24, 132, 380, 640, 624, 320, 66
sissiddow sissidic disphenoid, sissid atop fully orthogonal sissid 0.831254 24, 204, 744, 1190, 744, 204, 24
squahix square - hexateron duoprism, hixip prism, vertex figure of bro 0.957427 24, 84, 146, 155, 104, 43, 10
sethalq small terademified pentacontihexapentacosiheptacontihexaexon 2.828427 24192, 241920, 826560, 1249920, 896112, 272664, 17642
scala spil scal atop spil 1.322876 245, 1890, 4690, 5425, 3150, 875, 107
trahexpy trahex pyramid, vertex pyramid of barz 1.224745 25, 120, 272, 344, 251, 102, 20
rapatrapen rectified pentachoron atop triangle-pentachoron duoprism, rap-first cap of roc 0.866025 25, 135, 275, 295, 189, 71, 14
tetsteth (tet,steth)-duoprism 1.606894 256, 1152, 1952, 1776, 932, 270, 36
tetgittith (tet,gittith)-duoprism 1.080691 256, 1152, 2016, 1776, 932, 270, 36
quersa quasirhombated hepteract 0.845261 2688, 16128, 29792, 27440, 15064, 4564, 590
sersa small rhombated hepteract, cantellated hepteract 2.790257 2688, 16128, 29792, 27440, 15064, 4564, 590
betsa bitruncated hepteract 3.240370 2688, 9408, 14112, 11760, 5656, 1428, 142
trial trahex triangle atop inverted trahex 1 27, 147, 369, 512, 395, 153, 23
rixahixip rectified hexateron atop hexateron prism, rix-first cap of roc 0.866025 27, 156, 315, 330, 209, 78, 15
jaku jak-based ursaexon 1.335149 270, 2835, 8136, 10440, 6318, 1575, 128
haxabrox hax atop brox, hax-first cap of rolaq 1.732051 272, 2640, 6000, 5920, 2968, 756, 78
roc rectified octaexon, vertex figure of hocto, Gosset polytope 05,1 0.866025 28, 168, 336, 350, 224, 84, 16
froc facetorectified octaexon 0.866025 28, 168, 490, 840, 868, 504, 127
hopalril hop atop inverted ril, hop-first cap of naq 0.866025 28, 231, 840, 1575, 1554, 721, 107
jakpy icosihepta-heptacontidi-peton pyramid, vertex-first cap of naq 0.866025 28, 243, 936, 1800, 1728, 747, 100
spo small prismated octaexon, runcinated octaexon 1.391941 280, 2100, 4760, 4830, 2548, 756, 100
sco small cellated octaexon, stericated octaexon 1.322876 280, 2240, 5880, 7280, 4508, 1316, 170
spila (old: spilal spil) small prismated heptapeton atop inverted small prismated heptapeton 1.322876 280, 2940, 8260, 10150, 6160, 1736, 128
barz (old: drhio) birectified hecatonicosoctaexon 1.224745 280, 3360, 8960, 10640, 6048, 1428, 142
tattoc tritruncated octaexon 1.854050 280, 980, 1400, 1050, 448, 112, 16
moarojak mo-first monostratic cap of lin, mo atop rojak 1.322876 288, 3960, 13680, 16560, 8172, 1746, 128
toegippid truncated-octahedron - great-prismated-decachoron duoprism 2.738613 2880, 10080, 13920, 9600, 3444, 606, 44
jakte icosihepta-heptacontidi-peton tegum ... 29, 270, 1152, 2520, 2808, 1395, 198
gotanq (old: gotalq) great terated hecatonicosihexapentacosiheptacontihexaexon, omnitruncated Gosset polyexon 32,1, great terated pentacontihexapentacosiheptacontihexaexon, omnitruncated Gosset polyexon 21,3, great terated pentacontihexahecatonicosihexaexon, omnitruncated Gosset polyexon 12,3 9.987492 2903040, 10160640, 13789440, 9072000, 2938320, 415800, 17642
jakatrim jak atop trim, jak-first cap of stanq 1.658312 297, 2646, 9360, 16200, 13896, 5265, 560
n,n,n-tippip n-gon - n-gon - n-gon - triprismatic prism sqrt[1/4+3/(4 sin2(π/n))] 2n3, 7n3, 9n3+6n2, 5n3+15n2, n3+12n2+6n, 3n2+9n, 3n+2
n,m,k-tippip n-gon - m-gon - m-gon - triprismatic prism sqrt[1/4+1/(4 sin2(π/n))+1/(4 sin2(π/m))+1/(4 sin2(π/m))] 2nmk, 7nmk, 9nmk+2nm+2nk+2mk, 5nmk+5nm+5nk+5mk, nmk+4nm+4nk+4mk+2n+2m+2k, nm+nk+mk+3n+3m+3k, n+m+k+2
trippen triangle - pentachoron duoprism-prism, vertex figure of buffy 0.991632 30, 105, 175, 175, 111, 44, 10
octpen octahedron - pentachoron duoprism, vertex figure of tro 0.948683 30, 120, 220, 235, 156, 62, 13
tratac triangle - triacontiditeron duoprism, vertex figure of bark 1.154701 30, 150, 370, 520, 416, 179, 35
trapendafup triangular-pentachoron duoantifastegiaprism, trapen atop bidual trapen 0.866025 30, 210, 610, 910, 716, 272, 38
... Fxo xfo3oox5xxx&#zxt 300, 840, 828, 258
botlaq bitruncated pentacontihexapentacosiheptacontihexaexon 4.123106 30240, 151200, 252000, 191520, 72072, 12348, 758
sirlaq small rhombated pentacontihexapentacosiheptacontihexaexon 3.316625 30240, 272160, 534240, 443520, 186984, 38556, 2774
tettepe tetrahedron-tetrahedron duoprismatic prism, vertex figure of 03,3,1 1 32, 112, 184, 180, 112, 44, 10
tethex tetrahedron - hexadecachoron duoprism, vertex figure of tark 0.935414 32, 144, 304, 360, 252, 102, 20
hexal trahex hex atop gyrated trahex, hex-first cap of hesa 0.935414 32, 216, 592, 768, 516, 182, 28
gotaz great terated hecatonicosoctaexon, great terated heptacross 6.745369 322560, 1128960, 1532160, 1008000, 326032, 45528, 1738
haxpy hemihexeractic pyramid, vertex pyramid of laq 1 33, 272, 880, 1280, 892, 296, 45
haxt demihexeractic (line-)tegum, demihexeractic bipyramid ... 34, 304, 1120, 1920, 1532, 548, 88
bragasochax brag atop sochax, 2nd subsegment of lin in hax-first orientation 1.322876 352, 4800, 17440, 23920, 14020, 3388, 298
tratratet triangle-triangle-tetrahedron-triprism, vertex figure of Gosset polytope 03,2,2 1.020621 36, 126, 204, 195, 118, 45, 10
brilpy birectified-heptapetonal pyramid, vertex pyramid of pentacontihexahecatonicosihexaexon 1.322876 36, 245, 560, 595, 329, 98, 15
idinaq (alt.: trahixdap) icosa-diminished naq, triangular-hexateric duoalterprism 0.866025 36, 306, 1122, 2130, 2136, 1008, 152
corit cuboctahedron - rectified-tesseract duoprism 1.581139 384, 1920, 3808, 3776, 1916, 448, 38
ritgyco rectified-tesseractic gyro-cuboctahedronism 1.414214 384, 3840, 12864, 18528, 12396, 3624, 350
papaid, pap || id, K-4.142 pentagonal-antiprism atop icosidodecahedron 3.077684 40, 130, 124, 34
cubpen cube-pentachoron duoprism 1.072381 40, 140, 230, 225, 138, 52, 11
tetrap tetrahedron - rectified-pentachoron duoprism, vertex figure of torfy 0.987421 40, 180, 340, 350, 214, 76, 14
hexalhax hex atop alternate hax 0.866025 40, 392, 1504, 2640, 2237, 848, 101
bragabrox brag atop brox, brag-first rotunda of sez 1.414214 400, 4320, 9440, 8400, 3592, 788, 78
talq truncated pentacontihexapentacosiheptacontihexaexon 2.645751 4032, 32256, 90720, 100800, 47880, 10332, 758
shilq small demified pentacontihexapentacosiheptacontihexaexon 2.179449 4032, 42336, 131040, 151200, 78120, 22428, 2774
shanq small demified hecatonicosihexapentacosiheptacontihexaexon 2 4032, 52416, 201600, 302400, 192528, 48888, 5546
branq (old: dranq) birectified hecatonicosihexapentacosiheptacontihexaexon 1.936492 4032, 60480, 161280, 161280, 68040, 12345, 758
guph great petated hexadecaexon, hexipentisteriruncicantitruncated octaexon, omnitruncated octaexon, permutoexon of 8 elements 4.582576 40320, 141120, 191520, 126000, 40824, 5796, 254
berlin (old: shabrilq) birectified pentacontihexahecatonicosihexaexon (small demibirhombated pentacontihexapentacosiheptacontihexaexon) 3.570714 40320, 302400, 544320, 403200, 142632, 22428, 758
rillip rectified-heptapeton prism, vertex figure of robay 0.981981 42, 231, 455, 455, 266, 91, 16
hopabril heptapeton atop birectified heptapeton, hop-first monostratic cap of hesa 0.935414 42, 336, 910, 1085, 665, 231, 37
hopalbril hop atop inverted bril, hop-first cap of laq 1 42, 371, 1225, 1890, 1400, 476, 72
rila (old: rilalril) rectified heptapeton alterprism, rectified heptapeton atop inverted rectified heptapeton, hop-first medial segment of naq 0.866025 42, 420, 1610, 2800, 2226, 742, 86
sabro small birhombated octaexon, bicantellated octaexon 1.658312 420, 2520, 4480, 3850, 1960, 560, 72
sabach small bicellated hexadecaexon, bistericated octaexon 1.414214 420, 3360, 9520, 12600, 7952, 2128, 198
rojaka (alt.: pabdilin, old: rojakalrojak) rojak alterprism, parabidiminished lin, rojak atop alternate rojak 1.322876 432, 6480, 23040, 28080, 13500, 2538, 128
hagocad hexagon - great-cellated-dodecateron duoprism 3.122499 4320, 15120, 20880, 14400, 5172, 918, 68
gahax gee atop hax, gee-first segment of naq 0.866025 44, 492, 2240, 4880, 5244, 2452, 298
rasa (old: ras) rectified hepteract 1.732051 448, 2688, 5152, 5040, 2968, 980, 142
frasa facetorectified hepteract 1.732051 448, 2688, 6720, 8960, 6720, 2688, 448
suthesa small terated demihepteract, hexic hepteract 1.369306 448, 4704, 17920, 31360, 27272, 10640, 1066
trarix triangle-rix duoprism 1 45, 225, 435, 435, 251, 84, 15
... point || pseudo hax || gee, Dutour polyexon type A 45, 524, 2480, 5520, 5884, 2692, 329
grohp great-rhombihexahedron prism 0.890446 48, 120, 84, 20
ohix octagon - hexateron duoprism 1.457317 48, 168, 286, 295, 188, 71, 14
stohix octagram - hexateron duoprism 0.842354 48, 168, 286, 295, 188, 71, 14
octhex octahedron - hexadecachoron duoprism, vertex figure of troch 1 48, 240, 544, 680, 478, 172, 24
trahin triangle - hemipenteract duoprism, vertex figure of borfy 0.978945 48, 288, 736, 920, 598, 201, 29
trahex aico trahex atop ico 1 48, 336, 776, 888, 564, 190, 28
trahex dafup triangular-hexadecachoral duoantifastegiaprism, trahex atop dual-gyrated trahex 0.935414 48, 384, 1120, 1472, 934, 276, 32
hinaf, hin || alt. hinnip hemipenteractic alterfastegium, hin atop alternate hinnip, hin-first rotunda of hesa 0.935414 48, 416, 1280, 1640, 998, 313, 45
odinaq (alt.: hexgyo) octa-diminished naq, hexadecachoral gyro-octahedronism 0.866025 48, 552, 2496, 5280, 5478, 2508, 320
traginnont (triangle,ginnont)-duoprism 1.173127 480, 2400, 4000, 3400, 1636, 439, 55
trasinnont (triangle,sinnont)-duoprism 1.670461 480, 2400, 4000, 3400, 1636, 439, 55
hopastaf hop atop staf, half of suph (its hop-first rotunda), partial Stott expansion of oca 1 49, 273, 735, 1155, 1085, 567, 128
ratkus retroteriskewed hepteract 1.658312 5376, 40320, 106400, 143360, 101752, 32032, 1752
takus teriskewed hepteract 1.658312 5376, 40320, 106400, 143360, 101752, 32032, 1752
tratratrip triangle - triangle - triangle - triprismatic prism 1.118034 54, 189, 297, 270, 153, 54, 11
titridafup triangle-tridafup duoprism 1.040833 54, 270, 540, 558, 324, 105, 17
jakip icosihepta-heptacontidi-peton prism, vertex figure of riffy 0.957427 54, 459, 1656, 2880, 2376, 846, 101
jaka (alt.: pabdinaq, old: jakaljak) jak alterprism, jak atop inverted jak, vertex-first medial segment of naq, parabidiminished naq 0.866025 54, 702, 3600, 8640, 9936, 4806, 560
toc truncated octaexon 1.391941 56, 196, 336, 350, 224, 84, 16
hehah hexadecahemihexadecaexon 1 56, 336, 616, 630, 392, 140, 24
suph small petated hexadecaexon, hexicated octaexon, expanded octaexon, lattice A7 contact polytope (span of its roots) 1 56, 336, 980, 1680, 1736, 1008, 254
broc (old: droc) birectified octaexon, duorectified octaexon, vertex figure of bif, Gosset polytope 04,2 0.968246 56, 420, 840, 770, 392, 112, 15
rilalbril rectified heptapeton atop inverted birectified heptapeton, equatorial monostratic segment of demihepteract 0.935414 56, 525, 1575, 1925, 1127, 357, 51
quil pentacosiheptacontihexa-pentacontihexa-exon, vertex figure of yab 0.866025 56, 756, 4032, 10080, 12096, 4788, 632
naq (alt: rocalroc) hecatonicosihexapentacosiheptacontihexaexon, sideroexon, Gosset polyexon 32,1, alterelongated jak tegum, vertex figure of fy, (one of the) Delone cell(s) of lattice E7, tegum sum of 2 mutually inverted rectified octaexa, biambohexadecaexon, lattice E7* contact polytope (span of its roots) 0.866025 56, 756, 4032, 10080, 12096, 6048, 702
nal hecatonicosihexa-pentacontihexa-exon, vertex figure of fib 0.866025 56, 756, 4032, 10080, 12096, 6804, 182
stiroh small trirhombihexadecaexon, tricantellated octaexon 1.732051 560, 3360, 5880, 4900, 2408, 672, 86
sibpo small biprismated octaexon, biruncinated octaexon 1.561250 560, 4200, 10080, 10640, 5460, 1400, 142
sez (old: shio) hepteractihecatonicosoctaexon 1.414214 560, 6720, 15680, 14560, 6328, 1428, 142
hidlin hexadeca-diminished pentacontihexahecatonicosihexaexon 1.322876 560, 9520, 36960, 46480, 22456, 4172, 198
lin pentacontihexahecatonicosihexaexon, chrysoexon, Gosset polyexon 12,3, Voronoi cell of lattice E7* 1.322876 576, 10080, 40320, 50400, 23688, 4284, 182
copen cuboctahedron - pentachoron duoprism 1.183216 60, 240, 430, 445, 282, 104, 19
octrap octahedron - rectified-pentachoron duoprism 1.048809 60, 300, 620, 670, 396, 122, 18
rilastaf ril atop staf, ril-first rotunda of rez 1 63, 525, 1610, 2590, 2282, 966, 128
tettes tetrahedron-tesseract duoprism 1.172604 64, 224, 352, 320, 180, 62, 12
cubhex cube-hexadecachoron duoprism 1.118034 64, 288, 592, 664, 416, 140, 22
haxip hemihexeractic prism, vertex figure of rinquoh 1.060660 64, 512, 1520, 1920, 1144, 340, 46
hesa (old: hiss) hemihepteract, vertex figure of bay, Gosset polytope 14,1 0.935414 64, 672, 2240, 2800, 1624, 532, 78
rojaka hejak rojak atop hejak, rojak-first cap of rolaq 1.732051 648, 7560, 22680, 25920, 13140, 3330, 344
bersa (old: dars) birectified hepteract, Gosset polytope 04,1,1 1.581139 672, 6720, 13440, 11760, 5656, 1428, 142
n,hix-dip n-gon - hexateron duoprism sqrt[5/12 + 1/(2 sin(π/n))2] 6n, 21n, 35n+6, 35n+15, 21n+20, 7n+15, n+6
brillip birectified - heptapeton prism 1.052209 70, 455, 910, 840, 413, 112, 16
he (old: ache) hexadecaexon, trirectified octaexon, equatorial cross-section of (vertex first) 1/q-octo, Gosset polytope 03,3 1 70, 560, 1120, 980, 448, 112, 16
garag gee atop rag, gee-first rotunda of rez 1 72, 660, 1820, 2560, 1968, 716, 78
broxa sophax brox atop sophax, hax-first subsegment of rolaq 1.732051 720, 8160, 23520, 26560, 13192, 2948, 238
ranq rectified hecatonicosihexapentacosiheptacontihexaexon 1.414214 756, 12096, 44352, 70560, 48384, 11592, 758
goxaxogip goxaxog prism 1.242133 768, 4224, 6880, 5680, 2728, 740, 90
soxaxogip soxaxog prism 1.719624 768, 4224, 6880, 5680, 2728, 740, 90
brilastaf bril atop staf, hop-first subsegment of laq 1 77, 840, 3150, 5215, 4088, 1386, 128
oca (old: oc) octaexon, 7D simplex (α7), pyrozett(id), heptapetal pyramid, vertex figure of ene, (one of the) Delone cell(s) of lattice E7, Gosset polytope 06 0.661438 8, 28, 56, 70, 56, 28, 8
stafip small terated tetradecapeton prism 1.118034 84, 462, 1190, 1750, 1498, 686, 128
rez (old: rhio) rectified hecatonicosoctaexon, lattice B7 contact polytope (span of its small roots), lattice D7 contact polytope (span of its roots) 1 84, 840, 2520, 3920, 3360, 1344, 142
... oxo3ooo3ooo3xoo3ooo3oxx&#xt 1 84, 903, 3395, 5740, 4739, 1806, 233
botaz bitruncated hecatonicosoctaexon, bitruncated heptacross 2.121320 840, 4200, 9240, 10640, 6048, 1428, 142
sarz small rhombated hecatonicosoctaexon, cantellated heptacross 1.732051 840, 7560, 19320, 24080, 15456, 4200, 226
hejaka hejak alterprism, hejak atop alternate hejak 1.658312 864, 8640, 30960, 51120, 41580, 14922, 1280
mou mo-based ursaexon 1.738546 864, 8712, 20160, 19440, 8748, 1746, 128
quitasa quasitruncated hepteract 0.712292 896, 3136, 5152, 5040, 2968, 980, 142
tasa truncated hepteract 2.998773 896, 3136, 5152, 5040, 2968, 980, 142
guposaz great petated hepteractihecatonicosoctaexon 1.242133 896, 5376, 14560, 22400, 20328, 10192, 2186
quiposaz quasipetated hepteractihecatonicosoctaexon 1.242133 896, 5376, 14560, 22400, 20328, 10192, 2186
suposaz small petated hepteractihecatonicosoctaexon, hexicated hepteract 1.719624 896, 5376, 14560, 22400, 20328, 10192, 2186
gososaz great hepteractihepteractihecatonicosoctaexon 1.242133 896, 5376, 8512, 7280, 3808, 1148, 156
sososaz small hepteractihepteractihecatonicosoctaexon 1.719624 896, 5376, 8512, 7280, 3808, 1148, 156
squix square hixene, square atop fully orthogonal pentachoron 0.707107 9, 34, 71, 90, 71, 34, 9
thid triaconta-hexa-diminished pentacontihexapentacosiheptacontihexaexon 1 90, 990, 3570, 5520, 3972, 1224, 104
ihdlaq icositetra-hexa-diminished pentacontihexapentacosiheptacontihexaexon, hexadecachoral gyro-cuboctahedronism 1 96, 1152, 4632, 7488, 5244, 1416, 86
haxarag hemihexeract atop rectified hexacontitetrapeton, vertex-first subsegment of pentacontihexapentacosiheptacontihexaexon 1 96, 1200, 5120, 9200, 7068, 2116, 238
trapent triangle-penteract duoprism 1.258306 96, 336, 512, 440, 230, 73, 13
jakamo jak atop mo, jak-first half of parabidiminished laq 1 99, 1368, 6120, 11160, 8550, 2583, 344

Count of actually available polytopes: 208


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----
 8D
----

Acronym Name Circumradius Face vector
rapdip rectified-pentachoron duoprism 1.095445 100, 600, 1500, 2000, 1520, 660, 160, 20
spuho small petated hemiocteract 1.414214 1024, 14336, 69888, 161280, 203392, 140672, 45728, 3744
ritdip rectified-tesseractic duoprism 1.732051 1024, 6144, 14848, 18432, 12416, 4416, 752, 48
recto rectified octeract, rectified hexadecazetton 1.870829 1024, 7168, 16128, 19712, 15456, 7616, 2160, 272
fro facetorectified octeract 1.870829 1024, 7168, 21504, 35840, 35840, 21504, 7168, 1024
jakap jaka prism, jakip alterprism 1 108, 1458, 7902, 20880, 28512, 19548, 5926, 562
rek rectified diacosipentacontahexazetton, lattice B8 contact polytope (span of its small roots), lattice D8 contact polytope (span of its roots) 1 112, 1344, 4928, 10080, 12544, 8960, 3072, 272
broca (old: brocalbroc) broc alterprism, broc atop inverted broc, central segment of hocto 1 112, 1400, 5040, 7420, 5684, 2632, 704, 88
naqpe naq prism, prism of Gosset polyexon 32,1 , vertex figure of rigoh 1 112, 1568, 8820, 24192, 34272, 24192, 7452, 704
tark trirectified diacosipentacontahexazetton 1.414214 1120, 17920, 53760, 71680, 48384, 16576, 3184, 272
trene trirectified enneazetton, Gosset polytope 04,3 1.054093 126, 1260, 2940, 3150, 1890, 672, 144, 18
hocto (alt.: gecdify) hemiocteract, 64(=g)+48(=c)-diminished fy, Gosset polytope 15,1 1 128, 1792, 7168, 10752, 8288, 4032, 1136, 144
hextes hexadecachoron-tesseract duoprism 1.224745 128, 640, 1472, 1920, 1496, 696, 184, 24
linaranq pentacontihexahecatonicosihexaexon atop rectified pentacontihexapentacosiheptacontihexaexon, laq-first subsegment of bay 1.414214 1332, 34272, 205632, 463680, 445032, 194796, 45544, 4792
srek small rhombated diacosipentacontahexazetton, cantellated octacross 1.732051 1344, 14784, 47488, 81760, 82432, 44800, 10464, 384
tiffy truncated dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton 2.645751 13440, 188160, 1028160, 2661120, 3386880, 1935360, 375840, 19680
toby (old: tobay) truncated diacositetracont-myriaheptachiliadiacosioctaconta-zetton 4 138240, 1520640, 5322240, 7257600, 4717440, 1693440, 313440, 19680
puko petiskewed octeract 1.732051 14336, 129024, 422912, 752640, 784896, 459648, 123712, 5552
repuko retropetiskewed octeract 1.732051 14336, 129024, 422912, 752640, 784896, 459648, 123712, 5552
hauhocto hexadeca-augmented hemiocteract ... 144, 2816, 17920, 46592, 53088, 30016, 9648, 1376
penrapdit (pen,rap)-duotegum, tegum product of pentachoron and rectified pentachoron 15, 90, 290, 565, 700, 550, 250, 50
zeepy zee pyramid, heptacross pyramid, vertex pyramid of ek 0.707107 15, 98, 364, 840, 1232, 1120, 576, 129
xorene exirhombated enneazetton 1.732051 1512, 12852, 40824, 68670, 66192, 35028, 8532, 510
ek diacosipentacontahexazetton, octacross (β8), aeroyott(id), octaexal antiprism, vertex figure of vee, (one of the) Delone cell(s) of lattice E8, Gosset polytope 51,1, lattice C8 contact polytope (span of its small roots) 0.707107 16, 112, 448, 1120, 1792, 1792, 1024, 256
ocpe octaexon prism, vertex figure of reday 0.829156 16, 64, 140, 196, 182, 112, 44, 10
tijakdap triangle-jak duoalterprism 1 162, 3078, 20250, 59022, 83808, 56322, 15738, 1536
kadify heptacontadia-diminished dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton, tegum sum of two mutually inverted birectified enneazetta, bidiambooctadecazetton 1 168, 3192, 18648, 46872, 57960, 38052, 13320, 1980
satpeb small triprismated bi-enneazetton, triruncinated enneazetton 1.732051 1680, 15120, 42840, 55440, 38052, 14784, 3042, 270
bif diacositetracont-dischiliahectohexaconta-zetton, chrysozetton, Gosset polyzetton 14,2 2 17280, 483840, 2419200, 3628800, 2298240, 725760, 106080, 2400
bro birectified octeract, birectified hexadecazetton, Gosset polytopes 05,1,1 1.732051 1792, 21504, 50176, 55552, 36960, 14784, 3184, 272
tro trirectified octeract, trirectified hexadecazetton 1.581139 1792, 26880, 71680, 80640, 47712, 16576, 3184, 272
naqalaq naq atop laq, second stratos of vertex-first fy, E7 1/2 polytope 1 182, 4284, 33768, 120960, 219744, 202356, 81470, 7564
codify (alt.: hexgyi, trihexdip) tetracontaocta-diminished dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton, hexadacachoron gyro-icositetrachoronism, tegum sum of 3 pairwise bigyrated hexadecachoron duoprisms, tri-hexadecachoron-duoprism 1 192, 4224, 29184, 86784, 124464, 84672, 23808, 1968
gook great octeractiocteractidiacosipentacontahexazetton 1.338990 2048, 14336, 26880, 28672, 19936, 8960, 2384, 288
quaxoke quasi-exiocteracti-diacosipentacontahexazetton 1.338990 2048, 14336, 46592, 89600, 108416, 81536, 34976, 6560
saxoke small exiocteracti-diacosipentacontahexazetton, heptellated octeract 1.790840 2048, 14336, 46592, 89600, 108416, 81536, 34976, 6560
queto quasitruncated octeract 0.741790 2048, 8192, 16128, 19712, 15456, 7616, 2160, 272
tocto truncated octeract 3.232607 2048, 8192, 16128, 19712, 15456, 7616, 2160, 272
trihop triangle - heptapenton duoprism, vertex figure of breday 0.872872 21, 84, 175, 231, 203, 119, 45, 10
bay diacositetraconta-myriaheptachiliadiacosioctaconta-zetton, argyrozetton, Gosset polyzetton 24,1 1.414214 2160, 69120, 483840, 1209600, 1209600, 544320, 144960, 17520
tek truncated diacosipentacontahexazetton, truncated octacross 1.581139 224, 1456, 4928, 10080, 12544, 8960, 3072, 272
tethix tetrahedron-hexateron duoprism, vertex figure of treday 0.889757 24, 96, 194, 246, 209, 120, 45, 10
yab myriaheptachiliadiacosioctaconta-diacositetraconta-zetton 1 240, 6720, 60480, 241920, 483840, 483840, 153360, 17520
fy dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton, siderozetton, Gosset polyzetton 41,2, Witting polytope, vertex figure of goh, lattice E8 contact polytope (span of its roots) 1 240, 6720, 60480, 241920, 483840, 483840, 207360, 19440
fib dischiliahectohexaconta-diacositetraconta-zetton 1 240, 6720, 60480, 241920, 483840, 483840, 222480, 2400
torfy trirectified dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton, t3(41,2) 3.162278 241920, 4838400, 14515200, 16934400, 9313920, 2661120, 382560, 19680
pendip pentachoron duoprism, vertex figure of icoy 0.894427 25, 100, 200, 250, 210, 120, 45, 10
batene bitruncated enneazetton 1.795055 252, 1008, 1848, 2016, 1386, 588, 144, 18
srene small rhombated enneazetton, cantellated enneazetton 1.452966 252, 1764, 3864, 4536, 3402, 1596, 432, 54
laqpe pentacontihexapentacosiheptacontihexaexon prism 1.118034 252, 4158, 22176, 50400, 52416, 25704, 6052, 634
octo octeract, hexadecazetton, 8D measure-polytope (γ8), geoyott(id) 1.414214 256, 1024, 1792, 1792, 1120, 448, 112, 16
squahop square - heptapenton duoprism, vertex figure of barn 0.963624 28, 112, 231, 301, 259, 147, 53, 11
zeep hecatonicosoctaexon prism, vertex figure of riv 0.866025 28, 182, 644, 1400, 1904, 1568, 704, 130
rocpy rectified-octaexonal pyramid, vertex pyramid of demiocteract 1 29, 196, 504, 686, 574, 308, 100, 17
trajakdit (triangle,jak)-duotegum, tegum product of triangle and icosiheptaheptacontidipeton 30, 300, 1449, 3888, 6048, 5283, 2241, 297
haxesc (degenerate) demihexaractic scalene, line atop fully orthogonal demihexaract ∞   i.e. flat in euclidean space 34, 305, 1152, 2160, 2172, 1188, 341, 46
thocto truncated hemiocteract, cantic octeract 2.645751 3584, 23296, 50176, 55552, 36960, 14784, 3184, 272
sotho small terated hemiocteract, hexic octeract 1.732051 3584, 48384, 222208, 474880, 513856, 269248, 56496, 3632
triphix triangle - hexateron duoprismatic prism, vertex figure of ribfoh 1 36, 144, 285, 351, 286, 155, 54, 11
trigee triangle - hexacontitetrapeton duoprism, vertex figure of brav 0.912871 36, 216, 672, 1260, 1456, 1008, 387, 67
rene rectified enneazetton, vertex figure of henne, Gosset polytope 06,1 0.881917 36, 252, 588, 756, 630, 336, 108, 18
ocalroc oca atop inverted roc, oca-first cap of fy 1 36, 364, 1652, 4060, 5740, 4564, 1788, 228
goxeb great exi-octadecazetton, permutozetton of 9 elements 5.477226 362880, 1451520, 2328480, 1905120, 834120, 186480, 18150, 510
octa tethex oct atop tethex 1 38, 252, 744, 1241, 1220, 682, 198, 25
tettac tetrahedron-triacontiditeron duoprism, vertex figure of tarv 0.935414 40, 220, 600, 970, 968, 596, 214, 36
bark birectified diacosipentacontahexazetton 1.224745 448, 6720, 22400, 36960, 34048, 16128, 3184, 272
buffy diacositetracont-dischiliahectohexacont-myriaheptachiliadiacosioctaconta-zetton, rectified bif:  t1(12,4), birectified bay:  t2(21,4), tetrarectified fy:  t4(41,2), Gosset polytope 04,2,1 3.872983 483840, 7257600, 16934400, 16934400, 9072000, 2661120, 382560, 19680
penrap (pentachoron, rectified pentachoron)-duoprism, vertex figure of tergoh 1 50, 250, 550, 700, 565, 290, 90, 15
spene small prismated enneazetton, runcinated enneazetton 1.452966 504, 4536, 11844, 14616, 10374, 4620, 1188, 138
rocip rectified-octaexon prism, vertex figure of robyah 1 56, 364, 840, 1036, 798, 392, 116, 18
tethex aico tethex atop ico 1 56, 432, 1168, 1680, 1453, 754, 218, 29
icodip icositetrachoron duoprism 1.414214 576, 4608, 13824, 19584, 13872, 4800, 768, 48
borfy birectified dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton, t2(41,2) 2.449490 60480, 1451520, 5806080, 9918720, 7741440, 2600640, 382560, 19680
be octadecazetton, enneaenneazetton, bi-enneazetton, quadritruncated enneazetton, equatorial cross-section of (vertex first) q-enne 2 630, 2520, 4200, 3780, 2016, 672, 144, 18
hexdip hexadecachoron duoprism 1 64, 384, 1088, 1792, 1808, 1072, 320, 32
tethin tetrahedron - hemipenteract duoprism, vertex figure of trigoh 1 64, 416, 1184, 1776, 1544, 800, 230, 30
hesapy hemihepteractic pyramid, vertex pyramid of bay 1.414214 65, 736, 2912, 5040, 4424, 2156, 610, 79
riffy rectified dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton, t1(41,2) 1.732051 6720, 181440, 1028160, 2661120, 3386880, 1935360, 375840, 19680
robay rectified diacositetracont-myriaheptachiliadiacosioctaconta-zetton, t1(21,4) 2.645751 69120, 1451520, 5322240, 7257600, 4717440, 1693440, 313440, 19680
gupofy great petated dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton 17.606817 696729600, 2786918400, 4470681600, 3657830400, 1601268480, 357557760, 34508640, 881760
laqalin pentacontihexapentacosiheptacontihexaexon atop pentacontihexahecatonicosihexaexon, 21,3 atop 12,3 , laq-first cap of bay, 21,3 -first cap of 21,4 1.414214 702, 16128, 92736, 201600, 191016, 87192, 23242, 2776
bato bitruncated octeract 3.535534 7168, 28672, 51968, 55552, 36960, 14784, 3184, 272
qro quasirhombated octeract 0.870264 7168, 50176, 109312, 127232, 94304, 43456, 11376, 1296
soro small rhombated octeract, cantellated octeract 3.040171 7168, 50176, 109312, 127232, 94304, 43456, 11376, 1296
tene truncated enneazetton 1.414214 72, 288, 588, 756, 630, 336, 108, 18
soxeb small exiated bi-enneazetton, heptellated enneazetton, expanded enneazetton, lattice A8 contact polytope (span of its roots) 1 72, 504, 1764, 3780, 5208, 4536, 2286, 510
hexal hesa hex atop alternated hesa, hex-first cap of codify 1 72, 952, 4576, 10112, 11481, 6748, 1834, 151
sobteb small biterated bi-enneazetton, bipentellated enneazetton 1.414214 756, 7560, 27720, 50400, 49056, 24696, 5562, 438
zahesa zee || hesa 1 78, 1204, 7224, 21280, 33656, 28252, 10846, 1068
... point || pseudo hesa || zee, Dutour polyzetton type A 79, 1268, 7896, 23520, 36456, 29876, 11364, 1131
jakaf (old: jakaljakip) icosiheptaheptacontidipeton alterfastegium, icosiheptaheptacontidipeton atop inverted icosiheptaheptacontidipeton-prism 1 81, 1215, 6966, 19080, 26784, 18801, 5826, 561
triquip triangle-triangle-triangle-triangle-tetraprism (or: -quadprism) 1.154701 81, 324, 594, 648, 459, 216, 66, 12
trajak triangle - icosiheptaheptacontidipeton duoprism, vertex figure of bargoh 1 81, 729, 2835, 5616, 5904, 3321, 948, 102
rocalbroc roc atop inverted broc, oca-first subsegment of fy 1 84, 1148, 5376, 11200, 11256, 5656, 1432, 144
brene birectified enneazetton, Gosset polytope 05,2 1 84, 756, 1764, 2016, 1386, 588, 144, 18
rocasuph roc atop suph 1 84, 840, 3164, 6650, 8400, 6132, 2230, 256
idirek icositetra-diminished rectified diacosipentacontahexazetton 1 88, 864, 3296, 6992, 8840, 6424, 2336, 280
ene enneazetton, 8D simplex (α8), pyroyott(id), octaexal pyramid, vertex figure of day, (one of the) Delone cell(s) of lattice E8, Gosset polytope 07 0.666667 9, 36, 84, 126, 126, 84, 36, 9
tabif truncated diacositetracont-dischiliahectohexaconta-zetton 5.830952 967680, 7741440, 16934400, 16934400, 9072000, 2661120, 382560, 19680
zarez zee atop rez, rectified diacosipentacontahexazetton half 1 98, 1092, 3724, 7000, 7952, 5152, 1614, 144
n,n,n,n-quip n-gon - n-gon - n-gon - n-gon - tetraprism (or: -quadprism) sqrt[1/sin2(π/n)] n4, 4n4, 6n4+4n3, 4n4+12n3, n4+12n3+6n2, 4n3+12n2, 6n2+4n, 4n
n,m,p,q-quip n-gon - m-gon - p-gon - q-gon - tetraprism (or: -quadprism) sqrt[1/(4 sin2(π/n))+1/(4 sin2(π/m))+1/(4 sin2(π/p))+1/(4 sin2(π/q))] nmpq, 4nmpq, 6nmpq+nmp+nmq+npq+mpq, 4nmpq+3nmp+3nmq+3npq+3mpq, nmpq+3nmp+3nmq+3npq+3mpq+nm+np+nq+mp+mq+pq, nmp+nmq+npq+mpq+2nm+2np+2nq+2mp+2mq+2pq, nm+np+nq+mp+mq+pq+n+m+p+q, n+m+p+q

Count of actually available polytopes: 102


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----
 9D
----

Acronym Name Circumradius Face vector
day decayotton, 9D simplex (α9), pyroxenn(id), enneazettal pyramid, vertex figure of ux, Gosset polytope 08 0.670820 10, 45, 120, 210, 252, 210, 120, 45, 10
breday birectified decayotton, Gosset polytope 06,2 1.024695 120, 1260, 3360, 4620, 4032, 2310, 840, 180, 20
gripa (old: gripalgrip) grip alterprism, grip atop inverted grip, medial spid-first segment of spat 1.870829 120, 360, 400, 190, 32
riv rectified pentacosidodecayotton, lattice B9 contact polytope (span of its small roots), lattice D9 contact polytope (span of its roots) 1 144, 2016, 8736, 22176, 36288, 37632, 23040, 6912, 530
vee pentacosidodecayotton, enneacross (β9), aeroxenn(id), enneazettal antiprism, vertex figure of ka, Gosset polytope 61,1, lattice C9 contact polytope (span of its small roots) 0.707107 18, 144, 672, 2016, 4032, 5376, 4608, 2304, 512
enep enneazetton prism, vertex figure of ru 0.833333 18, 81, 204, 336, 378, 294, 156, 54, 11
tarv trirectified pentacosidodecayotton 1.414214 2016, 40320, 147840, 262080, 262080, 145152, 42144, 7056, 530
treday trirectified decayotton, Gosset polytope 05,3 1.095445 210, 2520, 6720, 8610, 6552, 3150, 960, 180, 20
ren rectified enneract, rectified octadecayotton 2 2304, 18432, 47616, 69888, 68544, 45024, 19104, 4752, 530
trioc triangle - octaexon duoprism, vertex figure of bru 0.877971 24, 108, 260, 406, 434, 322, 164, 55, 11
icoy icosayotton, quadrirectified decayotton, equatorial cross-section of (vertex first) 1/q-deker, Gosset polytope 04,4 1.118034 252, 3150, 8400, 10500, 7560, 3360, 960, 180, 20
henne demi-enneract, Gosset polytope 16,1 1.060660 256, 4608, 21504, 37632, 36288, 23520, 9888, 2448, 274
tethop tetrahedron-heptapeton duoprism, vertex figure of tru 0.896421 28, 126, 294, 441, 455, 329, 165, 55, 11
tiv truncated pentacosidodecayotton, truncated enneacross 1.581139 288, 2160, 8736, 22176, 36288, 37632, 23040, 6912, 530
penhix pentachoron - hexateron duoprism, vertex figure of teru 0.903696 30, 135, 310, 455, 461, 330, 165, 55, 11
squoc square - octaexon duoprism, vertex figure of brade 0.968246 32, 144, 344, 532, 560, 406, 200, 64, 12
ekip diacosipentacontahexazetton prism, vertex figure of rake 0.866025 32, 240, 1008, 2688, 4704, 5376, 3840, 1536, 258
renepy rectified-enneazettonal pyramid, vertex pyramid of demienneract 1.060660 37, 288, 840, 1344, 1386, 966, 444, 126, 19
trizee triangle - hecatonicosoctaexon duoprism, vertex figure of brake 0.912871 42, 294, 1106, 2604, 3976, 3920, 2400, 835, 131
reday rectified decayotton, vertex figure of hede, Gosset polytope 07,1 0.894427 45, 360, 960, 1470, 1512, 1050, 480, 135, 20
quiten quasitruncated enneract 0.770160 4608, 20736, 47616, 69888, 68544, 45024, 19104, 4752, 530
ten truncated enneract 3.450631 4608, 20736, 47616, 69888, 68544, 45024, 19104, 4752, 530
barn birectified enneract, birectified octadecayotton, Gosset polytope 06,1,1 1.870829 4608, 64512, 172032, 231168, 197568, 109536, 37536, 7056, 530
enne enneract, octadecayotton, 9D measure-polytope (γ9), geoxenn(id) 1.5 512, 2304, 4608, 5376, 4032, 2016, 672, 144, 18
brav birectified pentacosidodecayotton 1.224745 672, 12096, 48384, 102816, 133056, 102144, 41472, 7056, 530
teday truncated decayotton 1.431782 90, 405, 960, 1470, 1512, 1050, 480, 135, 20
thenne truncated hemienneract, cantic enneract 2.850439 9216, 69120, 172032, 231168, 197568, 109536, 37536, 7056, 530

Count of actually available polytopes: 27


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-----
 10D
-----

Acronym Name Circumradius Face vector
deker dekeract, icosaxennon, 10D measure-polytope (γ10), geodak(id) 1.581139 1024, 5120, 11520, 15360, 13440, 8064, 3360, 960, 180, 20
ux hendecaxennon, undecaxennon, 10D simplex (α10), pyrodak(id), decayottal pyramid, Gosset polytope 09 0.674200 11, 55, 165, 330, 462, 462, 330, 165, 55, 11
tu truncated hendecaxennon, truncated undecaxennon 1.445998 110, 550, 1485, 2640, 3234, 2772, 1650, 660, 165, 22
brade birectified dekeract, birectified icosaxennon, Gosset polytope 07,1,1 2 11520, 184320, 552960, 875520, 916608, 653184, 310560, 93120, 15540, 1044
bru birectified hendecaxennon, Gosset polytope 07,2 1.044466 165, 1980, 5940, 9570, 10164, 7392, 3630, 1155, 220, 22
rake rectified chilliaicositetraxennon, lattice B10 contact polytope (span of its small roots), lattice D10 contact polytope (span of its roots) 1 180, 2880, 14400, 43680, 88704, 120960, 107520, 57600, 15360, 1044
ka chilliaicositetraxennon, decacross (β10), aerodak(id), decayottal antiprism, Gosset polytope 71,1, lattice C10 contact polytope (span of its small roots) 0.707107 20, 180, 960, 3360, 8064, 13440, 15360, 11520, 5120, 1024
tru trirectified hendecaxennon, Gosset polytope 06,3 1.128152 330, 4620, 13860, 20790, 19404, 12012, 4950, 1320, 220, 22
take truncated chilliaicositetraxennon, truncated decacross 1.581139 360, 3060, 14400, 43680, 88704, 120960, 107520, 57600, 15360, 1044
teru tetrarectified hendecaxennon, quadrirectified hendecaxennon, Gosset polytope 05,4 1.167748 462, 6930, 20790, 30030, 25872, 14322, 5280, 1320, 220, 22
hede demi-dekeract, Gosset polytope 17,1 1.118034 512, 11520, 61440, 122880, 142464, 115584, 64800, 2400, 5300, 532
rade rectified dekeract, rectified icosaxennon 2.121320 5120, 46080, 134400, 230400, 271488, 223104, 126240, 47040, 10420, 1044
ru rectified hendecaxennon, rectified undecaxennon, Gosset polytope 08,1 0.904534 55, 495, 1485, 2640, 3234, 2772, 1650, 660, 165, 22
brake birectified chilliaicositetraxennon 1.224745 960, 20160, 94080, 245280, 411264, 443520, 291840, 103680, 15540, 1044

Count of actually available polytopes: 14


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