Site Map | Polytopes | Dynkin Diagrams | Vertex Figures | Incidence Matrices | Index |
Acronyms and some of the names are due to Jonathan Bowers.
Index is also available in 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.
---- 3D ----
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 | |
... | β2β5o, (mere) alternated pip | 0.986715 | 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 | |
digdom, ike-5-7 | diminished ike-gad morpher, 5-fold pyramidal-symmetric ike faceting with 5 trigs and 7 pigs | 11, 25, 12 | |
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 | |
... | 4fold teddi analog | 1.144123 | 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 |
stapper | star pentagonal retrohedron | 0.866025 | 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 |
stopper | star pentagonal rhombihedron | 0.866025 | 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), equatorial cross-section of tet-first spid, equatorial cross-section of oct-first ico | 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 (?) | 1 | 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 |
erhote | expanded rhombic triacontahedron | 120, 240, 122 | |
exrhote | expanded rhombic triacontahedron | 120, 240, 122 | |
... | β5/2x5β (?) | ... | 120, 240, 84 |
... | β3x5β (?) | 3.802395 | 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, granatahedron, Voronoi cell of face-centered cubic (fcc) lattice, terminally chamfered cube, terminally chamfered octahedron, surtegmated cube, surtegmated octahedron, Waterman polyhedron number 4 wrt. primitive cubic lattice C3 centered at a lattice point, Waterman polyhedron number 2 (and 6) wrt. body-centered cubic lattice C3* centered at a lattice point | 14, 24, 12 | |
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, equatorial cross-section of oct-first thex | 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 (?) | 1.581139 | 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 (?) | 1.778824 | 24, 60, 32 |
... | β3o4β (?) | 1.398966 | 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 (?) | 1 | 30, 120, 54 |
... | icosidodecahedron faceting | 1.618034 | 30, 120, 62 |
... | Holosnub icosidodecahedron | 1.618034 | 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, equatorial cross-section of vertex-first ex | 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 | |
gyepcuro, J47 | gyroelongated pentagonal cupolarotunda | 35, 80, 47 | |
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 (?) | 2.317611 | 48, 96, 44 |
resirco (alt.: amsirco) | rectified/ambified small-rhombated-cuboctahedron | 2.613126 | 48, 96, 50 |
erad | expanded rhombic dodecahedron | 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), equatorial cross-section of vertex-first hex | 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 |
siddy | small dodekicosahedron | 1.721489 | 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 (?) | 2.969449 | 60, 150, 62 |
... | x3β5o (?) | 2.478019 | 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 (?) | 2.232951 | 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 |
... | vertex figure of great antifrustary trishecatonicosachoron | 0.816497 | 8, 12, 6 |
... | vertex figure of great retrofrustary trishecatonicosachoron | 0.816497 | 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 |
... | vertex figure of small antifrustary trishecatonicosachoron | 0.816497 | 8, 12, 6 |
... | vertex figure of small retrofrustary trishecatonicosachoron | 0.816497 | 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 |
trazip | xx xw&#q, prism of (isosceles) trapezoid | 1.306704 | 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 |
... | vertex figure of small spinofrustary trishecatonicosachoron | 0.816497 | 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: 551
---- 4D ----
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 | |
ogasc | octagram-scalene, octagram-pyramidal pyramid, line atop fully orthogonal octagram | 0.621876 | 10, 25, 25, 10 |
tutrippy | external blend of 2 trippies | ... | 10, 26, 27, 11 |
cute (old: cubdipy) | cubical (line-)tegum, cubical bipyramid | ... | 10, 28, 30, 12 |
fitetaoct | faceted 3tet atop oct | 0.774597 | 10, 30, 30, 10 |
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 |
pafirp | partially faceted rap, reduced 3tet atop 2thah self-blend, tet atop "squares of thah" | 0.774597 | 10, 30, 31, 11 |
hotetahoct | hollow tet atop hollow oct | 0.774597 | 10, 30, 32, 12 |
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 | |
... | s4x2x3o, trip-alternated todip | ... | 12, 24, 19, 7 |
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 |
tutepe | blend of 2 tepes | 0.790569 | 12, 28, 26, 10 |
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, equatorial cross-section of tet-first dot | 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 |
tubidrap | blend of 2 bidraps | 0.774597 | 12, 32, 32, 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 | |
quit sissidagird | quit sissid atop gird | 0.874032 | 120, 330, 246, 56 |
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 |
... | s2x2s4x, square-alternated sodip | ... | 16, 32, 24, 8 |
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 |
tetacho | tetrahedron atop cubohemioctahedron | 1 | 16, 42, 38, 12 |
bautipip | biaugmented-triangular-prism prism | 16, 42, 39, 13 | |
hotet aoho | hollow 2tet atop oho | 1 | 16, 42, 40, 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 |
... | tricupe variant wx xx3oq&#q | 1.402029039 | 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 | |
hoctaoho | hollow 2oct atop oho | 1 | 18, 60, 52, 13 |
hothahacho | hollow tetrahemihexahedron atop cubohemioctahedron | 1 | 18, 60, 53, 15 |
... | cuboctahedral retro-cuploid | 1 | 18, 60, 53, 15 |
octacho | octahedron atop cubohemioctahedron | 1 | 18, 60, 54, 16 |
octaco, K-4.29 | octahedron atop cuboctahedron, half of icositetrachoron (its oct-first rotunda), rectified octahedron-pyramid | 1 | 18, 60, 58, 16 |
... | 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 |
tiggia gaquatid | truncated great icosahedron atop great quasitruncated icosidodecahedron | 1.120533 | 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 | |
gidditdid aidtid | great ditrigonary dodekicosidodecahedron atop icosidodecatruncated icosidodecahedron | 4.684471 | 180, 840, 268, 46 |
... | 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 |
pabdi skiviphado | parabidiminished small 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), equatorial cross-section of pen-first scad, equatorial cross-section of rap-first rat | 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 |
ohoa hotut | oho atop hollow 2tut | 1.183216 | 24, 66, 52, 13 |
choatut | cubohemioctahedron atop truncated tetrahedron | 1.183216 | 24, 66, 54, 16 |
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), equatorial cross-section of hex-first rat | 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 |
getatixady | great tritrigonary hexacosidishecatonicosachoron | 1.136572 | 2400, 10800, 9840, 840 |
stuttixady | small tritrigonary hexacosidishecatonicosachoron | 3.835128 | 2400, 10800, 9840, 840 |
... | 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 |
quithpy | quasitruncated-hexahedral pyramid | 0.613502 | 25, 60, 50, 15 |
..., 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 |
... | s-2N-x-2-x-M-o, M-prism-alternated 4N-gon - M-gon duoprism | ... | 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, equatorial cross-section of srip-first sibrid, equatorial cross-section of pen-first rin | 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, triangular antitegmatic icosachoron, 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 xfo3oox5xxx&#zxt | 300, 840, 828, 258 | |
... | 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, equatorial cross-section of ico-first nit | 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 |
pirgady | pseudorhombated great dishecatonicosachoron | 1.054256 | 3600, 10800, 8160, 960 |
pirsady | pseudorhombated small dishecatonicosachoron | 6.073594 | 3600, 10800, 8160, 960 |
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 |
girfixady | great retrofrustary hexacosidishecatonicosachoron | 2.236068 | 3600, 14400, 11040, 840 |
sirfixady | small retrofrustary hexacosidishecatonicosachoron | 2.236068 | 3600, 14400, 11040, 840 |
sirfixthi | small retrofrustic hexacositrishecatonicosachoron | 2.236068 | 3600, 14400, 11280, 960 |
girfthi | great retrofrustary trishecatonicosachoron | 2.236068 | 3600, 14400, 7680, 360 |
safthi | great retrofrustary trishecatonicosachoron | 2.236068 | 3600, 14400, 7680, 360 |
snifthi | small spinofrustary trishecatonicosachoron | 2.236068 | 3600, 14400, 7680, 360 |
gafthi | great antifrustary trishecatonicosachoron | 2.236068 | 3600, 14400, 8880, 360 |
sirfthi | small retrofrustary trishecatonicosachoron | 2.236068 | 3600, 14400, 8880, 360 |
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 | |
papaid, pap || id, K-4.142 | pentagonal-antiprism atop icosidodecahedron | 3.077684 | 40, 130, 124, 34 |
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 |
ikadobcu | ikadoe bicupola | ... | 44, 210, 292, 126 |
... | toroidally parabideepened dope, when drilled by two ikadoes | ... | 44, 222, 322, 144 |
... | toroidal (ikadobcu, ipe)-blend | ... | 44, 222, 322, 144 |
... | 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 | |
grohp | great-rhombihexahedron prism | 0.890446 | 48, 120, 84, 20 |
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, equatorial cross-section of hex-first tot | 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, joined icositetrachoron, 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 |
frogshi | facetorectified great stellated hecatonicosachoron | 1.175571 | 720, 3600, 2880, 240 |
ridhi | retroinverted dishecatonicosachoron | 1.902113 | 720, 3600, 2880, 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 |
froghi | facetorectified great hecatonicosachoron | 1.902113 | 720, 3600, 4320, 720 |
rihix | retroinverted hecatonicosihexacosachoron | 1.175571 | 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, equatorial cross-section of tet-first hin | 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 |
fitetaltet | faceted tet atop dual 3tet, vertex figure of phap | 0.707107 | 8, 24, 26, 10 |
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), equatorial cross-section of vertex-first tac | 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 |
gidtidagiid | great ditrigonary icosidodecahedron atop great icosicosidodecahedron, gidtid cap of getit phiddix | 1.136572 | 80, 240, 204, 54 |
sidtidasiid | small ditrigonary icosidodecahedron atop small icosicosidodecahedron, sidtid cap of stut phiddix | 3.835128 | 80, 240, 204, 54 |
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, equatorial cross-section of trig-first rix | 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 |
tutrippapy | tutrip pyramid, internal blend of 2 trippies | 0.774597 | 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 |
girdo | great rhombic disoctachoron | 0.765367 | 96, 288, 208, 48 |
sirdo | small rhombic disoctachoron | 1.847759 | 96, 288, 208, 48 |
frico | facetorectified icositetrachoron | 1.732051 | 96, 288, 240, 48 |
rico | rectified icosatetrachoron, cantellated hexadecachoron, hexadecachoron-derived Gévay polychoron, equatorial cross-section of ico-first sart | 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 |
... | s3s4o3o, mere hemiation of truncated icositetrachoron, snub rhombatohexadecachoron | 2.645751 | 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: 1491
---- 5D ----
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 |
phap | pentachoric hemiantiprism | 0.707107 | 10, 40, 80, 60, 17 |
hehad | hexadecahemidecateron, vertex figure of thox | 0.707107 | 10, 40, 80, 80, 21 |
nophap | spinopentachoric hemiantiprism, pseudo pentachoric hemiantiprism | 0.707107 | 10, 40, 80, 80, 25 |
tac | triacontiditeron, pentacross (β5), aeropet(id), pentachoral antiprism, vertex figure of gee, Gosset polytopes 21,1, lattice C5 contact polytope (span of its small roots), equatorial cross-section of vertex-first gee | 0.707107 | 10, 40, 80, 80, 32 |
... | 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 |
togdow | triangle-octagrammic disphenoid, triangle atop fully orthogonal octagram | 0.638475 | 11, 35, 50, 35, 11 |
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 |
gripa (old: gripalgrip) | grip alterprism, grip atop inverted grip, medial spid-first segment of spat | 1.870829 | 120, 360, 400, 190, 32 |
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, equatorial cross-section of hix-first jak | 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, equatorial cross-section of hex-first hax | 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 |
ogdow | octagrammic disphenoid, octagram atop fully orthogonal octagram | 0.629640 | 16, 80, 130, 80, 16 |
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, parabiapiculated demipenteract | ... | 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 |
sadiap | snub disicositetrachoric antiprism, triangle-alternation of truncated icositetrachoric prism | 2.692582 | 192, 1248, 2112, 1296, 242 |
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, equatorial cross-section of hix-first hax | 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, equatorial cross-section of nit-first ram | 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 |
quithesc | quasitruncated-hexahedral scalene, quasitruncated-hexahedral-pyramid pyramid, line atop fully orthogonal quasitruncated hexahedron | 0.633157 | 26, 85, 110, 65, 16 |
..., 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(π/n))+1/(1-cos(π/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), equatorial cross-section of hix-first staf, equatorial cross-section of rix-first rag, equatorial cross-section of vertex-first mo | 1 | 30, 120, 210, 180, 62 |
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 |
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), equatorial cross-section of tac-first rag, equatorial cross-section of hin-first mo | 1 | 40, 240, 400, 240, 42 |
ratchet | retrotriacontidicellihemitriacontaditeron | 1 | 40, 240, 600, 560, 88 |
durat | rectified-triacontiditeron dual, joined penteract | 42, 240, 400, 240, 40 | |
..., 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} atop gyrated 3,N-dip, (N-g, dual N-g, N-p)-trigonic | ... | 4n, 13n, 16n+4, 9n+6, 2n+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 |
prissia | prismatorhombisnub icositetrachoric alterprism, triangle-alternation of prismatorhombated icositetrachoric prism | 3.534493 | 576, 2880, 4224, 2256, 338 |
..., N-g || N-appip | N-gon atop N-appip, (N-gon, N-p, gyro N-p)-trigonic | ... | 5n, 17n, 21n+5, 11n+8, 2n+5 |
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 |
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 |
pirgadia | pirgady alterprism | 1.125151 | 7200, 36000, 45120, 15840, 1082 |
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, equatorial cross-section of tac-first tag | 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, equatorial cross-section of nit-first brox | 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, equatorial cross-section of rat-first brag | 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, equatorial cross-section of scad-first trim, equatorial cross-section of rix-first brox | 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 |
haop (old: hodippip) | hexagon octagonal-prism duoprism, hexagon-octagon duoprismatic prism | 1.719624 | 96, 240, 220, 90, 16 |
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 |
... | s4x2x3o4s, trip-alternated osirco | 1.914214 | 96, 336, 448, 256, 50 |
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 |
(n/d, m/b)-dow | n/d-grammal m/b-grammal disphenoid, {n/d} || perp {m/b} | sqrt[1+1/(4 sin2(π d/n))]+1/(4 sin2(π b7m))/2 | n+m, nm+n+m, 2nm+2, nm+n+m, n+m |
Count of actually available polytopes: 700
---- 6D ----
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), equatorial cross-section of vertex-first zee | 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, equatorial cross-section of gee-first taz | 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 |
bife | bitetradecapeton, tetradecapeton dual, 14-3-5 step prism | 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 |
hixaltriddip | hix atop alternate triddip, ({3}, perp. {3}, alt. triddip)-trigonic, 1/6-lune of jak | 0.816497 | 15, 69, 143, 147, 73, 15 |
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 |
dihinpy | diminished-demipenteractic pyramid, (rap, dual pen, point)-trigonic | 0.816497 | 16, 85, 200, 225, 117, 23 |
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*, equatorial cross-section of rag-first barz | 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 |
tritra ope | (triangle, dual triangle, trip, gyro trip) lace simplex | 0.866025 | 18, 78, 138, 121, 55, 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, equatorial cross-section of hax-first lin | 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, equatorial cross-section of brox-first bersa | 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, 1788, 268 |
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 | |
teta troct | tetrahedron atop triangle-octahedron duoprism | 0.925820 | 22, 96, 160, 130, 56, 12 |
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, equatorial cross-section of brag-first sez | 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, vertex figure of jaka | 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 |
tiquithdow | (triangle,quith)-disphenoid, triangle atop fully orthogonal quasitruncated hexahedron | 0.645976 | 27, 111, 195, 175, 81, 17 |
triddippa tridafup | triddip atop tridafup, ((3,3)-dip, (3,dual 3)-dip, (dual 3,3)-dip)-trigonic | 0.925820 | 27, 126, 225, 192, 81, 15 |
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 |
rappaf (alt.: rapalrappip) | rectified-pentachoral antifastegium, rectified pentachoron atop inverted rectified-pentachoral prism | 0.925820 | 30, 160, 270, 200, 73, 13 |
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 |
ogquithdow | (octagram,quith)-disphenoid, octagram atop fully orthogonal quasitruncated hexahedron | 0.639069 | 32, 236, 495, 425, 156, 22 |
hax | hemihexeract, vertex figure of laq, Gosset polytope 13,1, equatorial cross-section of gee-first naq | 0.866025 | 32, 240, 640, 640, 252, 44 |
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, alt.: rixadot) | birectified heptapeton, rectified hexateron atop dodecateron, 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 |
..., N,M-dip || N,M-dafup | (N,M)-duoprism atop (N,M)-duoantifastegiaprism, ((N,M)-dip, (N,dual M)-dip, (dual N,M)-dip)-trigonic | ... | 3nm, 14nm, 23nm+3n+3m, 16nm+8n+8m, 4nm+7n+7m+3, 2n+2m+3 |
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 |
icoahin | ico atop hin, 1/6-lune of mo | 1 | 40, 272, 592, 528, 195, 27 |
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), equatorial cross-section of hop-first suph, equatorial cross-section of ril-first rez, equatorial cross-section of hop-first laq | 1 | 42, 210, 490, 630, 434, 126 |
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 |
hexarat | hex atop rat, hex-first half of tedrag | 1 | 48, 328, 696, 656, 283, 43 |
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 |
tedrag | (cyclo-)tetra-diminished rag | 1 | 56, 416, 992, 1072, 516, 76 |
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/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), equatorial cross-section of gee-first rez, equatorial cross-section of vertex-first laq | 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 |
... | (N-g, dual N-g, para N-p, gyro N-p) lace simplex | ... | 6n, 26n, 44n+6, 36n+13, 14n+13, 2n+6 |
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), equatorial cross-section of jak-first laq | 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*, equatorial cross-section of rojak-first rolaq | 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 |
gacnetip | great-cellated-penteractitriacontiditeron prism | 4.855004 | 7680, 23040, 25920, 13440, 3124, 244 |
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: 411
---- 7D ----
Acronym | Name | Circumradius | Face vector |
trippepe | trip pennene | 0.866025 | 10, 39, 81, 100, 76, 35, 9 |
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 |
..., oct || perp oct | (degenerate) oct atop fully orthogonal oct, octahedron disphenoid | ∞ i.e. flat in euclidean space | 12, 60, 160, 242, 204, 88, 16 |
taccasc | triacontiditeron scalene, half of hexacontitetrapeton pyramid, quarter of hecatonicosoctaexon | 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 |
corap | cuboctahedron - rectified-pentachoron duoprism | 1.264911 | 120, 600, 1220, 1270, 702, 194, 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 |
hirlaq | demirectified pentacontihexapentacosiheptacontihexaexon | 2.958040 | 12096, 90720, 171360, 141120, 59976, 12348, 758 |
laq | pentacontihexapentacosiheptacontihexaexon, argyroexon, Gosset polyexon 21,3, vertex figure of naquoh, lattice E7 contact polytope (span of its roots), equatorial cross-section of vertex-first fy | 1 | 126, 2016, 10080, 20160, 16128, 4788, 632 |
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), equatorial cross-section of vertex-first ek | 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, equatorial cross-section of zee-first tek | 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 |
dijakpy | diminished-icosiheptaheptacontidipetic pyramid, (hin, tac, point)-trigonic | 0.866025 | 27, 226, 840, 1560, 1458, 622, 85 |
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, equatorial cross-section of rez-first bark | 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 |
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 |
tatsa | tritruncated hepteract | 2.915476 | 3360, 13440, 20160, 15120, 6328, 1428142 |
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 |
tridafupap | trigonal-duoantifastegiaprismatic alterprism, trigonal-duoantifastegiaprism atop lacing-ortho trigonal-duoantifastegiaprism | 0.935414 | 36, 216, 492, 552, 328, 102, 16 |
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 |
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 |
rapaltrarap | rectified-pentachoron atop alternate (triangle, rectified pentachoron)-duoprism | 0.968246 | 40, 240, 490, 490, 274, 86, 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, equatorial cross-section of roc-first bro | 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 | |
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 |
tetocta | tetrahedron-octahedron-duoprismatic alterprism, tet-first medial segment of broc | 0.968246 | 48, 312, 688, 728, 412, 124, 18 |
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 |
quithdow | (bi-)quithic disphenoid, quith atop fully orthogonal quith | 0.646447 | 48, 648, 1756, 1970, 1056, 268, 28 |
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 |
(N,M)-dafupap | (N,M)-duoantifastegiaprismatic alterprism, (N,M)-duoantifastegiaprism atop lacing-ortho (N,M)-duoantifastegiaprism | ... | 4nm, 24nm, 52nm+4n+4m, 52nm+14n+14m, 24nm+18n+18m+4, 4nm+10n+10m+6, 2n+2m+4 |
tetdippa octdip | tetrahedral-duoprism atop octahedral-duoprism, vertex-first subsegment of the hexadecaexon | 1 | 52, 336, 740, 776, 428, 124, 18 |
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), equatorial cross-section of oca-first soxeb, equatorial cross-section of roc-first rek | 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, equatorial cross-section of barz-first tark | 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 |
trarapdafup | (triangle, rectified-pentachoron)-duoantifastegiaprism, pentachoron-first parabidiminished hexadecaexon | 1 | 60, 420, 920, 930, 486, 132, 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, equatorial cross-section of laq-first bay | 1.414214 | 756, 12096, 44352, 70560, 48384, 11592, 758 |
scalq | small cellated pentacontihexapentacosiheptacontihexaexon | 2.236068 | 7560, 90720, 322560, 493920, 328608, 80892, 6806 |
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), equatorial cross-section of zee-first fy, equatorial cross-section of zee-first rek | 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 |
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: 218
---- 8D ----
Acronym | Name | Circumradius | Face vector |
rapdip | rectified-pentachoron duoprism | 1.095445 | 100, 600, 1500, 2000, 1520, 660, 160, 20 |
tetrappal octrap | (tetrahedron, rectified pentachoron)-duoprism atop alternate (octahedron, rectified pentachoron)-duoprism | 1.054093 | 100, 840, 2220, 2820, 1960, 770, 170, 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, equatorial cross-section of rene-first barn | 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), equatorial cross-section of ek-first riv | 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 |
rapepe | rap peppene | 1 | 14, 76, 214, 351, 351, 214, 76, 14 |
geeasc | hexacontitetrapeton scalene, half of hecatonicosoctaexon pyramid, quarter of diacosipentacontahexazetton | 0.707107 | 14, 85, 292, 620, 832, 688, 321, 66 |
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), equatorial cross-section of vertex-first vee | 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 (or: brena) | heptacontadia-diminished dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton, tegum sum of two mutually inverted birectified enneazetta, bidiambooctadecazetton | 1 | 168, 3192, 18648, 46872, 57960, 38052, 13320, 1980 |
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, equatorial cross-section of ek-first tiv | 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 |
jakoha | icosiheptaheptacontidipetic hexacomb alterprism | ∞ i.e. flat in euclidean space | 2N, 99N, 912N, 3060N, 4464N, 2814N, 670N, 75N+2 |
trajakdit | (triangle,jak)-duotegum, tegum product of triangle and icosiheptaheptacontidipeton | 30, 300, 1449, 3888, 6048, 5283, 2241, 297 | |
spiffy | small petated dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton | 2.236068 | 30240, 665280, 4475520, 13305600, 19837440, 15180480, 5206080, 397920 |
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, equatorial cross-section of rek-first brav | 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 |
jakapy (alt.: pabdinaqpy) | icosiheptaheptacontidipetic-alterprism pyramid, parabidimished-hecatonicosihexapentacosiheptacontihexaexon pyramid, (jak, alt. jak, point)-trigonic | 1 | 55, 756, 4302, 12240, 18576, 14742, 5366, 561 |
roca | (degenerate) rectified octaexon alterprism | ∞ i.e. flat in euclidean space | 56, 1176, 4032, 10220, 13048, 8120, 2160, 200 |
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 |
naqpy | hecatonicosihexapentacosiheptacontihexaexon pyramid, vertex-first cap of fy | 1 | 57, 812, 4788, 14112, 22176, 18144, 6750, 703 |
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), equatorial cross-section of rene-first riv | 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: 110
---- 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, vertex figure of hyperbolic 16,2 | 1.024695 | 120, 1260, 3360, 4620, 4032, 2310, 840, 180, 20 |
riv | rectified pentacosidodecayotton, lattice B9 contact polytope (span of its small roots), lattice D9 contact polytope (span of its roots), equatorial cross-section of vee-first rake | 1 | 144, 2016, 8736, 22176, 36288, 37632, 23040, 6912, 530 |
brena | (degenerate) birectified enneazetton alterprism | ∞ i.e. flat in euclidean space | 168, 3192, 18648, 46872, 58212, 39228, 15072, 3078, 272 |
vee | pentacosidodecayotton, enneacross (β9), aeroxenn(id), enneazettal antiprism, vertex figure of ka, Gosset polytope 61,1, lattice C9 contact polytope (span of its small roots), equatorial cross-section of vertex-first ka | 0.707107 | 18, 144, 672, 2016, 4032, 5376, 4608, 2304, 512 |
enep | enneazetton prism, vertex figure of ru | 0.833333 | 18, 81, 204, 336, 378, 294, 156, 54, 11 |
rapdafup | rectified-pentachoron duoantifastegium | 1.118034 | 200, 2100, 6600, 10000, 8440, 4180, 1240, 220, 22 |
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, equatorial cross-section of reday-first brade | 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, equatorial cross-section of vee-first take | 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, equatorial cross-section of riv-first brake | 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: 28
----- 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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