Site Map Polytopes Dynkin Diagrams Vertex Figures Incidence Matrices Index

Index of Polytopes, sorted by Dimension

Acronyms and some of the names are due to Jonathan Bowers.

Index is also available in alphabetical order. Parts of this index - as far as circumradii are explicitely given - are also available in an (accordingly) numerically sorted order.



---- 2D ----


Acronym Name Circumradius
aze apeirogon, infinitogon, horogon (esp. when used as tile in hyperbolic geometry)  
... hyperbolic [10,8,4,6] tiling with tetragonal Coxeter domain  
... 2hexat (?)  
... 2hoha (?)  
... 2rothat (?)  
... 2that (?)  
... 2that+∞{3} (?)  
... 2toxat (?)  
... hyperbolic [(33,4)4] tiling  
... hyperbolic [4,6,6,∞] tiling with tetragonal Coxeter domain  0.707107 i
... chamfered hexadecachoron  
azap apeirogonal antiprism  
azip apeirogonal prism  
bobipyr bowtie pyramid, crossed tetragonal pyramid, half of thah  0.707107
... c0 of hyperbolic [10,8,4,6] tiling with tetragonal Coxeter domain  
... c01 of hyperbolic [10,8,4,6] tiling with tetragonal Coxeter domain  
cha complexihexaapeirogonal tiling  
chata complexitrihexaapeirogonal tiling  
chatit complexitrihexagonal tiling  
cosa complexisquariapeirogonal tiling  
ditatha ditrigonary trigonal hemiapeirogonal tesselation, alternate triangular tiling  
etrat elongated triangular tiling  
ghaha great hexahexaapeirogonal tiling  
ghothat,
(inbetween: ghath)
great hexagonal-trigonal-hexagonal tiling  
gossa great squarisquariapeirogonal tiling  
... Gott's snic-based pseudopolyhedron  
graht great rhombihexagonal tiling  
hatha hexaapeirogonaltruncated hexaapeirogonal tiling  
hexat hexagonal tiling, Voronoi complex of hexagonal lattice  
hoha hexagonal hemiapeirogonal tesselation  
huht hexahexagonal tiling  
... hyperbolic tetrapentagonal tiling of family o3o4o5*a  0.438176 i
... hyperbolic order 3 heptagonal tiling  1.742610 i
... hyperbolic order 3 tritetragonal tiling  0.728238 i
... hyperbolic order 3 octagonal tiling  1.345608 i
... hyperbolic order 3 horocyclic tiling, hyperbolic order ∞ truncated horocyclic tiling, hyperbolic order 3 apeirogonal tiling  0.866025 i
... hyperbolic tritetragonal tiling of family o3o4o5*a  0.297397 i
... hyperbolic ditetragonal tiling of family o3o4o5*a  0.921730 i
... hyperbolic triheptagonal tiling  2.012192 i
... hyperbolic order 3 truncated heptagonal tiling  3.792295 i
... hyperbolic trioctagonal tiling  1.553774 i
... hyperbolic order 3 truncated octagonal tiling  2.947161 i
... hyperbolic trigonal-horocyclic tiling, hyperbolic triapeirogonal tiling  1 i
... hyperbolic order 3 truncated horocyclic tiling, hyperbolic order 3 truncated apeirogonal tiling  1.936492 i
... hyperbolic order 4 pentagonal tiling  0.899454 i
... hyperbolic order 4 hexagonal tiling  0.707107 i
... hyperbolic order 4 octagon tiling  0.594604 i
o4x4oP*a family of (generally hyperbolic) order 2P square tilings  
... hyperbolic tetrapentagonal tiling  1.272020 i
... hyperbolic order 4 truncated pentagonal tiling  2.246127 i
... hyperbolic tetrahexagonal tiling  1 i
... hyperbolic tetraoctagonal tiling  0.840896 i
... hyperbolic tetragonal-horocyclic tiling, hyperbolic square-apeirogon tiling  0.707107 i
... hyperbolic order 4 truncated horocyclic tiling, hyperbolic order 4 truncated apeirogonal tiling  1.322876 i
... hyperbolic order 5 decagonal tiling  0.154508 i
... hyperbolic order 4 horocyclic tiling  0.5 i
othat omnitruncated trihexagonal tiling, great rhombitrihexagonal tiling  
... partially bi-expanded hyperbolic order 8 triangular tiling, partially bi-contracted hyperbolic shieldotritetragonal tiling  
... partially contracted hyperbolic order 3 tritetragonal tiling  
pacrothat partially contracted rhombitrihexagonal tiling  
... partially contracted hyperbolic shieldotritetragonal tiling  
pextrat partially expanded triangular tiling  
... partially expanded hyperbolic order 8 triangular tiling  
qrasquit quasirhombated square tiling  
qrothat quasirhombitrihexagonal tiling  
quitothit quasitruncated trihexagonal tiling  
quitsquat quasitruncated square tiling  
quothat quasitruncated hexagonal tiling  
rarsisresa rhombiretrosnub squarirhombisquariapeirogonal tiling  
rassersa rhombisnub squarirhombisquariapeirogonal tiling  
retrat retroelongated trangular tiling  
... tri-hexagonal rhombic tiling  
rorisassa rhombiretrosnub squarisquariapeirogonal tiling  
rosassa rhombisnub squarisquariapeirogonal tiling  
rothat rhombitrihexagonal tiling  
... snub of hyperbolic [10,8,4,6] tiling with tetragonal Coxeter domain  
... hyperbolic snub tiling of family o3o3o∞*a  
... hyperbolic snub tiling of family o3o4o5*a  
... hyperbolic snub triheptagonal tiling  
... hyperbolic snub tritritetragonal tiling, hyperbolic snub tiling of family o3o3o4*a  
... hyperbolic snub trioctagonal tiling  
... hyperbolic snub trigonal-horocyclic tiling, hyperbolic snub triapeirogonal tiling  
... hyperbolic snub tetrapentagonal tiling  
... hyperbolic snub pentapentagonal tiling  
satsa squariapeirotruncated squariapeirogonal tiling  
sha square hemiapeirogonal tesselation, alternate square tiling  
sha square hemiapeirogonal tesselation, alternate square tiling  
shaha small hexahexaapeirogonal tiling  
shothat,
(inbetween: shath)
small hexagonal-trigonal-hexagonal tiling  
... hyperbolic snub di-horocyclic tiling  
snasquat snub square tiling  
snathat snub trihexagonal tiling  
sossa small squarisquariapeirogonal tiling  
sost squarisquaritiling  
squat square tiling, 2D hypercubical honeycomb2), Voronoi complex of square lattice, Delone complex of square lattice  
sraht small rhombihexagonal tiling  
tha trigonal hemiapeirogonal tesselation  
that trihexagonal tiling, Kagomé tiling  
thotithit trihexagonaltruncated trihexagonal tiling  
... infinite polyhedron from alternating tic/tut structure  
tosquat truncated square tiling  
toxat truncated hexagonal tiling  
trat triangular tiling, Delone complex of hexagonal lattice  
... partially contracted hexagonal tiling  
... uBxx3xoAo3xooA3*a&#zx  
... Wells' "hyperbolic" {4,5} polyhedron  
... Wells' infinite polyhedron from the ike/oct diamond structure  
... hyperbolic order 3 trigonal-horocyclic tiling  0.433013 i
... hyperbolic order 4 tritetragonal tiling, hyperbolic ditetragonal tritetratrigonal tiling, hyperbolic alternated order 4 hexagonal tiling  0.408248 i
... hyperbolic tripentagonal tiling of family o3o4o5*a  0.357770 i
... hyperbolic cantic order 4 hexagonal tiling  1.060082 i
... hyperbolic dipentagonal tiling of family o3o4o5*a  0.956676 i
... hyperbolic order 7 triangular tiling  0.873057 i
... hyperbolic rhombitriheptagonal tiling  2.728895 i
... hyperbolic order 8 triangular tiling  0.594604 i
... hyperbolic shieldotritetragonal tiling, hyperbolic tritetratrigonal tiling  1.446026 i
... hyperbolic rhombitrioctagonal tiling  2.096343 i
... hyperbolic order ∞ triangular tiling  0 i
... hyperbolic rhombi-trigonal-horocyclic tiling  1.322876 i
... hyperbolic shieldo-trigonal-horocyclic tiling  0.829156 i
... hyperbolic shieldotetrapentagonal tiling of family o3o4o5*a, ditrigonal tiling of family o3o4o5*a  0.874835 i
... hyperbolic omnitruncated tiling of family o3o4o5*a  1.456608 i
... hyperbolic order 7 truncated trigonal tiling  2.976586 i
... hyperbolic omnitruncated triheptagonal tiling  4.779184 i
... hyperbolic order 8 truncated trigonal tiling  2.276396 i
... hyperbolic omnitruncated trioctagonal tiling  3.699185 i
... hyperbolic order ∞ truncated trigonal tiling  1.414214 i
... hyperbolic omnitruncated trigonal-horocyclic tiling, hyperbolic truncated triapeirogonal tiling  2.397916 i
... hyperbolic order 5 square tiling  0.747674 i
... hyperbolic rhombisquarepentagonal tiling  1.794231 i
... hyperbolic order 6 square tiling  0.5 i
... hyperbolic rhombisquarehexagonal tiling  1.405256 i
... hyperbolic order 8 square tiling  0.321797 i
... hyperbolic rhombitetraoctagonal tiling  1.175154 i
... hyperbolic order ∞ square tiling  0 i
... hyperbolic rhombisquareapeirogonal tiling  0.978318 i
x4oPo family of (generally hyperbolic) order P square tilings  
... hyperbolic order 5 truncated square tiling  2.113125 i
... hyperbolic omnitruncated tetrapentagonal tiling  3.121470 i
... hyperbolic order 6 truncated square tiling  1.632242 i
... hyperbolic order 6 omnitruncated square tiling, hyperbolic order 4 omnitruncated hexagon tiling  2.474067 i
... hyperbolic truncated infinite-order square tiling  1.098684 i
... hyperbolic order 10 pentagonal tiling  0.206652 i
... hyperbolic order 5 pentagonal tiling  0.528686 i
... hyperbolic order 5 truncated pentagonal tiling  1.548400 i
... hyperbolic order 6 hexagonal tiling  0.353553 i
... hyperbolic quarter order 6 square tiling  
... hyperbolic truncated order 6 hexagonal tiling  1.221076 i
... hyperbolic order 7 heptagram tiling  0.484510 i
... hyperbolic order 7/2 heptagon tiling  0.873057 i
... hyperbolic order 8 octagonal tiling  0.227545 i
... hyperbolic order ∞ horocyclic tiling, hyperbolic order ∞ apeirogonal tiling  0 i
... family of (generally hyperbolic) P-gonal tilings of order P  

Count of actually available polygons: 153



top of page

---- 3D ----


Acronym Name Circumradius
..., 10Y4-8T-0 parallelly oct dissected octet  
..., 10Y4-8T-1-alt alternating staggered 1×60°-gyrated 10Y4-8T-0  
..., 10Y4-8T-1-hel helical staggered 1×60°-gyrated 10Y4-8T-0  
..., 10Y4-8T-2-alt alternating staggered 2×60°-gyrated 10Y4-8T-0  
..., 10Y4-8T-2-hel helical staggered 2×60°-gyrated 10Y4-8T-0  
..., 10Y4-8T-3 3×60°-gyrated 10Y4-8T-0, trat-mirrored 10Y4-8T-0  
... dodeca-augmented rhombicuboctahedron ...
... external blend of 12 raded-1-10-5-5 edge facetings  
... external blend of 20 sidtid-0-3-3-3 edge facetings  
... t24-s6-n8  2.431352
... 2cho (?)  1
... 2co (?)  1
... 2co+16{3} (?)  1
... 2cube (?)  0.866025
... 2did (?)  1
... 2ditdid+5cube (?)  0.866025
... 2doe (?)  1.401259
... 2gad (?)  0.951057
... 2gad+ike (?)  0.951057
... 2geihid (?)  0.618034
... 2gid (?)  0.618034
... 2gidhei (?)  1
... 2gidhid (?)  0.618034
... 2gidtid+5cube (?)  0.866025
... 2gike (?)  0.587785
... 2gike+sissid (?)  0.587785
... 2gissid (?)  0.535233
... 2id (?)  1.618034
... 2id+40{3} (?)  1.618034
... 2ike (?)  0.951057
... 2ike+4gad (?)  0.951057
... 2ike+gad (?)  0.951057
2n/2-p 2n-gonal prism of winding number 2 sqrt[1/4+1/(4 sin2(π/n))]
2n/d-p 2n/d-prism, 2n-prism with winding number d sqrt[1/4+1/(4 sin2(π d/2n))]
2n-p 2n-gonal prism sqrt[1/4+1/(4 sin2(π/2n))]
... 2oct (?)  0.707107
... 2oct+12{4} (?)  0.707107
... 2oct+6{4} (?)  0.707107
... 2oct+8{3} (?)  0.707107
... blend of 2 pentagonal antiprisms, pair of pentagonal butterfly wedges  0.951057
... pentagonal butterfly wedge, blend of 2 pentagonal pyramids, half of blend of 2 pentagonal antiprisms  0.951057
... 2pip (?), decagonal prism with winding number 2  0.986715
... 2quitgissid (?)  0.657550
... 2quith (?)  0.579471
... 2quitsissid (?)  0.852911
... 2raded (?)  1.322876
... 2seihid (?)  1.618034
... 2sidhei (?)  1
... 2sidhid (?)  1.618034
... 2sidtid+5cube (?)  0.866025
... 2sirco (?)  1.398966
... 2sissid (?)  0.587785
... 2sissid+4gike (?)  0.587785
... 2sissid+gike (?)  0.587785
... 2srid (?)  2.232951
... 2tet (?)  0.612372
... 2thah (?)  0.707107
... 2ti (?)  2.478019
... 2tic (?)  1.778824
... 2tid (?)  2.969449
... 2tiggy (?)  1.053292
... 2tigid (?)  1.876844
... 2trip (?), hexagonal prism with winding number 2  0.763763
... 2tut (?)  1.172604
... triaconta-augmented rhombicosidodeahedron ...
... 3doe (?)  1.401259
... 3gidtid (?)  0.866025
... 3gissid (?)  0.535233
... 3ike+3gad (?), 3cid (?)  0.951057
... 3ike+gad (?)  0.951057
..., 3Q3-S3-2P6-2P3-gyro parallelly that dissected, elongated rich  
..., 3Q3-S3-2P6-2P3-ortho parallelly that dissected, elongated gyrich  
..., 3Q4-T-2P8-P4 parallelly sirco dissected ratoh  
... 3sidtid (?)  0.866025
... 3sissid+gike (?)  0.587785
... 3tet (?)  0.612372
... Leonardo polyhedron of type {4,5;19}  
... Leonardo polyhedron of type {4,5;31}  
... 4ike+2gad (?)  0.951057
... 4oct (?)  0.707107
... 4sissid+2gike (?)  0.587785
... 4tet (?)  0.612372
... 4thah (?)  0.707107
... Leonardo polyhedron of type {5,4;13}  
... 5ike+gad (?)  0.951057
..., 5Y4-4T-4P4 elongated 10Y4-8T-0  
..., 5Y4-4T-6P3-sq-para para-staggered shear-elongated 10Y4-8T-0  
..., 5Y4-4T-6P3-sq-skew skew-staggered shear-elongated 10Y4-8T-0  
..., 5Y4-4T-6P3-tri-0 trat-elongated 10Y4-8T-0  
..., 5Y4-4T-6P3-tri-1-alt trat-elongated 10Y4-8T-1-alt  
..., 5Y4-4T-6P3-tri-1-hel trat-elongated 10Y4-8T-1-hel  
..., 5Y4-4T-6P3-tri-2-alt trat-elongated 10Y4-8T-2-alt  
..., 5Y4-4T-6P3-tri-2-hel trat-elongated 10Y4-8T-2-hel  
..., 5Y4-4T-6P3-tri-3 trat-elongated 10Y4-8T-3  
... 6doe (?)  1.401259
... 6gissid (?)  0.535233
..., 6Q3-2S3-gyro parallelly that dissected rich  
..., 6Q3-2S3-ortho (un)gyrated 6Q3-2S3-gyro  
..., 6Q4-2T parallelly squobcu dissected pacratoh  
... 6tet (?)  0.612372
... a3b3c, general variation of truncated octahedron sqrt[(3a2+4b2+3c2+4ab+2ac+4bc)/8]
... a3b4c, general variation of great rhombicuboctahedron sqrt[2a2+4b2+3c2+4ab+(2ac+4bc)sqrt(2)]/2
... a3b5c, general variation of great rhombicosidodecahedron sqrt[(f+2)a2+4(f+1)ab+2(2f+1)ac+4(f+1)b2+4(2f+1)bc+3(f+1)c2]/2
... terminally chamfered hexadecachoron  
addasi altered disnub icosahedron, compound of 20 oct (but not dasi)  0.707107
arie antirhombicosicosahedron, compound of 5 co  1
atich alternatedly truncated cubic honeycomb  
aud, J58 augmented dodecahedron  
auhip, J54 augmented hexagonal prism  
aupip, J52 augmented pentagonal prism  
auteddi, J64 augmented tridiminished icosahedron  
autic, J66 augmented truncated cube  
autid, J68 augmented truncated dodecahedron  
autip, J49 augmented triangular prism  
autut, J65 augmented truncated tetrahedron  
auwaco, J87 augmented sphenocorona  
... vertex figure of biprismatododecateron  0.816497
batatoh bitruncated alternated-cubic honeycomb, bitruncated tetrahedral-octahedral honeycomb, quarter cubic honeycomb  
batch bitruncated cubic honeycomb, truncated-octahedral honeycomb, Voronoi complex of body-centered cubic (bcc) lattice  
bauco bi-augmented cuboctahedron, 4fold rhombohedron ...
baupip, J53 biaugmented pentagonal prism  
bautic, J67 biaugmented truncated cube  
bautip, J50 biaugmented triangular prism  
... vertex figure of biprismatointercepted dodecateron  0.816497
bilbiro, J91 bilunabirotunda  
bitdi chiral Weimholt hexahedron, bitrigonally diminished icosahedron, vertex figure of bidex  0.951057
... cubically-diminished dodecahedron, bi-tetrahedrally-diminished dodecahedron  1.401259
... vertex figure of cellibiprismatohexateron  0.816497
cadditradid complex (ditrigonal) rhombidodecadodecahedron  0.866025
... vertex figure of cellidishexateron  0.816497
caquitpica cubatiquasitrunciprismated cubatiapeiratic honeycomb  
... vertex figure of cellihemidodecateron  0.866025
cho cubohemioctahedron, rhomballelohedron  1
... cho+4{6/2} (?)  1
chon cubic honeycomb, 3D hypercubical honeycomb3), Voronoi complex of primitive cubical lattice, Delone complex of primitive cubical lattice  
... cubically truncated rhombic dodecahedral honeycomb  
cid small complex icosidodecahedron  0.951057
co   (alt.: ratit – old: rotet) cuboctahedron, rhombitetratetrahedron, rectified cube, rectified octahedron, cantellated tetrahedron, expanded tetrahedron, trigonal gyrobicupola, vertex figure of octet  1
... (ico derived) tridpy variant, o3m4o3o cell  
... (tes derived) tridpy variant, o4m3o3o cell  
... (hi derived) tridpy variant, o5m3o3o cell  
... (ex derived) pedpy variant, o3m3o5o cell  
cotco cuboctatruncated cuboctahedron, cubitruncated cuboctahedron  1.322876
cube, 4-p cube, hexahedron, 3D measure-polytope3), geochor(id), square prism, triangular antitegum, Voronoi cell of primitive cubical lattice, Delone cell of primitive cubical lattice, terminally chamfered tetrahedron, surtegmated tetrahedron  0.866025
... pyrithohedral cube-doe-bilbiro honeycomb  
... cubically truncated rhombic dodecahedron, chamfered octahedron  
cutpica cubatitrunciprismated cubatiapeiratic honeycomb  
dap, 10-ap decagonal antiprism  1.674505
dasi disnub icosahedron, compound of 20 oct (but not addasi)  0.707107
datha ditetratihemiapeiratic honeycomb  
dawci, J90 disphenocingulum  
desided disnub icosidodecadodecahedron, compound of 2 sided  
... vertex figure of dodecabiprismatohemidodecateron  0.866025
did dodecadodecahedron, great dodecadodecahedron  1
... did+sidhei+gidhei (?)  1
dip (old: dep) decagonal prism  1.693527
dird dirhimbidodecahedron, compound of 12 pip  0.986715
dirid, J76 diminished rhombicosidodecahedron  2.232951
dis disnubihedron, compound of 12 tet  0.612372
disco disnub cuboctahedron, compound of 2 snic  
disdid disnub dodecadodecahedron, compound of 2 siddid  
disdi-verf vertex figure of disnub disicositetrachoron  0.866025
dissid disnub icosidodecahedron, compound of 2 snid  
dissit disnub tetrahedron, compound of 4 oct  0.707107
ditdid ditrigonal dodecadodecahedron, vertex figure of dittady  0.866025
... ditdid+gidtid (?)  0.866025
ditoh ditetrahedral-octahedral honeycomb  
doe dodecahedron, cosmohedron  1.401259
... rico-derived polychoron incorporating does  2.802517
... dodecahedrically truncated rhombic triacontahedron, chamfered icosahedron  
doso disnub octahedron, compound of 8 oct  0.707107
dri dirhombicosahedron, compound of 20 trip  0.763763
dro dirhombioctahedron, compound of 8 trip  0.763763
dudsi dual of D-stellation of icosahedron, D-faceting of dodecahedron, vertex figure of paphicki  0.866025
e icosiicosahedron, compound of 10 tet  0.612372
ebauco elongated bi-augmented cuboctahedron, 4fold elongated rhombohedron, bi-augmented pexco ...
editoh elongated ditetrahedral-octahedral honeycomb  
epcu, J20 elongated pentagonal cupola  
epedpy, J16 elongated pentagonal dipyramid  
epeppy, J9 elongated pentagonal pyramid  
epgybro, J43 elongated pentagonal gyrobirotunda  
epgycuro, J41 elongated pentagonal gyrocupolarotunda  
epigybcu, J39 elongated pentagonal gyrobicupola  
epobcu, J38 elongated pentagonal orthobicupola  
epocuro, J40 elongated pentagonal orthocupolarotunda  
epro, J21 elongated pentagonal rotunda  
erich parallelly that elongated rich  
escu, J19 elongated square cupola, diminished small rhombicuboctahedron  1.398966
esquidpy, J15 elongated square dipyramid  
esquigybcu, J37 elongated square gyrobicupola, pseudorhombicuboctahedron, Miller's solid  1.398966
esquipy, J8 elongated square pyramid  
etcu, J18 elongated triangular cupola  
etidpy, J14 elongated trigonal dipyramid  
etigybcu, J36 elongated triangular gyrobicupola  
etobcu, J35 elongated triangular orthobicupola  
etoh elongated tetrahedral-octahedral honeycomb, elongated alternated cubic honeycomb  
etoph elongated-triagonal prismatic honeycomb  
etripy, J7 elongated triangular pyramid  
... expanded dodeca-augmented great rhombicuboctahedron ...
exrad expanded rhombic dodecahedron  
exrhote expanded rhombic triacontahedron  
extoh expanded octahedral-tetrahedral honeycomb  
... f v10o, variation of decagonal prism, hull of 10/3-prism  1.286277
... f v3o, variation of triangular prism, vertex figure of rectified great grand hecatonicosachoron  0.884212
... f v5o, variation of pentagonal prism, vertex figure of righi  0.964832
... f x3o, variation of triangular prism, vertex figure of rectified hecatonicosachoron  0.993902
... f x4o, variation of cube  1.074481
... f x5/2o, variation of 5/2-prism, vertex figure of raghi  0.964832
... f x5o, variation of pentagonal prism  1.173932
... f3o3x, variation of cuboctahedron  1.327129
... f3o4x, variation of small rhombicuboctahedron  1.789732
... f3o5x, variation of srid, hull of siid, hull of quit gissid  2.785428
... f3v5v, variation of grid, hull of idtid  3.236068
... f3x5o, variation of ti, hull of tigid, hull of gaddid  3.036797
... f3x5x, variation of great rhombicosidodecahedron, hull of quitdid  4.341518
... vertex figure of facetoinverted decahexadecateron  0.919866
gacid great complex icosidodecahedron  0.587785
gacoca great cubaticubatiapeiratic honeycomb  
gacquitpica great cubatiquasitrunciprismated cubatiapeiratic honeycomb  
gactipeca great cubatitrunciprismated cubatiapeiratic honeycomb  
gad great dodecahedron, vertex figure of fix  0.951057
gaddid great dodekicosidodecahedron  0.716891
gadsid great disnub dodecahedron, compound of 12 pap  0.951057
... vertex figure of great facetosphenary penteract  0.776106
... vertex figure of great spinocelliprismated penteract  0.920055
gaqrich great quasirhombated cubic honeycomb  
gaquapech great quasiprismated cubic honeycomb  
gaquatid great quasitruncated icosidodecahedron, stellatruncated icosidodecahedron  1.020684
gari great antirhombicosahedron, compound of 5 cho  1
gassic (chiral) great snub cube, compound of 3 squap  0.822664
gassid great snub dodecahedron, compound of 6 pap  0.951057
geihid great icosihemidodecahedron  0.618034
getdoca (old: gotactictosquath) great tetradicubatiapeiratic honeycomb, great tetrahedral cubic tomocubic tomosquare tiling honeycomb  
getit cadoca great tritrigonary cubatidicubatiapeiratic honeycomb  
gibil biro great bilunabirotunda  
gicdatrid great complex (ditrigonal) rhombicosidodecahedron  0.866025
gid great icosidodecahedron  0.618034
... gid+geihid+gidhid (?)  0.618034
gidasid great invertidisnub dodecahedron, compound of 12 starp  0.587785
giddasid great disnub icosidodecahedron, compound of 2 gosid  
giddird great dirhombidodecahedron, compound of 12 stip  0.725530
gidditdid great ditrigonal dodekicosidodecahedron, great dodekified icosidodecahedron  1.134229
giddy great dodekicosahedron  1.134229
... giddy+12{10/2} (?)  1.134229
... giddy+20{6/2}  1.134229
gidhei great dodecahemicosahedron, small dodecahemiicosahedron (but not sidhei)  1
gidhid great dodecahemidodecahedron  0.618034
gidisdrid great disnub dirhombicosidodecahedron, Skilling's figure  0.707107
gidrid great dirhombicosidodecahedron, great snub disicosidisdodecahedron, Miller's monster  0.707107
gidrissid great diretrosnub icosidodecahedron, compound of 2 girsid  
gidsac great disnub cube, compound of 6 squap  0.822664
gidsid great invertidisnub icosidodecahedron, compound of 2 gisid  
gidtid great ditrigonal icosidodecahedron, vertex figure of gidtixhi  0.866025
giid great icosicosidodecahedron  1.134229
gike great icosahedron, retrosnub tetrahedron, retrosnub tetratetrahedron, vertex figure of gax  0.587785
gikkiv pacoca (old: sic vacpeca) great skewverted prismatocubaticubatiapeiratic honeycomb, small skewverted cubatiprismated cubatiapeiratic honeycomb  
gikkivcadach great skewverted cubatiapeiroducubatic honeycomb  
gikrid great chirorhombidodecahedron, compound of 6 stip  0.725530
... vertex figure of great prismated biprismatopenteract  0.837186
girco great rhombicuboctahedron (but not querco), truncated cuboctahedron  2.317611
gird great rhombidodecahedron  0.716891
... gird+12{10/4} (?)  0.716891
... gird+20{6/2} (?)  0.716891
girsid great (inverted) retrosnub icosidodecahedron, azathoth  
gisdid great snub dodekicosidodecahedron, shub-niggurath  0.707107
giship heptagrammic prism of winding number 3, great heptagrammic prism, great stellated heptagonal prism  0.512858
gisid great inverted snub icosidodecahedron, great vertisnub icosidodecahedron, cthulhu  
gissed great invertisnub dodecahedron, compound of 6 starp  0.587785
gissi great snub icosahedron, compound of 10 oct (but not si)  0.707107
gissid great stellated dodecahedron  0.535233
githawro great triangular hebesphenorotunda  
gocco great cubicuboctahedron  0.736813
gosid great snub icosidodecahedron, tsathoggua  
grassid great rhombisnub dodecahedron, compound of 6 stiddip  0.794963
gratoh great rhombated tetrahedral-octahedral honeycomb, cantitruncated alternated cubic honeycomb, cantitruncated tetrahedral-octahedral honeycomb, runcicantic cubic honeycomb  
grich great rhombated cubic honeycomb, cantitruncated cubic honeycomb  
grid great rhombicosidodecahedron (but not qrid), truncated icosidodecahedron  3.802395
griso great rhombisnub octahedron, compound of 4 hip  1.118034
groh great rhombihexahedron  0.736813
... groh+8{6/2} (?)  0.736813
gybadrid, J82 gyrate(d) bidiminished rhombicosidodecahedron  2.232951
gybef, J26 gyrobifastegium  
gyeditoh gyroelongated ditetrahedral-octahedral honeycomb  
gyepabro, J48 gyroelongated pentagonal birotunda  
gyepcu, J24 gyroelongated pentagonal cupola  
gyepcuro, J47 gyroelongated pentagonal cupolarotunda  
gyepibcu, J46 gyroelongated pentagonal bicupola  
gyepip, J11 gyroelongated pentagonal pyramid, diminished icosahedron  
gyepro, J25 gyroelongated pentagonal rotunda  
gyerich parallelly that elongated gyrich  
gyescu, J23 gyroelongated square cupola  
gyesp, J10 gyroelongated square pyramid  
gyesqidpy, J17 gyroelongated square dipyramid  
gyesquibcu, J45 gyroelongated square bicupola  
gyetaph gyroelongated triangular-prismatic honeycomb  
gyetcu, J22 gyroelongated triangular cupola  
gyetibcu, J44 gyroelongated triangular bicupola  
gyetoh gyroelongated tetrahedral-octahedral honeycomb, gyroelongated alternated cubic honeycomb  
gyrich gyrated rectified cubical honeycomb  
gyrid, J72 gyrated rhombicosidodecahedron  2.232951
gytoh gyrated tetrahedral-octahedral honeycomb, gyrated alternated cubic honeycomb  
gytoph gyrated triangular prismatic honeycomb  
hap, 6-ap hexagonal antiprism  1.087664
hawmco, J89 hebesphenomegacorona  
hep heptagonal prism  1.152382
hicu hexagonal cupola ∞   i.e. flat in euclidean space
hip hexagonal prism, Voronoi cell of unit-stacked hexagonal lattice  1.118034
hiph hexagonal prismatic honeycomb, Voronoi complex of unit-stacked hexagonal lattice  
hippy, 6pyr (degenerate) hexagonal pyramid ∞   i.e. flat in euclidean space
hirki hemirhombichiro-icosahedron, compound of 5 thah  0.707107
... vertex figure of hexadecateron  0.774597
... vertex figure of hexadecasphenohexadecateron  0.957427
hudsi dual of H-stellation of icosahedron, H-faceting of dodecahedron, vertex figure of paphacki, huitzilopochtli  0.866025
id icosidodecahedron  1.618034
... id+seihid+sidhid (?)  1.618034
iddei icosidisicosahedron, compound of 5 oho  1
ided icosidodecadodecahedron  1.322876
idisdid invertidisnub dodecadodecahedron, compound of 2 isdid  
idtid icosidodecatruncated icosidodecahedron, icositruncated dodecadodecahedron  2
ike   (alt.: snit) icosahedron, snub tetrahedron, snub tetratetrahedron, snub triangle antiprism, hydrohedron, gyroelongated pentagonal bipyramid, vertex figure of ex  0.951057
... ike+3gad (?)  0.951057
... icosahedrally truncated rhombic triacontahedron, chamfered dodecahedron  
... vertex figure of invertiretrolepidoteron  0.912871
... vertex figure of invertiretrohexadecalepidohemipenteract  0.912871
isdid inverted snub dodecadodecahedron, vertisnub dodecadodecahedron, nyarlathotep  
ki chiro-icosahedron, compound of 5 tet  0.612372
kred (old: red) chiro-rhombidodecahedron, compound of 6 pip  0.986715
kri chirorhombicosahedron, compound of 10 trip  0.763763
... lamina-truncate of hyperbolic o8o4x *b3x tesselation  0.321797 i
... lamina-truncate of hyperbolic x4x3o8o tesselation  0.594604 i
... dual of uniform triangular prism, triangular dipyramid (but not tridpy), o3m3o3o cell  
... dual of uniform n-gonal prism, n-gonal dipyramid  
mabaud, J60 metabiaugmented dodecahedron  
mabauhip, J56 metabiaugmented hexagonal prism  
mabautid, J70 metabiaugmented truncated dodecahedron  
mabgyrid, J74 metabigyrated rhombicosidodecahedron  2.232951
mabidrid, J81 metabidiminished rhombicosidodecahedron  2.232951
magydrid, J78 metagyrate diminished rhombicosidodecahedron  2.232951
mesdi-verf vertex figure of medial snub disicositetrachoron  0.866025
mibdi, J62 metabidiminished icosahedron  0.951057
mibkid metabikis dodecahedron, (subsymmetrically) metabistellated-dodecahedron, dual of mibdi  
... mono lowered small rhombicuboctahedron ...
... mono lowered truncated cube ...
n/2-ap n/2 antiprism sqrt[(32 cos(2π/n))/(88 cos(2π/n))]
n/d-ap n/d-antiprism, n-antiprism with winding number d (for d>n/2 also: n/(n-d)-retroprism, retrograde n/(n-d)-antiprism) sqrt[(32 cos(π d/n))/(88 cos(π d/n))]
n/d-cu n/d-gonal cupola sqrt[(7+4 cos(π d/n)-4 cos2(π d/n))/(12-16 cos2(π d/n))]
n/d-p n/d-prism, n-prism with winding number d sqrt[1/4+1/(4 sin2(π d/n))]
n/d-py n/d-gonal pyramid 1/sqrt[4-1/sin^2(πd/n)]
n-ap n-gonal antiprism sqrt[(32 cos(π/n))/(88 cos(π/n))]
n-azedip n-gonal - apeirogonal duoprism  
n-p n-gonal prism sqrt[1/4+1/(4 sin2(π/n))]
... hyperbolic o3o3o4s4*a tesselation  
... hyperbolic o3o3o4x4*a tesselation  0.5 i
... hyperbolic o3o3x3o3*b tesselation  0.816497 i
... hyperbolic rectified order 3 hexagonal tiling honeycomb  1.732051 i
... hyperbolic o3o4o4x tesselation, hyperbolic honeycomb with seed point in center of right-angled octahedron domain  0.707107 i
... hyperbolic o3o4o8x tesselation  0.400236 i
... hyperbolic o3o4s4o4*a tesselation  
... hyperbolic o3o4x4o tesselation  1.224745 i
... hyperbolic o3o4x4o4*a tesselation  0.292893 i
... hyperbolic o3o4x4o4*b tesselation  0.216606 i
... hyperbolic o3o5o10x tesselation  0.202376 i
... hyperbolic o3o5x5o5*b tesselation  
... o3q4x, variation of truncated cube  2.179449
... o3β4o (?) ...
... o3β4x (?) ...
... o3β5o (?) ...
... o3β5x (?) ...
... hyperbolic rectified order 6 tetrahedral honeycomb  1 i
... hyperbolic o3x3x3o4*a tesselation  1.189207 i
... hyperbolic o3x3x3o5*a tesselation  0.786151 i
... o3x4q, variation of truncated cube, hull of sno  2.121320
... o3x4u, variation of truncated cube  2.613126
... hyperbolic o3x4x3o4*a tesselation  0.944355 i
... hyperbolic o3x4x3o5*a tesselation  
... hyperbolic rectified order 3 icosahedral tesselation  1.427535 i
... hyperbolic bitruncated order 3 icosahedral tesselation  2.910693 i
... hyperbolic o3x5x3o5*a tesselation  
... hyperbolic o3x6o3o tesselation  1 i
... hyperbolic o3x6x3o tesselation  2.075910 i
... hyperbolic order 4 dodecahedral tesselation  0.899454 i
... hyperbolic order 4 hexagonal tiling honeycomb  0.707107 i
... hyperbolic o4o3x3o3*b tesselation  0.408248 i
... hyperbolic o4o3x3x3*b tesselation  1 i
... hyperbolic rectified order 4 dodecahedral tesselation  1.272020 i
... hyperbolic truncated order 4 dodecahedral tesselation  2.246127 i
... family of (generally hypercompact) hyperbolic o4s4o2Qo honeycombs (Q≥2)  
... family of hyperbolic o4s4oPo honeycombs (P≠2)  
... hyperbolic rectified order 5 cubic tesselation  1.057371 i
... hyperbolic rhombated order 4 dodecahedral tesselation, hyperbolic cantelated order 4 dodecahedral tesselation  2.131920 i
... hyperbolic bitruncated order 5 cubic tesselation  2.443795 i
... hyperbolic great rhombated order 5 cubic tesselation, hyperbolic cantitruncated order 5 cubic tesselation  3.466586 i
... family of (generally hypercompact) hyperbolic o4x4o2Qo honeycombs (Q≥2)  
... family of hyperbolic o4x4oPo honeycombs (P≠2)  
... hyperbolic o4x4x4o tesselation  1.553774 i
... o5/2β5o (?) ...
... o5/2β5x (?) ...
... hyperbolic order 5 hexagonal tiling honeycomb  0.381966 i
... hyperbolic o5o3x3o3*b tesselation  0.220528 i
... hyperbolic rectified order 5 dodecahedral tesselation  0.813126 i
... hyperbolic bitruncated order 5 dodecahedral tesselation  1.798907 i
... hyperbolic o6x3o6o tesselation  0.577350 i
... hyperbolic o8o4x *b3x tesselation  0.321797 i
oap, 8-ap octagonal antiprism  1.375549
oct octahedron, rectified tetrahedron, tricross3), tetratetrahedron, aerochor(id), trigonal antiprism, larger Delone cell of face-centered cubic (fcc) lattice, equatorial cross-section of (vertex first) 1/q-tes, vertex figure of hex  0.707107
... oct+6{4} (?)  0.707107
octet alternated cubic honeycomb, tetrahedral-octahedral honeycomb, Delone complex of face-centered cubic (fcc) lattice  
... alternated cubically truncated rhombic dodecahedral honeycomb  
... octahedrally truncated rhombic dodecahedron, chamfered cube  
oho octahemioctahedron, allelotetratetrahedron  1
... oho+8{3}  1
op octagonal prism, bidiminished small rhombicuboctahedron  1.398966
otathaph omnitruncated triangular-hexagonal prismatic honeycomb  
otch omnitruncated cubic honeycomb  
... vertex figure of ope  0.816497
... p12-h4  
... pentagonal antidipyramid, pentagonal antitegum, pentagonal kiteohedron, dual of pap, axial bi-kis-doe, deca-truncated sissid  
pabaud, J59 parabiaugmented dodecahedron  
pabauhip, J55 parabiaugmented hexagonal prism  
pabautid, J69 parabiaugmented truncated dodecahedron  
pabextet partially bi-expanded tetrahedron  
pabextut partially bi-expanded truncated tetrahedron  
pabgyrid, J73 parabigyrated rhombicosidodecahedron  2.232951
pabidrid, J80 parabidiminished rhombicosidodecahedron  2.232951
pac girco partially (mono-)contracted great rhombicuboctahedron ...
pacop partially Stott contracted octagonal prism  
pacprich partially contracted prismatorhombated cubic honeycomb  
pacratoh partially contracted runcinated tetrahedral-octahedral honeycomb  
pacsrich partially contracted small rhombated cubic honeycomb  
pactic partially (mono-)contracted truncated cube ...
... partially contracted hyperbolic x4o3x3o3*b tesselation  
... partially contracted hyperbolic x4o3x3x3*b tesselation  
pagydrid, J77 paragyrate diminished rhombicosidodecahedron  2.232951
pakid pentakis dodecahedron, apiculated dodecahedron  
pap pentagonal antiprism, para-bidiminished icosahedron  0.951057
paqrich prismated quasirhombated cubic honeycomb  
... para bi lowered truncated cube ...
passipsi pseudosnub pentagrammattic snub (pseudo)icosiicosahedron, compound of 5 sissid  0.587785
passipsido pseudosnub pentagrammatic snub (pseudo)disoctahedron, compound of 2 sissid  0.587785
patex cube partially tetrahedrally-expanded cube, tetrahedrally truncated cube, chamfered tetrahedron, partially tri-expanded tetrahedron  
patex sirco partially tetrahedrally-expanded small rhombicuboctahedron, tetrahedrally lowered small rhombicuboctahedron, partially tri-expanded truncated tetrahedron ...
pd{3,5,3} partial diminishing (old: truncation) of hyperbolic order 3 icosahedral tesselation  0.509376 i
pecu, J5 pentagonal cupola  2.232951
pedpy (alt.: pet),
J13
pentagonal dipyramid, (line-)pentagon-tegum  
pegybcu, J31 pentagonal gyrobicupola  
peppy, 5pyr, J2 pentagonal pyramid  0.951057
pero, J6 pentagonal rotunda, half of icosidodecahedron  1.618034
pexco partially (mono-)expanded cuboctahedron, 4fold elongated cuboctahedron ...
... partially extended hyperbolic o4o3x3o3*b tesselation  
... partially extended hyperbolic o4o3x3x3*b tesselation  
pexrich partially expanded rectified cubic honeycomb  
pextet partially (edge-)expanded tetrahedron  
pextich partially expanded truncated cubic honeycomb  
pextoe partially (mono-)expanded truncated octahedron ...
pextoh partially expanded tetrahedral-octahedral honeycomb  
pextut partially (edge-)expanded truncated tetrahedron  
phexdo partially hexa-expanded dodecahedron  
phexid partially hexa-expanded icosidodecahedron  
phexik partially hexa-expanded icosahedron  
pip pentagonal prism, 5-p, vertex figure of rox  0.986715
pobcu, J30 pentagonal orthobicupola  
pobro, J34 pentagonal orthobirotunda  1.618034
pocuro, J32 pentagonal orthocupolarotunda  
presipsi pseudoretrosnub pentagonal snub (pseudo)icosiicosahedron, compound of 5 gad  0.951057
presipsido pseudoretrosnub pentagonal snub (pseudo)disoctahedron, compound of 2 gad  0.951057
prich prismatorhombated cubic honeycomb, runcitruncated cubic honeycomb  
... q x3o, variation of triangular prism, vertex figure of rectified tesseract  0.912871
... q x4o, variation of cube, vertex figure of rectified cubic honeycomb  1
... q x5o, variation of pentagonal prism  1.106168
... q x8o, variation of octagonal prism  1.485633
... q3o3x, variation of cuboctahedron  1.215958
... q3o4x, variation of small rhombicuboctahedron, hull of tisso  1.658312
... q3o5x, variation of srid  2.601518
... q3x4x, variation of girco, hull of quitco  2.564844
qrid quasi rhombicosidodecahedron, great rhombicosidodecahedron (but not grid)  0.716891
... vertex figure of quasicellated penteractitriacontiditeron  1.118034
quequapech quasiquasiprismated cubic honeycomb  
querco quasirhombicuboctahedron, great rhombicuboctahedron (but not girco)  0.736813
quipqrich quasiprismated quasirhombated cubic honeycomb  
quiprich quasiprismatorhombated cubic honeycomb  
quit gissid quasitruncated great stellated dodecahedron, great stellated truncated dodecahedron, great stellatruncated dodecahedron  0.657550
quit sissid quasitruncated small stellated dodecahedron, small stellated truncated dodecahedron, small stellatruncated dodecahedron  0.852911
quitar (old: quahri) quasitruncated rhombihedron, quasihyperhombicosicosahedron, compound of 5 quith  0.579471
quitch quasitruncated cubic honeycomb  
quitco quasitruncated cuboctahedron, great truncated cuboctahedron, stellatruncated cuboctahedron  1.062393
quitdid quasitruncated dodecadodecahedron, stellatruncated dodecadodecahedron  1.658312
quith quasitruncated hexahedron, stellated truncated hexahedron, stellatruncated cube  0.579471
... rhombic enneacontahedron  
... vertex figure of retrocellitriacontadiahexadecateron  0.912871
rad (old: rhode) rhombic dodecahedron, Voronoi cell of face-centered cubic (fcc) lattice, terminally chamfered cube, terminally chamfered octahedron, surtegmated cube, surtegmated octahedron  
... vertex figure of retrodishexadecateron  0.774597
raded rhombidodecadodecahedron  1.322876
... edge faceting raded-1-10-5-5  1.322876
radh rhombic dodecahedral honeycomb, Voronoi complex of face-centered cubic (fcc) lattice  
rah rhombihexahedron, compound of 3 cube  0.866025
rahrie rhombihyperhombicosicosahedron, compound of 5 socco  1.398966
raquahri rhombiquasihyperhombicosicosahedron, compound of 5 gocco  0.736813
rasher rhombisnub hyperhombihedron, compound of 5 sroh  1.398966
rasisquat retrosnub square tiling  
rasquacu retrograde square cupola, 4/3-cupola  0.736813
rasquahr rhombisnub quasihyperrhombihedron, compound of 5 groh  0.736813
rasseri rhombisnub rhombicosicoahedron, compound of 5 sirco  1.398966
rassid rhombisnub dodecahedron, compound of 6 dip  1.693527
rastacu retrograde pentagrammic cupola, 5/3-cupola  0.716891
... vertex figure of retrotriacontidicellihemitriacontaditeron  0.866025
ratoh runcinated alternated cubic honeycomb, runcinated tetrahedral-octahedral honeycomb, runcic cubic honeycomb  
ratricu retrograde trigonal cupola, 3/2-cupola  0.707107
... vertex figure of retrosphenary cellihexateron  0.921954
rhom rhombihedron, compound of 5 cube  0.866025
... partially contracted hexagonal tiling, rhombic uBxx3uxBx3xooA3*a&#zx  
... partially expanded tri-hexagonal rhombic tiling, rhombic uBxx3xoAo3xooA3*a&#zx  
rhote (old: rattic) rhombic triacontahedron, terminally chamfered dodecahedron, terminally chamfered icosahedron, surtegmated dodecahedron, surtegmated icosahedron  
ri rhombicosahedron  1.322876
... ri+12{10/2} (?)  1.322876
... ri+12{10/4} (?)  1.322876
rich rectified cubic honeycomb  
ridatha rectified ditetratihemiapeiratic honeycomb  
... vertex figure of retropenteractihexadecateron  0.774597
risdoh rhombisnub dishexahedron, compound of 6 cube, Skilling's compound  0.866025
ro (chiral) rhombioctahedron, compound of 4 trip  0.763763
rosaqri (old: rasquahpri) rhombisnub quasirhombicosicosahedron, rhombisnub quasihyperpseudorhombicosicosahedron, compound of 5 querco  0.736813
rosi rhombisnub icosahedron, compound of 10 hip  1.118034
rothaph rhombitriangular-hexagonal prismatic honeycomb  
... β3/2o3β (?) ...
... β3/2β3x3*a (?) ...
... β3o4β (?) ...
... β3o5β (?) ...
... s3s3s3s3*a (?)  
... hyperbolic s3s4o4o tesselation ...
... hyperbolic s3s4o4x tesselation ...
... β3x4β (?) ...
... β3x5β (?) ...
... hyperbolic snub order 6 cubical honeycomb  0 i
... hyperbolic birectified alternated order-6 cubic tesselation, hyperbolic runcic order-6 cubic tesselation  1.168771 i
... hyperbolic s4o4o4s tesselation  
... hyperbolic o3o4s4o tesselation  
... family of (generally hyperbolic) s4oPo4s tesselation  
... s4s3s4o (?)  
... β5/2o5β (?) ...
... β5/2x5β (?) ...
... s60-r60-p12-h30  
saddid small dodekicosidodecahedron  2.232951
sadsid small disnub dodecahedron, compound of 12 stap  0.656431
sapisseri (chiral) snub pseudosnub rhombicosahedron, compound of 20 thah  0.707107
sassid (chiral) small snub dodecahedron, compound of 6 stap  0.656431
sassiph snub square prismatic honeycomb  
scuffi semicupolaically faceted icosahedron  0.951057
scufgi semicupolaically faceted great icosahedron  0.587785
se small icosiicosahedron, compound of 5 oct  0.707107
... hyperbolic honeycomb with seed point at edge of right-angled octahedron domain  
... hyperbolic honeycomb with seed point at face of right-angled octahedron domain  
seihid small icosihemidodecahedron  1.618034
seside small snub icosicosidodecahedron, snub disicosidodecahedron, holosnub icosahedron, hastur  1.458190
ship heptagrammic prism of winding number 2, small heptagrammic prism, small stellated heptagonal prism  0.639524
si snub icosahedron, compound of 10 oct (but not gissi)  0.707107
sicdatrid small complex (ditrigonal) rhombicosidodecahedron  0.866025
sidditdid small ditrigonal dodekicosidodecahedron, small dodekified icosidodecahedron  1.721489
siddo snub disoctahedron, octahedral compound of 2 ike  0.951057
siddy small dodekicosahedron  1.721489
... siddy+12{10/4} (?)  1.721489
... siddy+20{6/2} (?)  1.721489
siddykid small didyakis dodecahedron  
sided snub icosidodecadodecahedron, dagon  
sidhei small dodecahemicosahedron, great dodecahemiicosahedron (but not gidhei)  1
sidhid small dodecahemidodecahedron  1.618034
sidtid small ditrigonal icosidodecahedron, vertex figure of sidtixhi  0.866025
... sidtid+ditdid (?)  0.866025
... sidtid+ditdid+gidtid (?)  0.866025
... sidtid+gidtid (?)  0.866025
... edge faceting sidtid-0-3-3-3  0.866025
siid small icosicosidodecahedron  1.721489
sipstar "square-pentagon-pentagram(star)-thingy", vertex figure of retroantiprismatosnub disicositetrachoron  0.866025
sirco small rhombicuboctahedron  1.398966
sird small rhombidodecahedron  2.232951
... sird+12{10/2} (?)  2.232951
... sird+20{6/2} (?)  2.232951
sirsei small retrosnub icosiicosahedron, compound of 5 gike  0.587785
sirsid small (inverted) retrosnub icosicosidodecahedron, retrosnub disicosidodecahedron, yog sothoth  0.580695
sirsido small retrosnub disoctahedron, compound of 2 gike  0.587785
sis small snubihedron, compound of 6 tet (but not snu)  0.612372
sissid small stellated dodecahedron, vertex figure of gofix  0.587785
... sissid+3gike (?)  0.587785
skivcadach small skewverted cubatiapeiroducubatic honeycomb  
skivpacoca small skewverted prismatocubaticubatiapeiratic honeycomb  
sladid (old: sit) small lanceal disdodecahedron, strombic icositetrahedron, deltoidal icositetrahedron, tetragonal icosikaitetrahedron  
sladit small lanceal ditriacontahedron, strombic hexecontahedron, deltoidal hexecontahedron, tetragonal hexecontahedron  
snadow, J84 snub disphenoid, snub digonal antiprism  
snathaph snub trigonal-hexagonal prismatic honeycomb  
sne snub icosiicosahedron, compound of 5 ike  0.951057
snic snub cube, snub cuboctahedron  1.343713
snich s4s3s4s (?), (full) snub cubical honeycomb  
snid snub dodecahedron, snub icosidodecahedron  2.155837
snisquap, J85 snub square antiprism  
sno snub octahedron, compound of 4 oct  0.707107
snu snubihedron, compound of 6 tet (but not sis)  0.612372
so stella octangula, compound of 2 tet  0.612372
socco small cubicuboctahedron  1.398966
spd{3,5,3}   (old: spt{3,5,3}) semi partial diminishing (old: truncation) of hyperbolic order 3 icosahedral tesselation  0.509376 i
squacu, J4 square cupola  1.398966
squap square antiprism  0.822664
squigybcu, J29 square gyrobicupola  
squippy, 4pyr, J1 tetragonal pyramid, half of oct  0.707107
squobcu, J28 square orthobicupola  
srich small rhombated cubic honeycomb, cantellated cubic honeycomb  
srid small rhombicosidodecahedron  2.232951
sroh small rhombihexahedron  1.398966
... sroh+8{6/2} (?)  1.398966
stacu pentagrammic cupola, star cupola  0.866025
stap stellar antiprism, 5/2-antiprism  0.656431
stappy, 5/2-pyr pentagrammic pyramid, stellated pentagonal pyramid  0.587785
starp (old: restap) stellar retroprism (retrograde stellar antiprism), 5/3-antiprism  0.587785
stiddip stellated decagonal prism, 10/3-prism, 10-prism with winding number 3  0.794963
stip stellated pentagonal prism, 5/2-prism, 5-prism with winding number 2, vertex figure of raggix  0.725530
stiscu pentagrammic cuploid, star semicupola  0.866025
stop (old: sop) stellated octagonal prism, 8/3-prism, 8-prism with winding number 3  0.736813
stut cadoca small tritrigonary cubatidicubatiapeiratic honeycomb  
... rhombical dodeca-augmented snub-dodecahedral variant, rhombi-propello-icosahedron  
... rhombical octa-augmented truncated-octehedral variant  
... expanded octa-augmented truncated-octehedral variant  
... rhombical hexa-augmented snub-cubical variant, rhombi-propello-octahedron  
tagyrid, J74 trigyrated rhombicosidodecahedron  2.232951
taki truncated chiro-icosahedron, compound of 5 tut  1.172604
tar (old: harie) truncated rhombihedron, hyperhombicosicosahedron, compound of 5 tic  1.778824
targi trireplinished great icosahedron  0.587785
tassiph truncated square prismatic honeycomb  
tatoh truncated tetrahedral-octahedral honeycomb, truncated alternated cubic honeycomb, cantic cubic honeycomb  
taud, J61 metabiaugmented dodecahedron  
tauhip, J57 triaugmented hexagonal prism  
tautid, J71 triaugmented truncated dodecahedron  
tautip, J51 triaugmented trigonal prism  
te truncated icosiicosahedron, compound of 10 tut  1.172604
teddi, J63 tridiminished icosahedron, ursahedron, vertex figure of sadi  0.951057
tedrid, J83 tridiminished rhombicosidodecahedron, magnaursahedron  2.232951
tekah tetrakis hexahedron, apiculated cube  
tepcus tetrapod-cut-sirco  1.398966
tet tetrahedron, 3D simplex3), pyrochor(id), triangle pyramid, digonal antiprism, hemicube, smaller Delone cell of face-centered cubic (fcc) lattice, regular line-scalene, regular (point-)tettene, vertex figure of pen  0.612372
... tetrahedrally diminished dodecahedron, vertex figure of pd{3,5,3}  1.401259
thah tetrahemihexahedron, vertex figure of tho  0.707107
thaph truncated-hexagonal prismatic honeycomb  
thawro, J92 triangular hebesphenorotunda  
thiph triangular-hexagonal prismatic honeycomb  
ti truncated icosahedron, buckyball  2.478019
tic truncated cube, truncated hexahedron  1.778824
tich truncated cubic honeycomb  
tid truncated dodecahedron  2.969449
tiggy truncated great icosahedron, great truncated icosahedron  1.053292
tigid truncated great dodecahedron  1.876844
tikit triakis tetrahedron, apiculated tetrahedron  
tikko triakis octahedron, apiculated octahedron  
... vertex figure of triacontadipenteract  0.935414
tiph triangular prismatic honeycomb, Delone complex of unit-stacked hexagonal lattice  
tisso truncated stella octangula, compound of 2 tut  1.172604
titdi tri-trigonally diminished icosahedron, (subsymmetrically) tristellated-dodecahedron, tri-kis-dodecahedron, dual of teddi, vertex figure of tridex  
tobcu, J27 triangular orthobicupola, vertex figure of gytoh  1
toe truncated octahedron, Voronoi cell of body-centered cubic (bcc) lattice  1.581139
topfu two-op-fusion  1.398966
... toroidal pentagrammic bicuploid, star semicupolaic diabolo  
tricu, J3 triangular cupola, half of cuboctahedron  1
tridex tri-icositetradiminished hexacosachoron  1.618034
tridpy (alt.: trit),
J12
trigonal dipyramid, (line-)triangle-tegum  
trip, 3-p triangular prism, digonal cupola, Delone cell of unit-stacked hexagonal lattice, vertex figure of rap  0.763763
trirp (degenerate) trigonal retroprism, retrograde trigonal antiprism ∞   i.e. flat in euclidean space
tupip orthogonal blend of pentagonal prisms, vertex figure of sadsadox  0.986715
tuquith blend of 2 quasitruncated cubes  0.579471
tustip orthogonal blend of pentagagramic prisms, vertex figure of gadsadox  0.725530
tut truncated tetrahedron, cantic cube  1.172604
tutic blend of 2 truncated cubes  1.778824
tutrip two trip cupolaic blend, gyrated blend of 2 digonal cupola, Phillips head  0.763763
twip dodecagonal prism  1.995508
... u x3o, variation of triangular prism, vertex figure of rectified hecatonicosachoron  1.154701
... u x4o, variation of cube  1.224745
... u x5o, variation of pentagonal prism  1.312862
... u x6o, variation of hexagonal prism  1.414214
... u3o3x, variation of cuboctahedron  1.541104
... u3o4x, variation of small rhombicuboctahedron  2.040640
... u3x3o, variation of truncated tetrahedron  1.732051
... u3x4o, variation of truncated octahedron  2.236068
... v f3o, variation of triangular prism, vertex figure of rasishi  0.983956
... v f5/2o, variation of 5/2-prism, vertex figure of ragashi  0.905040
... v x3o, variation of triangular prism, vertex figure of rectified great grand stellated hecatonicosachoron  0.654847
... v x5o, variation of pentagonal prism, vertex figure of ragishi  0.905040
... v3o3x, variation of cuboctahedron, vertex figure of gadtaxady  0.820211
... v3o5f, variation of srid, hull of tiggy  1.704262
... v3x3o, variation of truncated tetrahedron, vertex figure of sidtaxhi  0.975835
... v3x5f, variation of grid, hull of gaquatid  4.323687
... axially trigonal variant of pentagonal rotunda ...
... w x4o, variation of cube  1.398966
... w x8o, variation of octagonal prism, hull of 8/3-prism  1.778824
... w3x3o, variation of truncated tetrahedron  1.973010
... w3x4x, variation of girco, hull of cotco  3.193704
waco, J86 sphenocorona  
wamco, J88 sphenomegacorona  
wavicoca sphenoverted cubaticubatiapeiratic honeycomb  
... x f3o, variation of triangular prism  1.059565
... x f5/2o, variation of 5/2-prism, vertex figure of rofix  0.986715
... x q3o, variation of triangular prism, vertex figure of rectified icositetrachoron  0.957427
... x u3o, variation of triangular prism  1.258306
... x v5o, variation of pentagonal prism, vertex figure of rigfix  0.725530
... x3/2β3x (?) ...
... x3f4o, variation of truncated octahedron, hull of siddo, hull of passipsido  2.176251
... x3f5o, variation of ti, hull of raded, hull of kri  3.463334
... hyperbolic alternated order 5 cubical tesselation  0.393076 i
... hyperbolic birectified alternated order-5 cubic tesselation, hyperbolic runcic order-5 cubic tesselation  1.507495 i
... hyperbolic x3o3o3x4*a tesselation  1.553774 i
... hyperbolic x3o3o3x5*a tesselation  1.272020 i
... hyperbolic x3o3o4o3*a tesselation  0.511081 i
... hyperbolic x3o3o5o3*a tesselation  0.250437 i
... hyperbolic x3o3x3o4*a tesselation  1.429970 i
... hyperbolic x3o3x3o5*a tesselation  1.118425 i
... hyperbolic x3o4o3x5*a tesselation  
... hyperbolic order 4 octahedral honeycomb  0 i
... hyperbolic x3o4o4o4*a tesselation  0 i
... x3o4q, variation of small rhombicuboctahedron  1.732051
... hyperbolic x3o4x3o4*a tesselation  1.045866 i
... hyperbolic x3o4x3o5*a tesselation  0.919229 i
... hyperbolic order 3 icosahedral tesselation  0.509376 i
... hyperbolic prismated order 3 icosahedral tesselation, hyperbolic runcinated order 3 icosahedral tesselation  1.272020 i
... hyperbolic rhombated order 3 icosahedral tesselation, hyperbolic cantelated order 3 icosahedral tesselation  2.120267 i
... hyperbolic x3o5x3o5*a tesselation  
... hyperbolic x3o6o3o tesselation  0 i
... hyperbolic x3o6o3o6*a honeycomb, hyperbolic triangular-tiling - hexagonal-tiling honeycomb  0 i
... hyperbolic x3o6o3x tesselation  0.759836 i
... hyperbolic x3o6x3o tesselation  1.467890 i
... x3q3o, variation of truncated tetrahedron  1.442951
... x3β3o (?) ...
... x3β4o (?) ...
... x3β5o (?) ...
... x3u3o, variation of truncated tetrahedron  1.837117
... x3u4o, variation of truncated octahedron  2.549510
... x3v3o, variation of truncated tetrahedron, vertex figure of dattady  0.935414
... x3w3o, variation of truncated tetrahedron  2.120453
... x3w4o, variation of truncated octahedron, hull of rah, hull of snu  2.956796
... hyperbolic truncated alternated order-5 cubic tesselation, hyperbolic cantic order-5 cubic tesselation  1.841352 i
... hyperbolic bitruncated alternated order-5 cubic tesselation, runcicantic order-5 cubic tesselation  2.850727 i
... hyperbolic x3x3o3o3*a3*c honeycomb  0.816497 i
... hyperbolic x3x3o3o4*a tesselation  1.391625 i
... hyperbolic x3x3o3o5*a tesselation  1.072098 i
... hyperbolic x3x3o3x4*a tesselation  2.256021 i
... hyperbolic x3x3o3x5*a tesselation  1.816256 i
... x3x3u, variation of truncated octahedron  2.091650
... hyperbolic x3x3x3o4*a tesselation  2.085865 i
... hyperbolic x3x3x3o5*a tesselation  1.601395 i
... hyperbolic x3x3x3x4*a tesselation  2.942253 i
... hyperbolic x3x3x3x5*a tesselation  2.339260 i
... hyperbolic x3x4o3o4*a tesselation, cyclotruncated octahedral-cubic honeycomb  1 i
... hyperbolic x3x4o3o5*a tesselation  0.869999 i
... hyperbolic x3x4o3x5*a tesselation  
... hyperbolic truncated order 4 octahedral tesselation  1.414214 i
... hyperbolic x4x4o *b3x tesselation, hyperbolic runcicantic o3o4o4x tesselation  2.090770 i
... hyperbolic prismatotruncated order 4 octahedral tesselation, hyperbolic runcitruncated order 4 octahedral tesselation  2.345208 i
... x3x4q, variation of great rhombicuboctahedron  2.645751
... hyperbolic x3x4x3o4*a tesselation  1.599084 i
... hyperbolic x3x4x3o5*a tesselation  
... hyperbolic x3x4x3x4*a tesselation  2.197368 i
... hyperbolic x3x4x3x5*a tesselation  
... x3(-x)5f, variation of grid  1.618034
... hyperbolic truncated order 3 icosahedral tesselation  2.082108 i
... hyperbolic x3x5o3o5*a tesselation  
... hyperbolic prismatotruncated order 3 icosahedral tesselation, hyperbolic runcitruncated order 3 icosahedral tesselation  2.809263 i
... hyperbolic great rhombated order 3 icosahedral tesselation, hyperbolic cantitruncated order 3 icosahedral tesselation  3.601065 i
... hyperbolic omnitruncated order 3 icosahedral tesselation  4.308399 i
... hyperbolic x3x5x3x5*a tesselation, hyperbolic omnitruncated dodecahedral-icosahedral honeycomb  1.798907 i
... hyperbolic order 3 hexagonal tiling honeycomb  1.414214 i
... hyperbolic x3x6o3x tesselation  1.931852 i
... hyperbolic x4o3o3o3*a tesselation  0.722778 i
... hyperbolic order 6 cubical honeycomb  0 i
... hyperbolic x4o3o4o3*a tesselation, cubic-octahedral honeycomb  0.377964 i
... hyperbolic order 5 cubic tesselation  0.555893 i
... hyperbolic x4o3o5o3*a tesselation  0.208191 i
... hyperbolic prismated order 5 cubic tesselation, hyperbolic runcinated order 5 cubic tesselation, hyperbolic prismated order 4 dodecahedral tesselation, hyperbolic runcinated order 4 dodecahedral tesselation  1.723155 i
... hyperbolic prismated order 6 cubical honeycomb, hyperbolic runcinated order 6 cubical honeycomb  1.313295 i
... hyperbolic x4o3x3o3*b tesselation  0.934758 i
... hyperbolic x4o3x3x3*b tesselation  1.553774 i
... hyperbolic rhombated order 5 cubic tesselation, hyperbolic cantelated order 5 cubic tesselation  2.053119 i
... hyperbolic prismatotruncated order 4 dodecahedral tesselation, hyperbolic runcitruncated order 4 dodecahedral tesselation, hyperbolic runcicantellated order 5 cubic tesselation  3.081165 i
... hyperbolic x4o4o4o tesselation, hyperbolic honeycomb with seed point at vertex of right-angled octahedron domain  0 i
... hyperbolic x4o4o4x tesselation  0.840896 i
... hyperbolic x4o4o *b3o tesselation, hyperbolic alternated o3o4o4x tesselation  0.5 i
... family of (generally hyperbolic) x4oPo4x honeycombs  
... hyperbolic x4s4o *b3s tesselation ...
... hyperbolic truncated order 5 cubic tesselation  1.734413 i
... hyperbolic prismatotruncated order 5 cubical tesselation, hyperbolic runcitruncated order 5 cubical tesselation  2.878623 i
... hyperbolic x4x3o8o tesselation  0.594604 i
... hyperbolic great rhombated order 5 cubic tesselation, hyperbolic cantitruncated order 5 cubic tesselation  3.185991 i
... hyperbolic omnitruncated order 5 cubical tesselation, hyperbolic omnitruncated order 4 dodecahedral tesselation  4.248159 i
... hyperbolic x4x4o4o tesselation  1.098684 i
... hyperbolic x4x4o4o4*a tesselation  0.353553 i
... hyperbolic x4x4x4o tesselation  2.030104 i
... x5/2β5o (?) ...
... hyperbolic x5o3o3o3*a tesselation  0.573060 i
... hyperbolic x5o3o4o3*a tesselation  0.336860 i
... hyperbolic order 5 dodecahedral tesselation  0.427486 i
... hyperbolic x5o3o5o3*a tesselation  
... hyperbolic prismated order 5 dodecahedral tesselation, hyperbolic runcinated order 5 dodecahedral tesselation  1.272020 i
... hyperbolic rhombated order 5 dodecahedral tesselation, hyperbolic cantelated order 5 dodecahedral tesselation  1.546658 i
... hyperbolic truncated order 5 dodecahedral tesselation  1.383373 i
... hyperbolic prismatotruncated order 5 dodecahedral tesselation, hyperbolic runcitruncated order 5 dodecahedral tesselation  2.212971 i
... hyperbolic great rhombated order 5 dodecahedral tesselation, hyperbolic cantitruncated order 5 dodecahedral tesselation  2.456999 i
... hyperbolic omnitruncated order 5 dodecahedral tesselation  3.176503 i
... hyperbolic x8o4o *b3o tesselation  0.321797 i
... xfo3foo5oxf&#zx  
... p60-r60, 41st stellation of ti  
... expansion of 41th stellation of truncated icosahedron  
... xo oq&#q, tetrahedron with one shorter edge, vertex figure of tisdip  0.836660
... xo ox&#q, longer variant of digonal antiprism, vertex figure of triddip  0.790569
... xo3oo&#q, longer variant of trigonal pyramid, vertex figure of tepe  0.774597
... xo3ox&#q, longer variant of trigonal antiprism, vertex figure of spid  0.866025
... vertex figure of small prismated icositetrachoron  0.541196
... pentagonal rhombic barrel  
... higher digonal cupola, vertex figure of srip  0.906327
... vertex figure of cope  0.894427

Count of actually available polyhedra: 811



top of page

---- 4D ----


Acronym Name Circumradius
... 1/10-luna of hexacosachoron  1.618034
10,n-dip decagon - n-gon duoprism sqrt[(3+sqrt(5))/2+1/(4 sin2(π/n))]
..., K-4.133 antipentawedge, decagon - pentagonn-antiprismatic wedge, pentagonal gyrobicupolaic ring, {10} || pap, {5} || gyrated pecu  3.077684
12,n-dip dodecagon - n-gon duoprism sqrt[2+sqrt(3)+1/(4 sin2(π/n))]
... mono-augmented trigonal mibdi-laced wedge ...
... 2/10-luna of hexacosachoron  1.618034
... 2affic (?)  1.414214
... 2cont (?)  3.414214
... 2deca (?)  1.414214
... 2dittafady (?)  1.414214
... 2ex (?)  1.618034
... 2ex+fix (?)  1.618034
... 2firgaghi (?)  1.070466
... 2firgogishi (?)  0.661585
... 2firp (?)  0.774597
... 2firsashi (?)  2.802517
... 2fix (?)  1.618034
... 2frico (?)  1.732051
... 2fry (?)  4.534568
... 2gadtifady (?)  0.874032
... 2gaghi (?)  1
... 2gaghi+2paphacki (?)  1
... 2gahi (?)  1.618034
... 2gashi (?)  0.618034
... 2gax (?)  0.618034
... 2gidditpix+2dithix (?)  1.732051
... 2gifdahihox (?)  1
... 2gippapivady (?)  0.726543
... 2giprapivady (?)  1.902113
... 2gishi (?)  0.618034
... 2gitphi (?)  0.874032
... 2gofix (?)  0.618034
... 2gogishi (?)  0.540182
... 2gohi (?)  1.618034
... 2grahi (?) 11.252107
... 2grico (?)  4.299451
... 2grip (?)  1.843909
... 2grit (?)  3.005916
... 2grix (?)  9.124101
... 2hex+8oct (?)  0.707107
... 2hi (?)  3.702459
... 2huhoh+3tes+8co (?)  1
... 2ico (?)  1
... 2ico+2gico (?)  1
... 2ico+48{4}+128{3} (?)  1
2n,2m-dip 2n-gonal - 2m-gonal duoprism sqrt[1/(4 sin2(π/2n))+1/(4 sin2(π/2m))]
2n,m-dip 2n-gonal - m-gonal duoprism sqrt[1/(4 sin2(π/2n))+1/(4 sin2(π/m))]
... anti-n-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))]
... 2oh (?)  1
... 2papvixhi (?)  1.902113
... 2pen (?)  0.632456
... 2prahi (?)  8.278950
... 2prapvixhi (?)  1.175571
... 2prico (?)  3.498949
... 2prip (?)  1.612452
... 2prit (?)  2.370932
... 2prix (?)  9.744610
... 2proh (?)  2.613126
... 2quiphi (?)  0.726543
... 2rahi (?)  4.534568
... 2rahi+2400tet (?)  4.534568
... 2rap (?)  0.774597
... 2rap+20tet (?)  0.774597
... 2ratho (?)  1
... 2rico (?)  1.732051
... 2rico+64{6}+128{3} (?)  1.732051
... 2rico+64{6}+192{3} (?)  1.732051
... 2rit+64tet (?)  1.224745
... 2rox (?)  3.077684
... 2rox+1440{5}+2400{3} (?)  3.077684
... 2rox+sophi (?)  3.077684
... 2sadtifady (?)  2.288246
... 2sidditpix+2dithix (?)  1.732051
... 2sifdahihox (?)  1
... 2sishi (?)  1
... 2sishi+2paphicki (?)  1
... 2sitphi (?)  2.288246
... 2sophi (?)  3.077684
... 2spapivady (?)  1.175571
... 2sprapivady (?)  3.077684
... 2srahi (?)  6.735034
... 2srahi+1440{10}+4800{3} (?)  6.735034
... 2srahi+2400trip (?)  6.735034
... 2srico (?)  2.613126
... 2srico+144{8}+576{3} (?)  2.613126
... 2srico+192trip (?)  2.613126
... 2srip (?)  1.183216
... 2srip+20{6}+40{3} (?)  1.183216
... 2srip+20{6}+60{3} (?)  1.183216
... 2srip+20trip (?)  1.183216
... 2srit (?)  1.847759
... 2srit+48{8}+128{3} (?)  1.847759
... 2srit+64trip (?)  1.847759
... 2srix (?)  6.073594
... 2srix+2400{6}+4800{3} (?)  6.073594
... 2srix+2400{6}+7200{3} (?)  6.073594
... 2tah (?)  2.121320
... 2tes (?)  1
... 2thahp (?)  0.866025
... 2thex (?)  1.581139
... 2tho (?)  0.707107
... 2tho+24{4} (?)  0.707107
... 2titho (?)  1.581139
... 2xhi (?)  7.579634
3,n-dip, K-4.175 triangle - n-gon duoprism, n-gon - n-prismatic wedge sqrt[1/3+1/(4 sin2(π/n))]
... 3/10-luna of hexacosachoron  1.618034
..., {3} || gybef {3} || gyrobifastegium ...
..., {3} || teddi, K-4.33 {3} atop teddi, teddi based wedge  1
... 3doe-1pap-10mibdi-10teddi-diminished ex  1.618034
... 3ex+2fix+gaghi (?)  1.618034
... 3ex+fix (?)  1.618034
... 3pen (?)  0.632456
4,2n-dip square - 2n-gon duoprism sqrt[1/2+1/(4 sin2(π/2n))]
4,n-dip, K-4.177 square - n-gonal duoprism sqrt[1/2+1/(4 sin2(π/n))]
... 4/10-luna of hexacosachoron  1.618034
..., {4} || co, K-4.28 square atop cuboctahedron, bidiminished octaco, square first rotunda of cytau tes  1
... tetracontadisdiminished ex  1.618034
... tetracontadisdiminished sidpixhi  5.236068
... 4ike+gad (?)  0.951057
..., K-4.16 squippy atop gyro cube  0.879465
... 4pen+160{3} (?)  0.632456
5,n-dip pentagon - n-gon duoprism sqrt[(5+sqrt(5))/10+1/(4 sin2(π/n))]
..., K-4.146 pentagon - pentagonal-rotunda wedge, {5} || pero  3.077684
... pentadiminished 2/10-luna of hexacosachoron  1.618034
6,n-dip hexagon - n-gonal duoprism sqrt[1+1/(4 sin2(π/n))]
..., K-4.27 antitriwedge, hexagon - octahedral wedge, triangular gyrobicupolaic ring, {6} || oct, {3} || gyrated tricu, 1/6-luna of ico  1
... 6tes (?)  1
8,n-dip octagon - n-gonal duoprism sqrt[(2+sqrt(2))/2+1/(4 sin2(π/n))]
..., K-4.64 antitetrawedge, octagon - square-antiprismatic wedge, square gyrobicupolaic ring, {8} || squap, {4} || gyrated squacu  1.447009
... tetracontoctachoron-derived Gévay polychoron ...
afdec antifrustic distetracontoctachoron  1.414214
affic antifrustary tetracontoctachoron  1.414214
affip antifustric prismatochoron, compound of 16 hiddip  1.414214
affixthi antifrustic hexacositrishecatonicosachoron  2.236068
afpox antifustric prismatohexacosachoron, compound of 60 gippid  2.236068
arse aurap around-symmetrically expanded augmented rectified pentachoron  
arse biscrahi bistratic icosidodecahedron-first subsegment of small rhombihexacosachoron, around-symmetrically expanded biscrahi  6.073594
arspabd biscrox around-symmetrically parabidiminished bistratic icosahedron-first cap of rectified hexacosachoron  3.077684
arsted biscrox around-symmetrically tridiminished bistratic icosahedron-first cap of rectified hexacosachoron  3.077684
aubautipip augmented biaugmented-triangular-prism prism  
aurap augmented rectified pentachoron  
auteddipe augmented-tridiminished-icosahedron prism ...
autipip augmented-triangular-prism prism ...
autodip augmented 3-8-duoprism ...
autpen augmented truncated pentachoron ...
badhidy (old: buthi) blendic dishecatonicosa-dishecatonicosachoron, compound of tigaghi and quit sishi  2
badohi blendic dishecatonicosachoron  2
baticot bitruncated icositetrachoric tetracomb, small tetracontaoctachoric tetracomb  
batitit bitruncated tesseractic tetracomb  
bauautipip biaugmented augmented-triangular-prism prism ...
baudeca biaugmented decachoron  
bautipip biaugmented-triangular-prism prism  
... BAVFfxoo xFofxFVo3xxFxooxo5xooxFfoV&#zx  
bicypdex (alt.: bicypaugap) bi-cyclopentadiminished hexacosachoron, bi-cyclopentaaugmented great antiprism  1.618034
bicypdrahi (bistratic) bi-cyclopentadiminished rectified hexacosachoron  4.534568
bicypdrox (bistratic) bi-cyclopentadiminished rectified hexacosachoron  3.077684
bicyte ausodip bicyclotetraugmented square-octagon duoprism ...
bicyte gysrit bicyclotetragyrated small rhombitesseract  1.847759
bidex bi-icositetradiminished hexacosachoron  1.618034
bidrap, K-4.8 bidiminished rectified pentachoron, antiduowedge, square - tetrahedral wedge, digonal gyrobicupolaic ring, {4} || tet, line || ortho trip  0.774597
bidsrip bidiminished small rhombated pentachoron  1.183216
... bilbiro wedge ...
bipgy srit bipara(bi)gyrated small rhombitesseract, pseudo cantellated tesseract  1.847759
birgax bi-icositetra-replinished grand hexacosachoron  0.618034
biscex bistratic vertex-first cap of hexacosachoron  1.618034
biscpoxic bistratic vertex-first cap of poxic  
biscrahi bistratic icosidodecahedron-first cap of rectified hecatonicosachoron  4.534568
biscrox bistratic icosahedron-first cap of rectified hexacosachoron  3.077684
biscsrico bistratic cuboctahedron-first cap of small rhombated icositetrachoron  2.613126
biscsrip bistratic trip-cap of srip, {3}-diminished small rhombated pentachoron  1.183216
bithi blendic trishecatonicosachoron  2
bithit bitruncated hexadecachoric tetracomb, bitruncated demitesseractic tetracomb, runcicantic tesseractic tetracomb  
bricot birectified icositetrachoric tetracomb, birectified demitesseractic tetracomb, runcic tesseractic tetracomb  
... BxxFxfofx3oooxxxFFF3xBxfFxxof *b3xxBxfFfxo&#zx  
capicot celliprismated icositetrachoric tetracomb, great prismatotetracontaoctachoric tetracomb  
capirsit celliprismatorhombisnub ico tetracomb  
capoht celliprismated demitesseractic tetracomb, tomoicositetrachoric-diprismatotesseractic tetracomb  
capotat celliprismated tesseractic tetracomb, tomotesseractic-diprismatotesseractic tetracomb, steritruncated tesseractic tetracomb  
capshot celliprismatosnub hex tetracomb  
capsthat celliprismatosnub truncated hex tetracomb  
captatit celliprismatotruncated tesseractic tetracomb, great tomocubic-diprismatotesseractic tetracomb, steriruncitruncated tesseractic tetracomb  
capticot celliprismatotruncated icositetrachoric tetracomb, celliprismatotruncated demitesseractic tetracomb  
... longer antiduowedge, vertex figure of cellirhombated dodecateron  0.953463
chi chirohecatonicosachoron, chiral compound of 5 ico  1
chope cubohemioctahedron prism  1.118034
chopy, pt || cho (degenerate) cubohemioctahedron pyramid ∞   i.e. flat in euclidean space
... augmented axially-octahedral ursachoron ofxo3xooo4oooo&#xt ...
coaop, co || op, K-4.63 cuboctahedron atop octagonal-prism  1.447009
coasirco, co || sirco, K-4.61 cuboctahedron atop small rhombicuboctahedron  1.447009
coatic, K-4.129 cuboctahedron atop truncated cube, cuboctahedral cap of small rhombated icositetrachoron  2.613126
coaticbicu coatic bicupola  
coatobcu coatoe bicupola, equatorially contracted rectified icositetrachoron  
coatoe, co || toe, K-4.95 cuboctahedron atop truncated octahedron, cuboctahedral cap of rectified icosatetrachoron  1.732051
coatotum bistratic co-cap of prip, tut-diminished prip, Stott expansion of tip, (co,toe)-based tutsachoron, (co,toe)-based tutism  1.612452
coatut, co || tut, K-4.48 cuboctahedron atop truncated tetrahedron, cuboctahedral cap of small rhombated pentachoron  1.183216
coatutu expanded axially-tetrahedral ursachoron, (co,tut)-based ursulate  1.328131
cont tetracontoctachoron, octagonny, bitruncated icositetrachoron  3.414214
cope, K-4.43 cuboctahedron prism  1.118034
copy, pt || co (degenerate) cuboctahedron pyramid ∞   i.e. flat in euclidean space
coqroc tetracontoctiquasirhombated tetracontoctachoron  1.325654
cotcope cuboctatruncated-cuboctahedron prism, cubitruncated-cuboctahedron prism  1.414214
croc tetracontoctirhombated tetracontoctachoron  3.200413
cubaco, cube || co, K-4.35 cube atop cuboctahedron, cubical cupola  1.031784
cubaike, cube || ike, K-4.21 cube atop icosahedron  1
cubasirco, cube || sirco, K-4.71 cube atop small rhombicuboctahedron, cubical cap of small disprismatotesseractihexadecachoron  1.485633
cubatic, cube || tic (degenerate) cube atop truncated cube ∞   i.e. flat in euclidean space
cubpy, K-4.26 cubical pyramid, vertex-pyramid of ico  1
cute (old: cubdipy) cubical (line-)tegum, cubical bipyramid ...
cydadex cyclical decadiminishing of ex  1.618034
cypit cyclopentachoric tetracomb, pentachoric-dispentachoric tetracomb, Delone complex of lattice A4  
cypropit cycloprismatorhombated pentachoric tetrachomb, great prismatodispentachoric tetracomb, runcitruncated pentachoric tetrachomb  
cytau tes cyclotetraaugmented tesseract, cyclotetradiminished icositetrachoron  1
cyte cubau sodip cyclotetra cubaugmented sodip ...
cyte gysrit cyclotetragyrated small rhombitesseract  1.847759
cyte opau sodip cyclotetra octagon-prism-augmented sodip ...
cyted spic cyclotetradiminished small prismatotetracontoctachoron  1.847759
cyted srit cyclotetradiminished small rhombitesseract, cyclotetraugmented octagonal duoprism  1.847759
cythdex cyclical triangularily-hexagonally diminished hexacosachoron  1.618034
cytid rico cyclotridiminished rectified-icositetrachoron, metatridiminished rectified-icositetrachoron  1.732051
cytid srico cyclotridiminished small rhombated icositetrachoron  2.613126
cytopit cyclotruncated pentachoric tetracomb, small truncated-pentachoric tetracomb  
dadip (old: dedip) decagon-decagon duoprism  2.288246
dahi dishecatonicosachoron  3
dahiquatady dishecatonicosiquasitruncated dishecatonicosachoron  4.134026
dahitady dishecatonicositruncated dishecatonicosachoron  2.431014
damibdrox deep metabidiminished rectified hexacosachoron  3.077684
dapabdi poxic (alt.: hau sircope) deep parabidiminished poxic, hexa-augmented sircope  
dapabdi spic deep parabidiminished small prismatotetracontoctachoron, hexa-gyro-augmented truncated-cube prism  1.847759
dappip, K-4.96 decagonal-antiprism prism  1.747560
dard tipady diretroditetrahedronary prismatodishecatonicosachoron  1.414214
dastop dodeca-star toroidi-prism  0.707107
... dastop + 2x 2did (?)  0.707107
datap ditetrahedronary prismatochoron, compound of 100 hiddip  1.414214
datcathi ditetrahedronary coincidic trishecatonicosachoron  1.414214
dattady ditetrahedronary dishecatonicosachoron  1.414214
dattathi ditetrahedronary trishecatonicosachoron  1.414214
... DCBAVFfxoo xxxFofxFVo3xoxxFxooxo5ofxooxFfoV&#zx  
deca decachoron, bitruncated pentachoron, equatorial cross-section of (vertex first) q-pent  1.414214
didamibdrox diminished deep metabidiminished rectified hexacosachoron  3.077684
diddatigid, did || tigid dodecadodecahedron atop truncated great dodecahedron, did-first cap of sirfix  4.352502
diddip dodecadodecahedron prism  1.118034
didhi dodecahedronary dishecatonicosachoron  1
didpy, pt || did (degenerate) did pyramid ∞   i.e. flat in euclidean space
... mono-diminished vertex-first rotunda of hexacosachoron  1.618034
... diminished thawro-wedged 1/6-luna of hexacosachoron, {6},ike-wedge, ike,thawro,thawro-multiwedge ...
dippit disprismatotesseract  1.485633
diquitdi disicositetraquasitruncated disicositetrachoron  1.608038
dirico diminished rectified icosatetrachoron  1.732051
disdi disnub disicositetrachoron  1
distadedip decagon-decagram duoprism  1.732051
ditdi disicositetratruncated disicositetrachoron  2.326846
ditdidap ditrigonal-dodecadodecahedron antiprism  0.955838
ditdiddip ditrigonal-dodecadodecahedron prism  1
dithix ditrigonary hecatonicosihexacosichoron  1.732051
dittadphi ditetrahedronary disprismatohecatonicosachoron  1.414214
dittady ditrigonary dishecatonicosachoron  1
... dittady+dox (?)  1
dittafady ditetrahedrofissary dishecatonicosachoron  1.414214
doaid, doe || id, K-4.77 dodecahedron atop icosidodecahedron, dodecahedral cupola  1.618034
doasrid, doe || srid, K-4.152 dodecahedron atop small rhombicosidodecahedron, dodecahedral cap of small disprismatohexacosihecatonicosachoron  5.236068
doasridaid doe atop srid atop id  
doc distetracontoctachoron  2.449490
dod honho disoctidishemioctintercepted hemioctachoron  1
..., doe || 6-dim-id || f-ike || doe axially-pyritohedral (2,12,6)-diminishing of ex  1.618034
doh honho disoctihemihexadekintercepted hemioctachoron  1
dohitipady dishecatonicositruncated prismatodishecatonicosachoron  4.472136
dope, K-4.74 dodecahedron prism  1.487792
dopix dodecahedronary prismatohexacosachoron, compound of 60 spid  1
dox (old: gex) dodecahedronary hexacosachoron (great hexacosachoron), compound of 25 ico  1
dudeca decachoron dual, bi-apiculated pentachoron  0.816497
duhd decahemidecachoron  1
duspid small-prismated-decachoron dual, crystalic icosachoron  
dutip truncated-pentachoron dual, apiculated pentachoron  
dygytpuf, K-4.13 dyadic gyrotegmipucofastegium, 3-prism atop reflected ortho 3-prism  0.866025
ebdah hithi exoblendic dishemihecatonicostrishecatonicosachoron  2
ebuthi exotic blendic tetrishecatonicosachoron  2
ecubedpy elongated cubical bipyramid, hexadiminished icositetrachoron  1
ecubpy elongated cubical pyramid, heptadiminished icositetrachoron  1
ecypit elongated cyclopentachoric tetracomb, elongated pentachoric-dispentachoric tetracomb  
efdit xithi exofissary ditrigonal hexacositrishecatonicosachoron  1.732051
eikedpy elongated icosahedral bipyramid  
eikepy elongated icosahedral pyramid  
eocta sirco elongated octasirco ...
eoctaco elongated octaco  
eoctatut elongated octatut  
eoctpy elongated octahedral pyramid, diminished pex hex  
epipdapy elongated pentagonal-prismatic bipyramid ...
epippy elongated pentagonal-prismatic pyramid ...
epobro, J42 elongated pentagonal orthobirotunda  
esircoatic elongated sircoatic, diminished srit  
esquippidpy elongated square-pyramidal bipyramid, esquidpy-wedge, half of partially (mono-)expanded hex  
esquipuf elongated square pucofastegium, square atop octagon-prism atop octagon-prism  
etedpy elongated tetrahedral bipyramid  
etepy elongated tetrahedral pyramid  
etetaco elongated tetaco ...
etripdapy elongated trigonal-prismatic bipyramid ...
etrippy elongated trigonal-prismatic pyramid ...
etripuf elongated trigonal pucofastegium ...
etutatoe elongated tutatoe ...
ex hexacosachoron, 600-cell, hydrochoron  1.618034
... ex+fix (?)  1.618034
... ex+gohi+120id (?)  1.618034
... FAxoAFxoxx3FxAAoxFxox oxofofxFof3ooxofxfoFf&#zx  
... FAxoFFxoox3foFFxofoxo oxofofxFof3ooxofxfoFf&#zx  
... FAxoFFxxox3foFFxofxxo oxofofxFof3ooxofxfoFf&#zx  
... FAxoFFxxox3foFFxofxxo xoxFxFoAxF3oxxofxFoFf&#zx  
... vertex figure of facetospinopenteractidishexadecateron  0.919866
... Ffxo oxFx3xfox5xoxx&#zx  
... Ffxo xofo3ofox5xoxx&#zx  
firgaghi faceted rectified great grand hecatonicosachoron  1.070466
firgogishi facetorectified great grand stellated hecatonicosachoron  0.661585
firp faceted rectified pentachoron, vertex figure of dah  0.774597
... firp+rap+15{4} (?)  0.774597
firsashi faceted rectified small stellated hecatonicosachoron  2.802517
firt facetorectified tesseract  1.224745
fix icosahedral hecatonicosachoron, faceted hexacosichoron  1.618034
... fix+gahi+120id (?)  1.618034
... fooo3xxoF3xfxo *b3oxFo&#zx  
frico facetorectified icositetrachoron  1.732051
frogfix faceted rectified great faceted hexacosichoron  0.726543
frox faceted rectified hexacosichoron  3.077684
... frox+600 2thah (?)  3.077684
fry facetorectified hecatonicosachoron  4.534568
... dodeca-diminished equatorial tetrastratic segment of rox  3.077684
... Fxo oxf3xox5xfo&zxt  
... equatorial tetrastratic segment of rectified hexacosachoron  3.077684
... Fxox3xoxf3oFxx *b3oxfo&#zx  
... Fxxox5ofxfo xofox5oxofx&#zx  
... Fxxx3xxoF3xfxo *b3oxFo&#zx  
... Fxxx5ofxo xofx5oxox&#zx  
gabbadipady great blendic disprismatodishecatonicosachoron  2
... gabbadipady+ganbathi (?), sanbathi+tigaghi (?)  2
gabbathi great blendic trishecatonicosachoron  2
... vertex figure of great biprismatodiscellipenteract  1.118034
gabippady (old: gabbippady) great blendic prismatodishecatonicosachoron  2
gadatady grand ditetrahedral dishecatonicosachoron  0.874032
gadathiphi grand ditetrahedronary hecatonicosaprismatohecatonicosachoron  0.874032
... gadathiphi+600 2tet (?)  0.874032
gaddadid, gad || did great dodecahedron atop dodecadodecahedron, great-dodecahedral cupola  1.064815
gaddaraded, gad || raded great dodecahedron atop rhombidodecadodecahedron, gad-first cap of quipdohi  1.328131
gaddatigid, gad || tigid (degenerate) gad atop tigid ∞   i.e. flat in euclidean space
gaddiddip great-dodekicosidodecahedron prism  0.874032
gaddip great-dodecahedron prism  1.074481
gaddit thix grand ditrigonal trishecatonicosihexacosachoron  1.732051
... vertex figure of great dispinocellirhombated penteract  0.907821
gadixady great dishexacosadishecatonicosachoron  3.139124
gadixhix (old: gixhix) great dodecahedronary hexacosahemihexacosachoron, compound of 25 ihi (but not sadixhix)  1
gadpy great-dodecahedral pyramid, vertex cap of fix  1.618034
gadsadox great disnub dihexacosachoron  0.726543
gadtap great ditetrahedronary prismatochoron, compound of 36 stadidip  0.874032
gadtaxady grand ditetrahedronary hexacosadishecatonicosachoron  0.874032
gadtaxhi great ditetrahedronary hexacosihecatonicosachoron  0.874032
gadtef pixady great ditetrahedronary exofissary prismatohexacosadishecatonicosachoron  0.874032
gadtifady (old: gadtafady) great ditetrahedronarofissary dishecatonicosachoron  0.874032
gaedit pathi grand exoditetrahedronary prismatotriakishecatonicosachoron  0.874032
gaghi great grand hecatonicosachoron  1
... gaghi+didhi (?)  1
... gaghi+idhi (?)  1
... gaghi+paphacki+sridaphi (?)  1
... gaghi+sridixhi (?)  1
gahfipto great hexadecafeceted prismatotesseractioctachoron  0.890446
gahi grand hecatonicosachoron  1.618034
... gahi+gohi (?)  1.618034
ganbathi great spinoblendic trishecatonicosachoron  2
ganbippady great spinoblendic prismatodishecatonicosachoron  2
gap great antiprism, grand antiprism, pentagonal double antiprismoid (but not: great duoantiprism), bicyclical decadiminishing of ex  1.618034
... dual of great antiprism ...
... cell of gap dual, adjacent bikis doe  
gapript great pseudorhombated prismatotesseract  0.765367
... gapript+16 2thah (?)  0.765367
gapthi grand prismatotriakishecatonicosachoron  2.400819
gaqri great quasirhombated icositetrachoron  1.230739
gaqrigafix great quasirhombated great faceted hexacosachoron  1.080363
gaqrigaghi great quasirhombated great grand hecatonicosachoron  1.679184
gaqrigagishi great quasirhombated great grand stellated hecatonicosachoron  1.179024
gaqrigashi great quasirhombated great stellated hecatonicosachoron  2.700333
gaqript grand quasirhombated prismatotesseract  0.765367
gaqrisashi great quasirhombated small stellated hecatonicosachoron  5.018002
gaqrit great quasirhombated tesseract  1.401594
gaquapac great quasiprismatotetracontoctachoron  1.127864
gaquatiddip great-quasitruncated-icosidodecahedron prism  1.136572
gaquidapixhi great quasidisprismatohexacosihecatonicosachoron  1.581630
gaquidipdy grand quasidisprismatodishecatonicosachoron  1.695697
gaquidphihi great quasidisprismatohecatonicosihecatonicosachoron  4.242641
gaquidpoth great quasidisprismatotesseractihexadecachoron  1.938391
gaquipadah great quasiprismatodishexadecachoron  0.890446
garawv hixhi great retrosphenoverted hecatonicosihexacosihecatonicosachoron  1.054256
gard tadhix grand retroditetrahedronary dishecatonicosihexacosachoron  0.874032
gardatady grand retroditetrahedral dishecatonicosachoron  0.874032
... gardatady+1440{5}  0.874032
gardatathi grand retroditetrahedronary trishecatonicosachoron  0.874032
gardtapaxhi grand retroditetrahedronary hexacosidishecatonicosachoron  0.874032
gardtaxady grand retroditetrahedronary hexacosidishecatonicosachoron  0.874032
garpit grand rhombated dishexadecachoron  1.847759
garpop grand rhombated prismatopentachoron  1.183216
gashi grand stellated hecatonicosachoron  0.618034
... vertex figure of great pteroprismated penteract  0.837186
gax grand hexacosachoron  0.618034
... gax+gashi+120gid (?)  0.618034
... gax+gofix (?)  0.618034
geedatepthi great exoditetrahedrary prismatotrishecatonicosachoron  1.414214
gefdit dixdy great exofissary ditrigonal dihexacosadihecatonicosachoron  1.732051
gefidtethi great exofissary ditetrahedronary tetrakishecatonicosachoron  0.874032
gefirdit xethi great exofissary retroditetrahedronary hexacositrishecatonicosachoron  1.414214
gefradit thix great exofissary retroditetrahedronary triakishecatonicosihexacosachoron  0.874032
gefridit xethi great exofissary retroinverted ditetrahedronary hexacositrishecatonicosachoron  1.414214
getit dixady great tritrigonal dihexacosidihecatonicosachoron  1.136572
getit phiddix great tritrigonal prismatohecatonicosidishexacosachoron  1.136572
getit pixady great tritrigonal prismatohexacosidihecatonicosachoron  1.136572
getit thix great tritrigonal trishecatonicosihexacosachoron  1.136572
getit xethi great tritrigonal hexacositrishecatonicosachoron  1.136572
ghahoh great hexadecahemihexadecachoron  1
ghihi great hecatonicosihecatonicosachoron  0.854102
ghipady great hecatonicosiprismatodishecatonicosachoron  4.087567
gibricot great birhombated icositetrachoric tetracomb, great grand prismatodisicositetrachoric tetracomb  
gic great tetracontoctachoron, octagrammy  0.585786
gicaricot great cellirhombated icositetrachoric tetracomb, runcicantic hexadecachoric tetracomb  
gicaroht great cellirhombated hexadecachoric tetracomb, runcicantic icositetrachoric tetracomb  
gicartit great cellirhombated tesseractic tetracomb, great rhombitesseractic-prismatotesseractic tetracomb, stericantitruncated tesseractic tetracomb  
gichado great cubihexadecadisoctachoron  1.174172
gico great icositetrachoron, stella prismata, compound of 3 tes  1
... gico+8co+16 2thah (?)  1
gid thipady great ditrigonal hecatonicosiprismatodishecatonicosachoron  4.087567
gid tipathi great ditrigonal prismatotriakishecatonicosachoron  2.920251
gidard tipady great diretroditetrahedronary prismatodishecatonicosachoron  1.414214
giddatady great ditetrahedronary dishecatonicosachoron  1.414214
giddic great distetracontoctachoron  0.765367
giddip great-icosidodecahedron prism  0.794963
giddit thix great ditrigonal trishecatonicosihexacosachoron  1.732051
gidditdiddip great-ditrigonal-dodekicosidodecahedron prism  1.239546
gidditpix great ditrigonary prismatohexacosichoron  1.732051
gidhiquit paddy great dishecatonicosaquasitruncated prismatodishecatonicosachoron  2.140933
gidipthi great dipental trishecatonicosachoron  1.328131
gidpith great disprismatotesseractihexadecachoron, great prismated tesseract, omnitruncated tesseract  3.498949
gidpixathi great dipentagonal hexacositrihecatonicosachoron  1.328131
gidpixhi great disprismatohexacosihecatonicosachoron, omnitruncated hecatonicosachoron, omnitruncated hexacosachoron 12.786651
gidthidy hi great ditrigonal hecatonicosadishecatonicosihecatonicosachoron  1.732051
gidthixhi great ditrigonal hecatonicosihexacosihecatonicosachoron  3.139124
gidtidap great-ditrigonal-icosidodecahedron antiprism  0.955838
gidtiddip great-ditrigonal-icosidodecahedron prism  1
gidtixhi great ditrigonary hexacosihecatonicosachoron  1
... gidtixhi+dox (?)  1
gifdahihox great fissary dodecahedronary hecatonicosihemihexacosachoron  1
giidip great-icosicosidodecahedron prism  1.239546
gik vipathi great skewverted prismatotriakishecatonicosachoron  2.828427
gik vixathi great skewverted hexacositriakishecatonicosachoro  2.013884
gikagid, gike || gid great icosahedron atop great icosidodecahedron, great icosahedral cap of rectified grand hexacosachoron, great-icosahedral cupola  0.726543
gikepy great-icosahedral pyramid, vertex cap of gax  0.618034
gikkiv datapixady great skewverted ditrigonary prismatohexacosadishecatonicosachoron  2.013884
gikviphado great skewverted prismatohexadecadisoctachoron  1.414214
gipe great-icosahedron prism  0.771681
giphado great prismatohexadecadisoctachoron  1.082392
giphatit great prismated demitesseractic tetracomb, great diprismatodemitesseractic tetracomb, steriruncicantic tesseractic tetracomb  
giphiddix great prismatohecatonicosadishexacosachoron  1.624598
giphidy great prismated hecatonicosadishecatonicosachoron  1.348948
giphihix great prismatohecatonicosahecatonicosahexacosachoron  1.893038
giphixhi great prismatohecatonicosihexacosihecatonicosachoron  2.920251
gippapivady great pentagrammal antiprismatoverted dishecatonicosachoron  0.726543
gippic great prismatotetracontoctachoron, omnitruncated icositetrachoron  5.169905
gippict great prismated icositetrachoric tetracomb  
gippid great prismatodecachoron, Voronoi cell of lattice A4*  2.236068
gippittit great prismated tesseractic tetracomb, great diprismatotesseractic tetracomb, runcicantitruncated tesseractic tetracomb  
gippixady great prismatohexacosadishecatonicosachoron  1.207883
gippixhihy great prismatohexacosihecatonicosihecatonicosachoron  1.021064
giprapivady great pentagonal retroprismatoverted dishecatonicosachoron  1.902113
gipriphi great pseudorhombated prismatohecatonicosachoron  0.799575
... gipriphi+600 2thah (?)  0.799575
gipthi great prismatotriakishecatonicosachoron  3.531591
gipti great prismatotriakisicositetrachoron  1.938391
girc great retrotetracontoctachoron  0.765367
gircope, K-4.125 great-rhombicuboctahedron prism  2.370932
girfaddic great retrofrustic distetracontoctachoron  1.414214
girfix great rhombated faceted hexacosachoron  7.404918
girfixthi great retrofrustic hexacositrishecatonicosachoron  2.236068
girpdo great rhombiprismatodisoctachoron  1.174172
girpith great rhombiprismated tesseractihexadecachoron  1.082392
girsiddip great-(inverted)-retrosnub-icosidodecahedron prism  
gisdiddip great-snub-dodekicosidodecahedron prism  
gisdipthi great stellated dipental trishecatonicosachoron  1.328131
gishi great stellated hecatonicosachoron  0.618034
... gishi+gashi (?)  0.618034
gisiddip great-inverted-snub-icosidodecahedron prism  
gisp great swirlprism  0.618034
gissiddip great-stellated-dodecahedron prism  0.732444
git thixady great tritrigonal hecatonicosihexacosidishecatonicosachoron  1.136572
gitphi great tripesic hecatonicosachoron  0.874032
gitpodady great (intersected) tripesic dodecahedronary dishecatonicosachoron  1
gittifcoth great tesseractifaceted cubitesseractihexadecachoron  0.890446
gittith great tesseractitesseractihexadecachoron  0.890446
gixathi great hexacositriakishecatonicosachoron  3.804226
gixhi great hexacosihecatonicosachoron  1.244649
gixhidy great hexacosihecatonicosadishecatonicosachoron  1.464888
gixhihy great hexacosihecatonicosihecatonicosachoron  0.763932
gixipady great hexacosiprismatodishecatonicosachoron  1.624598
gnappoth great spinoprismatotesseractihexadecachoron  0.890446
goccope great-cubicuboctahedron prism  0.890446
gocypapit bitruncated pentachoric tetracomb, great cycloprismated pentachoric tetrachomb, grand prismatodispentachoric tetracomb  
gocyropit great cyclorhombated pentachoric tetrachomb, great truncated-pentachoric tetracomb, cantitruncated pentachoric tetrachomb  
gofix great icosahedral hecatonicosachoron, great faceted hexacosichoron  0.618034
... gofix+gishi+120gid (?)  0.618034
gogishi great grand stellated hecatonicosachoron  0.540182
gohi great hecatonicosachoron  1.618034
gohihix great hecatonicosihecatonicosihexacosachoron  1.464888
gohiny great hecatonicosintercepted hecatonicosachoron  0.661585
gondip great octagonal spinoduoprism  0.890446
goquidipdy great quasidisprismatodishecatonicosachoron  6.566933
gosiddip great-snub-icosidodecahedron prism  
gotdatixhi great toroidoditrigonary hexacosihecatonicosachoron  1.732051
gotditpix great toroidoditrigonary prismatohexacosichoron  1.732051
gotto great trisoctachoron, great triakisoctachoron  1.224745
grad tathi great retroditetrahedronary trishecatonicosachoron  1.414214
graggix great rhombated grand hexacosachoron  1.658546
graghi great rhombated grand hecatonicosachoron  4.550627
grahi great rhombated hecatonicosachoron, cantitruncated hecatonicosachoron 11.252107
graphi grand retropental hecatonicosachoron  0.726543
grawv ditathi great retrosphenoverted ditrigonary triakishecatonicosachoron  2.093315
grawv hidy great retrosphenoverted hecatonicosadishecatonicosachoron  1.589926
grawv hixhi great retrosphenoverted hecatonicosihexacosihecatonicosachoron  1.513868
grawvathi great retrosphenoverted triakishecatonicosachoron  2.572554
grawvixady great retrosphenoverted hexacosadishecatonicosachoron  2.036148
grico great rhombated icositetrachoron, cantitruncated icositetrachoron  4.299451
gricot great rhombated icositetrachoric tetracomb, great prismatodisicositetrachoric tetracomb  
..., xFoFx3xxxxx5xofox&#xt  
(F=ff=x+f)
bilunabirotundic great rhombicosidodecahedron prism  
gridaphi great retroinverted dodecahedronary prismatohecatonicosachoron  1
griddip, K-4.150 great-rhombicosidodecahedron prism  3.835128
gridixhi great retroinverted dodecahedronary hexacosahecatonicosachoron  1
gridtathi great retroinverted ditetrahedronary trishecatonicosachoron  1.414214
grip great rhombated pentachoron, cantitruncated pentachoron  1.843909
griphi great retropental hecatonicosachoron  1.175571
grit great rhombated tesseract, cantitruncated tesseract  3.005916
grittit great prismatotesseractic tetracomb, cantitruncated tesseractic tetracomb  
grix great rhombated hexacosachoron, cantitruncated hexacosachoron  9.124101
grohp great-rhombihexahedron prism  0.890446
gudap (old: gedap) great duoantiprism, (old: great double antiprism) (but not: great antiprism)  1
guti great tetrakisicositetrachoron  2.326846
gwav ditathi great sphenoverted ditrigonary triakishecatonicosachoron  2.036148
gwavathi great sphenoverted triakishecatonicosachoron  1.027486
gwavixady great sphenoverted hexacosadishecatonicosachoron  0.799575
gyautisdip gyro-augmented 3-4-duoprism ...
gyepipa pero, K-4.140 gyroelongated pentagonal pyramid atop pentagonal rotunda  3.077684
gypasp great pyramidic swirlprism  0.618034
gyprip gyrated prip  1.612452
gyspid (alt: tetacobcu) gyrated small prismatodecachoron, orthobicupola of runcinated pentachoron, tetaco orthobicupola  1
haddet demidistesseract, compound of 2 hex  0.707107
hadedip hexagon - decagon duoprism  1.902113
haf, K-4.46 hexagonal antifastegium, hexagon - hap wedge, {6} || gyro hip  1.130454
hagy gircope hexa-gyro-augmented gircope  
happip, K-4.53 hexagonal-antiprism prism  1.197085
hau gircope hexa-augmented gircope  
hau ticcup hexa-(ortho-)augmented ticcup  
haucope hexa-augmented cope  
hautope hexa-augmented tope  
hedip heptagonal-heptagonal duoprism  1.629715
hex, K-4.2
(alt: octit, trapt)
hexadecachoron, tetracross4), hemitesseract, hemioctachoron, 16-cell, aeroter(id), tetrahedral antiprism, vertex figure of tac, (line-)octahedral tegum, (line-)trigonal-antirprismatic tegum  0.707107
... hex+8oct (?)  0.707107
hext hexadecachoric tetracomb, demitesseractic tetracomb, Delone complex of body-centered tesseractic lattice  
hi hecatonicosachoron, 120-cell, dodecacontachoron, cosmochoron  3.702459
... hi dimpled in by 120 ikadoes ...
hibbit hexagonal duoprismatic tetracomb  
hiddip hexagonal-hexagonal duoprism, Voronoi cell of lattice A2×A2  1.414214
hihiquatady hecatonicosihecatonicosiquasitruncated dishecatonicosachoron  3.605551
hinhi hecatonicosintercepted hecatonicosachoron  2.802517
hinnit hexadekintercepted tesseract  1.224745
hippyp hexagon-pyramidal prism, line || hip ∞   i.e. flat in euclidean space
histodip hexagon - octagram duoprism  1.137055
hitwadip hexagon - dodecagon duoprism  2.175328
hixady hecatonicosihexacosidishecatonicosachoron  3
hixquathix hecatonicosihexacosaquasitruncated hecatonicosihexacosachoron  2.174739
hixquitixhi hecatonicosihexacosiquasitruncated hexacosihecatonicosachoron  2.351141
hixquitphix hecatonicosihexacosiquasitruncated prismatohecatonicosihexacosachoron  2.483382
hixtaphix hecatonicosihexacositruncated prismatohecatonicosihexacosachoron  7.735167
hixthix hecatonicosihexacositruncated hecatonicosihexacosachoron  6.186316
hixtixhi hecatonicosihexacositruncated hexacosihecatonicosachoron  3.804226
hodho hexadecoctidishemioctachoron  1
hodip hexagon - octagon duoprism  1.645329
hoh honho hexadecoctihemihexadekintercepted hemioctachoron  1
hohoh hexadecoctihemihexadecachoron  1
hossdap hollow small stellated dodecahedral antiprism, pseudo sissid atop pseudo sissid  0.754386
hot thibbit hexagonal-omnitruncated-trihexagonal duoprismatic tetracomb  
huhoh hexadecahemihexadecachoron  1
icau pretasto icositetra-augmented pentagonorhombic-trisnub-trisoctachoron  
icau prissi icositetra-augmented prismatorhombisnub icositetrachoron  
ico icositetrachoron, 24-cell, xylochoron, rectified hexadecachoron, birectified tesseract, vertex figure of hext, Voronoi cell of lattice F4, Voronoi cell of lattice D4*, surtegmated tesseract  1
... ico+gico+72{4} (?)  1
... ico+gico+24co (?)  1
icot icositetrachoric tetracomb, Voronoi complex of body-centered tesseractic (bct) lattice  
... (0,0,20,0,0)-diminished vertex-first-rotunda of ex, icosi-diminished vertex-first-rotunda of ex, mono-augmented axially-icosahedral ursachoron ofxo3xooo5oooo&#xt  1.618034
... id - srid - F-ike - ti tower, thawro'd rox ...
idasrid, id || srid, K-4.131 icosidodecahedron atop small rhombicosidodecahedron, icosidodecahedron cupola, ike-first supra-cap of rox  3.077684
idasridati id atop srid atop ti  
idati, id || ti, K-4.158 icosidodecahedron atop truncated icosahedron, icosidodecahedral cap of small rhombated hexacosachoron  6.073594
iddip, K-4.90 icosidodecahedron prism  1.693527
idhi invertidodecahedronary hecatonicosachoron  1
ididdip icosidodecadodecahedron prism  1.414214
idim sidpixhi icosa-diminished small disprismatohexacosihecatonicosachoron  5.236068
idimex spid-diminished ex, icosidiminished ex  1.618034
idimsrahi icosa-diminished small rhombated hecatonicosachoron  6.735034
idimsrix icosa-diminished small rhombated hexacosachoron  6.073594
idprahi icositetra-diminished prismatorhombated hecatonicosachoron  8.278950
idtiddip icosidodecatruncated-icosidodecahedron prism, icositruncated-dodecadodecahedron prism  2.061553
ihi icositetrahemiicositetrachoron  1
ikadoaid (1,0,0,12,0)-diminished vertex-first-rotunda of ex, trideca-diminished vertex-first rotunda of hexacosachoron, ike atop (pseudo) doe atop id  1.618034
ikadoe (alt.: ikap),
ike || doe, K-4.78
icosahedron atop dodecahedron, icosahedral antiprism, dodecahedral antiprism  1.618034
ikaid, ike || id, K-4.137 icosahedron atop icosidodecahedron, icosahedral cap of rectified hexacosachoron, icosahedral cupola  3.077684
... (1,0,8,12,0)-diminished vertex-first-rotunda of ex, (subsymmetrical) icosiena-diminished vertex-first rotunda of hexacosachoron  1.618034
... (1,0,4,12,0)-diminished vertex-first-rotunda of ex, heptadeca-diminished vertex-first rotunda of hexacosachoron  1.618034
ikepy, K-4.84 icosahedral pyramid, vertex cap of hexacosachoron  1.618034
iktum bistratic icosahedron-first cap of truncated hexacosachoron, ike-based tutsatope, ike-based tutism  4.643523
iku (1,0,20,0,0)-diminished vertex-first-rotunda of ex, (full-symmetrical) icosiena-diminished vertex-first-rotunda of ex, axially-icosahedral ursachoron ofx3xoo5ooo&#xt, ike-based ursulate  1.618034
ini icositetrintercepted icositetrachoron  1.732051
inpac icositetraintercepted prismatotetracontaoctachoron  1.847759
... inpac+72{4} (?)  1.847759
ipe, K-4.36 icosahedron prism  1.074481
ipixady invertopental hexacosadishecatonicosachoron  3.077684
iquatoc icositetraquasitruncated tetracontoctachoron  2
iquatpic icositetraquasitruncated prismatotetracontoctachoron  2.828427
iquipadah inverted quasiprismatodishexadecachoron  1.485633
isdiddip inverted-snub-dodecadodecahedron prism  
it (old: ikedpy) (line-)ikosahedron-tegum, icosahedral bipyramid  
... vertex figure of spikifacetospinodishexadecateron  0.951190
kavipathi skewverted prismatotrishecatonicosachoron  2.828427
kaviphdit skewverted prismatohexadecadistesseract  1.414214
lifpipixhi polar facetopental prismatohexacosahecatonicosachoron  3.077684
... great-rhombated-pentachoron dual  
... triangle duotegum, dual of triangle duoprism  1.060660
... small-rhombated-pentachoron dual  
mardatathi medial retroditetrahedral triakishecatonicosachoron  1.414214
mesdi medial snub disicositetrachoron  1
mibdipy, K-4.87 metabidiminished-icosahedral pyramid  1.618034
mibdirit metabidiminished rectified tesseract, wedge-diminished rectified tesseract, bistratic cuboctahedron based wedge  1.224745
middit thix medial ditrigonal trishecatonicosihexacosachoron  1.732051
mif pixady circumfacetopental hexacosadishecatonicosachoron  4.534568
mipthi medial prismatotriakishecatonicosachoron  3.199386
mix medial hexacosachoron, mete-star, compound of 120 pen  0.632456
mohiny medial hecatonicosintercepted hecatonicosachoron  1.070466
mrawv hixhi medial retrosphenoverted hecatonicosihexacosihecatonicosachoron  3.963358
mriphi medial retropental hecatonicosachoron  1.902113
n,m-dip n-gon - m-gon duoprism sqrt[1/(4 sin2(π/n))+1/(4 sin2(π/m))]
n,n-dip n-gon - n-gon duoprism 1/(sqrt(2)*sin(π/n))
n/d,2n/d-dip n/d-gram - 2n/d-gram duoprism sqrt[1/(4 sin2(π d/n))+1/(4 sin2(π d/2n))]
n/d,m/b-dip n/d-gram - m/b-gram duoprism sqrt[1/(4 sin2(π d/n))+1/(4 sin2(π b/m))]
n/d-af n/d-grammal antifastegium, n/d-grammal - n/d-antiprismatic wedge, {n/d} || gyro n/d-prism sqrt[(1+2 cos(π d/n)-2 cos2(π d/n))/(2+4 cos(π d/n)-6 cos2(π d/n))]
n/d-appip n/d-antiprism prism sqrt[(5-4 cos(π d/n))/(88 cos(π d/n))]
n/d-cuf n/d-grammal cupofastegium, 2n-gon - n/d-prismatic wedge, n/d-grammal orthobicupolaic ring, {2n/d} || n/d-prism, {n/d} || n/d-cupola sqrt[(5+2 cos(π d/n)-4cos2(π d/n))/(8-12 cos2(π d/n))]
n/d-cupe n/d-cupola prism, n/d-prism atop 2n/d-prism sqrt[(5+2 cos(π d/n)-4 cos2(π d/n))/(6-8 cos2(π d/n))]
n/d-pyp n/d-pyramidal prism, line || n/d-prism sqrt[1/4+1/(4-1/sin2[π d/n])]
n-af, K-4.174 n-gonal antifastegium, n-gonal - n-antiprismatic wedge, {n} || gyro n-prism sqrt[(1+2 cos(π/n)-2 cos2(π/n))/(2+4 cos(π/n)-6 cos2(π/n))]
n-appip, K-4.176 n-antiprism prism sqrt[(5-4 cos(π/n))/(88 cos(π/n))]
n-appy n-antiprismatical pyramid sqrt[(2-2 cos(π/n))/(5-6 cos(π/n))]
n-apt (line-)n-antiprismatic tegum, n-antiprismatic bipyramid, n-pyramidal antiprism  
... vertex figure of spinotriacontaditeron  0.912871
n-cuf n-gonal cupofastegium, 2n-gon - n-prismatic wedge, n-gonal orthobicupolaic ring, {2n} || n-prism, {n} || n-cupola sqrt[(5+2 cos(π/n)-4cos2(π/n))/(8-12 cos2(π/n))]
n-cufbil n-gonal cupofastegia biluna  
n-gytpuf n-gonal gyrotegmicupolafastegium, n-cupola atop inverted gyrated n-cupola, 2n-prismatic gyrated bi-wedge  
nipixady intercepted invertopental hexacosadishecatonicosachoron  3.077684
n-pidpy n-prismatic bipyramid  
n-pipy n-prism pyramid, general vertex pyramid of o-3-x-3-o-n-o 1/sqrt[3 - 1/sin2(π/n)]
n-puf n-gonal pucofastegium, n-gon - 2n-prismatic wedge, n-gonal magnabicupolaic ring, {n} || 2n-prism, {2n} || n-cupola sqrt[(2 cos2(π/n)-2 cos(π/n)-3)/(6 cos2(π/n)-2)]
..., n-pyr-pyr {n}-pyramidal pyramid, {n}-scalene, n tet rosette, line atop fully orthogonal {n} sqrt[(4 sin2(π/n)-1)/(3 sin2(π/n)-1)]/2
n-tepuf n-gonal tegmipucofastegium, n-cupola atop inverted ortho n-cupola, 2n-prismatic ortho bi-wedge  
... tetracontoctachoron dual, bi-apiculated icositetrachoron, tetradisphenoidal 288-cell  1.306563
... hyperbolic order 3 hecatonicosachoric tesselation  2.301105 i
... hyperbolic order 3 small-stellated-hecatonicosachoral tetracomb  0.242934 i
... o3o3β4o (?) ...
... o3o3β4x (?) ...
... o3o3β5o (?) ...
... o3o3β5x (?) ...
... hyperbolic order 4 icositetrachoral tetracomb  0.5 i
... hyperbolic great-hecatonicosachoral tetracomb  0.393076 i
... o3β3o4β (?) ...
... o3β3o5β (?) ...
... o3β3β3o (?) ...
... o3β3β4o (?) ...
... o3β3β4β (?) ...
... o3β3β5o (?) ...
... o3β3β5β (?) ...
... o3β3x3o (?) ...
... o3β3x4o (?) ...
... o3β3x4β (?) ...
... o3β3x4x (?) ...
... o3β3x5o (?) ...
... o3β3x5β (?) ...
... o3β3x5x (?) ...
... o3β4o3o (?) ...
... o3β4β3o (?) ...
... o3β4x3o (?) ...
... o3x3β4o (?) ...
... o3x3β5o (?) ...
... rectified-tesseract dual, surtegmated hexadecachoron  
... hyperbolic order 4 hecatonicosachoric tetracomb  0.899454 i
... hyperbolic birectified order 5 hecatonicosachoric tetracomb  0.747674 i
... icositetrachoron-derived Gévay polychoron, rectified o3m4o3o ...
... tesseract-derived Gévay polychoron, rectified o4m3o3o ...
... hecatonicosachoron-derived Gévay polychoron, rectified o5m3o3o ...
oaf, K-4.58 octagonal antifastegium, octagon - oap wedge, {8} || gyro op  1.409438
oappip, K-4.65 octagonal-antiprism prism  1.463603
... omni-pecu-augmented (10,20)-duoprism  
... omni-peppy-augmented (5,20)-duoprism  
... (hi derived) truncated tridpy variant, o2o3o symmetric co relative ...
... (ico derived) truncated tridpy variant, o2o3o symmetric co relative ...
... (tes derived) truncated tridpy variant, o2o3o symmetric co relative ...
... augmented axially-tetrahedral ursachoron ofxo3xooo3oooo&#xt ...
... oxFxofx3xooxFxo3ofxfooo&#xt   (F=ff=x+f)  
... oxFxoo3xooxFx3ofxfox&#xt   (F=ff=x+f)  
... oxFxofx3xfoxFxo3ooxfooo&#xt   (F=ff=x+f)  
... oxFxoo3xfoxFx3ooxfox&#xt   (F=ff=x+f)  
octaco, K-4.29 octahedron atop cuboctahedron, half of icositetrachoron (its oct-first rotunda), rectified octahedron-pyramid  1
octacube (alt.: octap),
oct || cube, K-4.15
octahedron atop cube, octahedral antiprism, cubical antiprism, vertex figure of icoap  0.879465
octasirco, oct || sirco, K-4.107 octahedron atop small rhombicuboctahedron, octahedral cap of small prismatotetracontoctachoron  1.847759
octasircoacube oct atop sirco atop cube  
octatoe, oct || toe (degenerate) octahedron atop truncated octahedron ∞   i.e. flat in euclidean space
octatricu, oct || tricu, K-4.30 octahedron atop trigonal cupola, 2/6-luna of icositetrachoron  1
octatut, oct || tut, K-4.52 octahedron atop truncated tetrahedron, octahedral cap of small rhombated pentachoron  1.183216
octatutbicu octatut bicupola ...
... octatut,tricuf-blend  
octpy, K-4.3 octahedral pyramid, half of hex (its vertex-first rotunda)  0.707107
octu axially-octahedral ursachoron ofx3xoo4ooo&#xt, oct-based ursulate, vertex figure of s3s4o3o4o  1.144123
octum octahedron-first rotunda of truncated hexadecachoron, oct-based tutsatope, oct-based tutism  1.581139
odedip octagon-decagon duoprism  2.079697
odho octidishemioctachoron  1
... octa-diminished thawro-wedged 2/6-luna of hexacosachoron ...
odip octagon-octagon duoprism  1.847759
... oFfoo3ooxxF3Fxoxo3ooffx&#zx  
... oFFxx3xxoof3fooxo3ooffx&#zx  
... oFFxx3xxoof3fooxx3xxFFo&#zx  
... oFFxx3xxoxf3Fxxox3oofFx&#zx  
ofiddady omnifacetododecahedronary dishecatonicosachoron  1
... ofoxFxo3xxFxoox3xoofxfo&#xt   (F=ff=x+f)  
ofpipixhi omnifacetopental prismatohexacosahecatonicosachoron  0.726543
... oFxFox5AxFoFx2oxofox5ooxofx&#zx  
... oFxx3xxof3foxo3oofx&#zx  
... axially pyritohedral octa-diminishing of telex, hexa-diminishing of oofoo3oxoxo5xooox&#xt  
... oFxxox5Fofxfo oxofox5ooxofx&#zx  
... oFxxx5Fofxo oxofx5ooxox&#zx  
... omni-pecu-gyroaugmented (10,20)-duoprism  
oh octihemihexadecachoron  1
ohope octahemioctahedron prism  1.118034
ohopy, pt || oho (degenerate) octahemioctahedron pyramid ∞   i.e. flat in euclidean space
ohuhoh octihexadecahemihexadecachoron  1
omfapaxady omnicircumfacetopental hexacosadishecatonicosachoron  0.726543
ondip octagonal spinoduoprism  1.485633
... medial tetrastratic segment of telex  
... ooofxfooo3xoxxoxxox5ofxofoxfo&#xt  
... ooofxxFfooFxofx3oxFxoFxxxFoxFxo3xfoxFoofFxxfooo&#xt  
... oooxfxooo3xoxoxoxox5ofxfofxfo&#xt  
ope, K-4.11
(alt: dytpuf)
octahedron prism, vertex figure of rat, dyadic tegmipucofastegium  0.866025
... pentachoron-derived Gévay polychoron, rectified o3m3o3o  1.095445
... hexacosachoron-derived Gévay polychoron, rectified o3m3o5o  6.412847
... rectified m m3o, o2o3o symmetric co relative  0.816497
... truncated pedpy variant, o2o5o symmetric co relative  1.203002
ostodip octagon-octagram duoprism  1.414214
otathisbit omnitruncated-trihexagonal-square duoprismatic tetracomb  
otatit omnitruncated tesseractic tetracomb  
otbaquitit octagonnally tetrablended quasitruncated tesseract  0.615370
otbott octagonnally tetrablended truncated tesseract  2.149726
otcypit omnitruncated cyclopentachoric tetracomb, great-prismatodecachoric tetracomb, Voronoi complex of lattice A4*  
otit omnitruncated icositetrachoric tetracomb  
otwadip octagon - dodecagon duoprism  2.332200
owau prit   (alt.: pox spic,
alt.: phic prico)
octa-augmented prismatorhombated tesseract, partially octa-expanded small prismated (dis)icositetrachoron, partially hexadeca-contracted prismatorhombated icositetrachoron  
owaudope omni-augmented dodecahedral-prism  
... oxFxofo3xfoxFxx3ooxfoox&#xt   (F=ff=x+f)  
... oxofofoxo3oofoxofoo5xxoxxxoxx&#xt  
... oxofxfooo3xxxxoxxox5ooxofoxfo&#xt  
... oxofxfoxo3xxFxoxFxx5xxoxFxoxx&#xt  
... oxofxfoxo3xxxxoxxxx5ooxofoxoo&#xt  
... oxoofooxo3oofxoxfoo5xxoxxxoxx&#xt  
... oxoxfxooo3xxxoxoxox5ooxfofxfo&#xt  
... oxoxfxoxo3xxxoxoxxx5ooxfofxoo&#xt  
... oxqw wxwx3ooxx4qwox&#zx  
... oxqwQ wxwxx3ooxxx4qwoxo&#zx  
... octagonal Leonardo style "polyhedron of renaissance", vertex figure of lamina-trunc(o8o4xb3x)  1.847759
... proh-cap augmented bistratic prit-cap ...
... oxwQ wxoo3xxxx4oxxo&#zx ...
... point atop tet atop co  
... oct atop tut atop toe  
... oxxFxoAFxxFoxFx3xofxxFoooFxxfox3xFxoFxxFAoxFxxo&#xt  
pabdico parabidiminished icositetrachoron, hexa-augmented tesseract  1
pabdiproh parabidiminished prismatorhombated hexadecachoron, tristratic tic-first central segment of proh  2.613126
pabdirico parabidiminished rectified icosatetrachoron, bistratic co-first central segment of rico, axis-orthogonal partial Stott expanded rit  1.732051
pabex thex partially biexpanded truncated hexadecachoron, partially bicontracted prismatorhombated tesseract ...
pabexrico partially bi-expanded rico, partially bi-contracted proh  
pabexrit partially bi-expanded rit, partially bi-contracted tat  
pabextah partially bi-expanded tesseractihexadecachoron, partially bi-contracted great rhombated tesseract  
pabextico partially bi-expanded tico, partially bi-contracted gidpith  
pac gidpith partially (mono-)contracted gidpith  
pac grit partially (mono-)contracted great rhombated tesseract  
pacprit partially (mono-)contracted prit ...
pacproh partially (mono-)contracted proh  
pacsid pith (alt: cuba sircobcu) partially (mono-) contracted sidpith, partially expanded quawros, cubasirco bicupola  
pacsrit partially (mono-)contracted small rhombated tesseract ...
pactat partially (mono-)contracted tat  
padedip pentagon - decagon duoprism  1.828016
padiap prismatic double inverted antiprism, pentagrammic double antiprismoid  0.618034
padohi prismatodishecatonicosachoron  2.497212
paf, K-4.22 pentagonal antifastegium, pentagon - pap wedge, {5} || gyro pip  1
pahtex prit partially demitesseractic-expanded prit, partially demitesseractic-contracted gidpith  
pahtex sidpith partially demitesseractic-expanded sidpith, partially demitesseractic-contracted proh  
pahtex srit partially demitesseractic-expanded srit, partially demitesseractic-contracted grit  
pahtex tes partially demitesseractic-expanded tesseract, partially demitesseractic-contracted truncated tesseract, hexadecachorally truncated tesseract  
paltite prismatoaltitruncated ico tetracomb  
papadoe, pap || doe, K-4.81 pentagonal-antiprism atop dodecahedron  1.618034
papaid, pap || id, K-4.142 pentagonal-antiprism atop icosidodecahedron  3.077684
paphacki pentagon-prismatic heptacosicosachoron, great prismasaurus (also: great prismosaurus)  1
paphicki pentagram-prismatic heptacosicosachoron, small prismasaurus (also: small prismosaurus)  1
pappip, K-4.39 pentagonal-antiprism prism  1.074481
pappy pentagon-antiprismatical pyramid  1.618034
papvixhi pentagonal prismatoverted hexacosahecatonicosachoron  1.902113
paqraghi prismatoquasirhombated grand hecatonicosachoron  3.199386
paqri prismatoquasirhombated icositetrachoron  1.938391
paqrigafix (old: paquerfix) prismatoquasirhombated great facetted hexacosachoron  1.878261
paqrigagishi (old: paqrahi) prismatoquasirhombated great grand stellated hecatonicosachoron  1.207883
paqrit prismatoquasirhombated tesseract  1.174172
pataht prismatotruncated demitesseractic tetracomb, prismatodiprismatodisicositetrachoric tetracomb  
paticot prismatotruncated icositetrachoric tetracomb, small diprismatodisicositetrachoric tetracomb  
pautpen penta-augmentated truncated pentachoron ...
pecuf, K-4.154 pentagonal cupofastegium, decagon - pentagon-prismatic wedge, pentagonal orthobicupolaic ring, {10} || pip, {5} || pecu, 2/5-luna of stawros  5.236068
pecupe pentagonal-cupola prism, pentagonal-prism atop decagonal-prism  2.288246
pedip pentagon-pentagon duoprism  1.203002
pegycuro, J33 pentagonal gyrocupolarotunda  
pen, K-4.1 pentachoron, 4D simplex4), 5-cell, pyroter(id), tetrahedral pyramid, triangle-pyramidal pyramid, regular triangle-scalene, regular line-tettene, regular (point-)pennene, 3 tet rosette, vertex figure of hix  0.632456
peppyp, K-4.38 pentagon-pyramidal prism, J2 prism, line || pip  1.074481
pepuf, K-4.165 pentagonal pucofastegium, pentagon - decagon-prismatic wedge, pentagonal magnabicupolaic ring, {5} || dip, {10} || pecu, {5}-first cap of srahi  6.735034
perope, K-4.92 pentagonal-rotunda prism  1.693527
pesc (old: peppypy),
K-4.86
pentagon scalene, pentagon-pyramidal pyramid, line atop fully orthogonal pentagon, 5 tet rosette  1.618034
pex hex partially (mono-)expanded hex, partially contracted quawros  
pex thex partially (mono-)expanded thex ...
pexic partially (mono-)expanded icositetrachoron ...
pexrico partially (mono-)expanded rico  
pexrit partially (mono-)expanded rit  
pextah partially (mono-)expanded tesseractihexadecachoron  
pextico partially (mono-)expanded tico  
phiddip pentagon hexagon duoprism  1.312862
pibhaki rectified-hexacosachoron dual, pentagonal-bipyramidal heptacosiicosachoron, surtegmated hecatonicosachoron  
pibox srico partially bi-octa-expanded small rhombitetracontoctachoron  
pibox tico partially bi-octa-expanded truncated icositetrachoron  
picnut prismatocubiintercepted tesseract  0.890446
pinnip prismatointercepted pentachoron, vertex figure of han  0.774597
... pinnip+5 2thah (?)  0.774597
pinnipdip pentaintercepted prismatodispentachoron, prismatopentaintercepted dispentachoron  1.183216
... pinnipdip+15{4} (?)  1.183216
pinpith prismatointercepted prismatotesseractihexadecachoron  1.847759
... pinpith+48{4}  1.847759
pinpixhi prismatointercepted prismatohexacontahecatonicosachoron  6.735034
... pinpixhi+1800{4} (?)  6.735034
piphid prismatopentahemidecachoron  1
... piphid+10tet (?)  1
pippindip prismatopentintercepted dispentachoron  1.183216
pippy, K-4.141 pentagonal-prismatic pyramid, vertex pyramid of the rectified hexacosachoron  3.077684
pirgaghi prismatorhombated great grand hecatonicosachoron  1.893038
pirghi prismatorhombated great hecatonicosachoron  4.917351
pirhatit prismatorhombated demitesseractic tetracomb, great prismatodemitesseractic tetracomb, steriruncic tesseractic tetracomb  
pirpop pseudorhombated prismatopentachoron  1.183216
... pirpop+5 2thah (?)  1.183216
pirshi prismatorhombated (small) stellated hecatonicosachoron  5.515107
pistadedip pentagon - decagram duoprism  1.051462
pistodip pentagon - octagram duoprism  1.008216
pithatit prismatotruncated demitesseractic tetracomb, small prismatodemitesseractic tetracomb, stericantic tesseractic tetracomb  
pittip prismatotriakispentachoron  1.612452
poc gippic partially octa-contracted great prismatotetracontoctachoron  
poc prico   (alt.: phex spic) partially octa-contracted prismatorhombated icositetrachoron, partially hexadeca-expanded small prismated (dis)icositetrachoron ...
poccont partially octa-contracted tetracontoctachoron  
pocsric   (alt.: phixic) partially octa-contracted small rhombated icositetrachoron, partially hexadeca-expanded icositetrachoron, octa-augmented truncated tesseract ...
... pocuro wedge ...
podip pentagon - octagon duoprism  1.559075
potatit prismatotruncated tesseractic tetracomb, small tomocubic-diprismatotesseractic tetracomb, runcitruncated tesseractic tetracomb  
pox prico partially octa-expanded prismatorhombated icositetrachoron  
pox rico partially octa-expanded rectified icositetrachoron  
pox srico partially octa-expanded small rhombated icositetrachoron  
pox tico partially octa-expanded truncated icositetrachoron  
poxic   (alt.: phic srico,
alt.: owau sidpith)
partially octa-expanded icositetrachoron, partially hexadeca-contracted small rhombated icositetrachoron, octa-augmented small diprismated tesseractithexadecachoron ...
prahi prismatorhombated hecatonicosachoron, runcitruncated hexacosachoron  8.278950
prap vixhi pentagonal retroprismatoverted hexacosahecatonicosachoron  1.175571
prarsi prismatorhombiretrosnub icositetrachoron  1.328131
pretasto pentagonorhombic trisnub trisoctachoron  
prico prismatorhombated icositetrachoron, runcitruncated icositetrachoron  3.498949
pricot prismatorhombated icositetrachoric tetracomb, great diprismatodisicositetrachoric tetracomb  
prip prismatorhombated pentachoron, runcitruncated pentachoron  1.612452
prissi prismatorhombisnub icositetrachoron, prismato-semistruncated icositetrachoron, runcic snub icositetrachoron  2.497212
prit prismatorhombated tesseract, prismatotruncated hexadecachoron, runcitruncated hexadecachoron  2.370932
prittit prismatorhombated tesseractic tetracomb, rhombitesseractic-diprismatotesseractic tetracomb, runcicantellated tesseractic tetracomb  
prix prismatorhombated hexacosichoron, runcitruncated hecatonicosachoron  9.744610
proh prismatorhombated hexadecachoron, prismatotruncated tesseract, runcitruncated tesseract  2.613126
... (0,0,0,12,0)-diminished vertex-first-rotunda of ex, dodeca-diminished vertex-first rotunda of hexacosachoron  1.618034
pta cubaike cube-augmented cubaike  1
ptaika cube ike-augmented cubaike  
... q x3o3o, variation of tetrahedron prism, vertex figure of rectified penteract  0.935414
qragishi (old: qraghi) quasirhombated grand stellated hecatonicosachoron  1.662508
qrico quasirhombated icositetrachoron  1.082392
qriddip quasi-rhombicosidodecahedron prism  0.874032
qrigfix (old: querfix) quasirhombated great faceted hexacosachoron  1.027486
qrigogishi (old: qrahi) quasirhombated great grand stellated hecatonicosachoron  0.799575
qrit quasirhombated tesseract  0.765367
quad pagaxhi quasidisprismatogrand hexacosihecatonicosachoron  0.874032
quadippady quasidisprismatodishecatonicosachoron, Unholey Terror  1.414214
quawros quadratic ({8} || cube-)wedge rosette, bridge cyclotetraaugmented tesseract, ring-augmented tesseract, cube || {8} || cube, {4} || squobcu || {4}  
quercope quasirhombicuboctahedron prism  0.890446
quidex quatro-icositetradiminished hexacosachoron, dual of sadi  
quidpith (old: qippith) quasi(dis)prismatotesseractihexadecachoron  0.890446
quidpixhi quasidisprismatohexacosihecatonicosachoron  0.763932
quipdohi quasiprismatodishecatonicosachoron  1.328131
quiphi quasiprismatohecatonicosachoron  0.726543
quippic quasiprismatotetracontoctachoron  0.765367
quippirfix quasiprismatorhombated faceted hexacosachoron  3.531591
quippirgashi quasiprismatorhombated grand stellated hecatonicosachoron  1.348948
quippirgax quasiprismatorhombated grand hexacosachoron  1.021064
quippirghi quasiprismatorhombated grand hecatonicosachoron  2.400819
quiproh quasiprismatorhombated hexadecachoron  1.082392
quit gashi quasitruncated grand stellated hecatonicosachoron  0.953850
quit gishi quasitruncated great stellated hecatonicosachoron  0.953850
quit gissiddip quasitruncated-great-stellated-dodecahedron prism  0.826058
quit gogishi quasitruncated great grand stellated hecatonicosachoron  0.677481
quit sishi quasitruncated small stellated hecatonicosachoron  2
quit sissiddip quasitruncated-small-stellated-dodecahedron prism, small-stellated-truncated-dodecahedron prism  0.988665
quitcope quasitruncated-cuboctahedron prism  1.174172
quitdiddip quasitruncated-dodecadodecahedron prism  1.732051
quithip quasitruncated-hexahedron prism  0.765367
quitit quasitruncated tesseract  0.615370
radatathi retroditetrahedronary dishecatonicosachoron  1.414214
radiddip (old: radedip) rhombidodecadodecahedron prism  1.414214
rafficdi retrofrustic tetracontoctadisicositetrachoron  1.414214
raffixthi retrofrustic hexacositrishecatonicosachoron  2.236068
ragaghi rectified great grand hecatonicosachoron  1.070466
ragashi rectified grand stellated hecatonicosachoron  1.175571
raggix rectified grand hexacosachoron  0.726543
raghi rectified grand hecatonicosachoron  1.902113
ragishi rectified great stellated hecatonicosachoron  1.175571
rahi rectified hecatonicosachoron  4.534568
rap (old: rip,
alt.: tetaoct), tet || oct,
K-4.5
rectified pentachoron, tetrahedral cupola, vertex figure of hin, tetrahedron atop octahedron  0.774597
rappisdi retroantiprismatosnub disicositetrachoron  1
... rappisdi+mesdi+288{4} (?)  1
rapsady retroantiprismatosnub dishecatonicosachoron ...
rasdi retrosnub icositetrachoron, retrosnub disicositetrachoron  0.618034
rasishi rectified small stellated hecatonicosachoron  2.802517
ratho rectified tesseractihemioctachoron  1
rathotathibit rhombitrihexagonal-omnitruncated-trihexagonal duoprismatic tetracomb  
rawvathi retrosphenoverted triakishecatonicosachoron  2.689994
rawvatoth retrosphenoverted tesseractitesseractihexadacachoron  1.847759
rawvaty retrosphenoverted triakisicositetrachoron  2.613126
rawvhiddix retrosphenoverted hecatonicosadishexacosachoron  1.258409
rawvhitto retrosphenoverted hexadecatesseractioctachoron  1.732051
rawvid tixady retrosphenoverted ditrigonary hexacosadishecatonicosachoron  5.330704
rawvtip retrosphenoverted triakispentachoron  1.183216
rico rectified icosatetrachoron, cantellated hexadecachoron, hexadecachoron-derived Gévay polychoron  1.732051
... rico-cap augmented thex-rotunda ...
ricot rectified icositetrachoric tetracomb  
ridatathi retroinverted ditetrahedral triakishecatonicosachoron  1.414214
ridimex (alt.: idimrox) rectified icosidiminished hexacosachoron, icosidiminished rectified hexacosachoron  3.077684
ridtidohi rectified ditrigonal dishecatonicosachoron  1.732051
rigfix rectified great faceted hexacosichoron  0.726543
riggidtixhi rectified great ditrigonal hexacosihecatonicosachoron  1.732051
righi rectified great hecatonicosachoron  1.902113
rigogishi rectified great grand stellated hecatonicosachoron  0.661585
ripahi retroinverted prismatohecatonicosachoron  4.534568
... ripahi+600 2thah (?)  4.534568
ripdip rhombiprismato dispentachoron  1.612452
risadi (alt.: idrox) rectified snub icositetrachoron, icositetradiminished rectified hexacosachoron  3.077684
rissidtixhi rectified small ditrigonal hexacosihecatonicosachoron  1.732051
rit rectified tesseract, rectified octachoron, birectified hexadecachoron, runcic tesseract  1.224745
rithsithbit rhombitrihexagonal-simotrihexagonal duoprismatic tetracomb  
rittit rectified tesseractic tetracomb, quartertesseractic tetracomb  
rixhi retroinverted hexacosahecatonicosachoron  3.077684
rofix rectified faceted hexacosichoron  3.077684
... vertex-first rotunda of hexacosachoron  1.618034
rox rectified hexacosachoron  3.077684
... rox+720pip (?)  3.077684
... β3o3o4β (?) ...
... β3o3o5β (?) ...
... β3o3β3o (?) ...
... β3o3β4β (?) ...
... β3o3β4x (?) ...
... β3o3β5o (?) ...
... β3o3β5β (?) ...
... β3o3β5x (?) ...
... β3o4o3β (?) ...
... β3o4β3o (?) ...
... β3β3o3β (?) ...
... β3β3o4β (?) ...
... β3β3o5β (?) ...
... β3β3β3o (?) ...
... β3β3β3x (?) ...
... s3s3s4x (?) ...
... β3β3β5o (?) ...
... β3β3β5x (?) ...
... β3β3x *b3o (?) ...
... β3β3x3β (?) ...
... β3β3x4β (?) ...
... β3β3x5β (?) ...
... alternated truncated hyperbolic order 4 icositetrachoral tetracomb  
... β3β4o3β (?) ...
... β3β4β3o (?) ...
... β3β4β3x (?) ...
... β3β4x3β (?) ...
... β3x3o4β (?) ...
... β3x3o5β (?) ...
... β3x3β3o (?) ...
... β3x3β3x (?) ...
... β3x3β4β (?) ...
... β3x3β4x (?) ...
... β3x3β5o (?) ...
... β3x3β5β (?) ...
... β3x3β5x (?) ...
... β3x3x3β (?) ...
... β3x3x4β (?) ...
... β3x3x5β (?) ...
... β3x4β3o (?) ...
... β3x4β3x (?) ...
... β3x4x3β (?) ...
... octahedra-alternated faceting of scartit  
... s4x2s4x (?) ...
sabbadipady small blendic disprismatodishecatonicosachoron  2
... sabbadipady+sanbathi (?), ganbathi+quitsishi (?)  2
sabbathi small blendic trishecatonicosachoron  2
sabippady (old: sabbippady) small blendic prismatodishecatonicosachoron  2
saddiddip small-dodekicosidodecahedron prism  2.288246
sadi   (alt.: idex) snub icositetrachoron, snub disicositetrachoron, semistruncated icositetrachoron, icositetradiminished hexacosachoron  1.618034
sadit snub icositetrachoric tetracomb, Gosset's non-Wythoffian tetracomb  
sadixady small dishexacosadishecatonicosachoron  1.773668
sadixhix (old: sixhix) small dodecahedronary hexacosahemihexacosachoron, compound of 25 ihi (but not gadixhix)  1
sadsadox small disnub dihexacosachoron  3.077684
sadtap small ditetrahedronary prismatochoron, compound of 36 dadip  2.288246
sadtef pixady small ditetrahedronary exofissary prismatohexacosadishecatonicosachoron  2.288246
sadtifady small ditetrahedronarofissary dishecatonicosachoron  2.288246
sanbathi small spinoblendic trishecatonicosachoron  2
sanbippady small spinoblendic prismatodishecatonicosachoron  2
sand tathi small intercepted ditetrahedronary trishecatonicosachoron  2.288246
saquid paxhi small quasidisprismatohexacosihecatonicosachoron, Holey Terror  2.288246
scaricot small cellirhombated icositetrachoric tetracomb, great disicositetrachoric tetracomb  
scartit small cellirhombated tesseractic tetracomb, small rhombitesseractic-prismatotesseractic tetracomb, stericantellated tesseractic tetracomb  
scicot small cellated demitesseractic tetracomb, stericated icositetrachoric tetracomb  
scyropot small cyclorhombated pentachoric tetrachomb, small prismatodispentachoric tetracomb, cantellated pentachoric tetrachomb  
sedit pathi small exoditetrahedronary prismatotriakishecatonicosachoron  2.288246
seedatepthi small exoditetrahedrary prismatotrishecatonicosachoron  1.414214
sefdit dixdy small exofissary ditrigonal dihexacosadihecatonicosachoron  1.732051
sefidtethi small exofissary ditetrahedronary tetrakishecatonicosachoron  2.288246
sefradit thix small exofissary retroditetrahedronary triakishecatonicosihexacosachoron  2.288246
sesidip small-snub-icosicosidodecahedron prism  1.541531
sgysrahi swirl-gyrated small rhombated hecatonicosachoron, swirl-gyrated cantellated hecatonicosachoron  6.735034
shafipto small hexadecafaceted prismatotesseractioctachoron  1.485633
... shafipto+32tet (?)  1.485633
shahoh small hexadecahemihexadecachoron  1
shiddip, K-4.54 square - hexagon duoprism  1.224745
shihi small hecatonicosihecatonicosachoron  5.854102
shihix small hecatonicosihecatonicosihexacosachoron  2.975584
shinhi small hecatonicosintercepted hecatonicosachoron  4.534568
shipady small hecatonicosiprismatodishecatonicosachoron  1.814331
sibricot small birhombated icositetrachoric tetracomb, grand prismatodisicositetrachoric tetracomb  
sichado small cubihexadecadisoctachoron  2.370932
sid thipady small ditrigonal hecatonicosiprismatodishecatonicosachoron  1.814331
sid tipathi small ditrigonal prismatotriakishecatonicosachoron  4.179968
siddapady small disprismatodishecatonicosachoron  2
siddatady small ditetrahedral dishecatonicosachoron  2.288246
siddic small distetracontoctachoron  1.847759
siddid (old: siided) snub dodecadodecahedron, chaugnar faugn  
siddiddip snub-dodecadodecahedron prism  
siddit paxhi small ditetrahedronary hexacosidishecatonicosachoron  2.288246
siddit thix small ditrigonal trishecatonicosihexacosachoron  1.732051
sidditdiddip small-ditrigonal-dodekicosidodecahedron prism  1.792631
sidditpix small ditrigonary prismatohexacosichoron  1.732051
sidhiquit paddy small dishecatonicosaquasitruncated prismatodishecatonicosachoron  5.605034
sididdip snub-icosidodecadodecahedron prism  
sidipthi small dipental trishecatonicosachoron  2.497212
sidpith small disprismatotesseractihexadecachoron, runcinated tesseract, small prismated tesseract  1.485633
sidpitit small prismatotesseractic tetracomb, small diprismatotesseractic tetracomb, runcinated tesseractic tetracomb  
sidpixathi small dipentagonal hexacositrihecatonicosachoron  2.497212
sidpixhi small disprismatohexacosihecatonicosachoron, runcinated hecatonicosachoron, runcinated hexacosachoron  5.236068
sidrebcu stellidodecahedral rectibicupola, orbiform bistratc stack of small stellated dodecahedron atop pseudo dodecadodecahedron atop great dodecahedron  1.064815
sidsrahi swirl-diminished small rhombated hecatonicosachoron, swirl-diminished cantellated hecatonicosachoron  6.735034
sidtaxady small ditetrahedronary hexacosidishecatonicosachoron  2.288246
sidtaxhi small ditetrahedronary hexacosihecatonicosachoron  2.288246
sidthidy hi small ditrigonal hecatonicosadishecatonicosihecatonicosachoron  1.732051
sidthixhi small ditrigonal hecatonicosihexacosihecatonicosachoron  1.773668
sidtidap small-ditrigonal-icosidodecahedron antiprism  0.955838
sidtiddip small-ditrigonal-icosidodecahedron prism  1
sidtixhi small ditrigonary hexacosihecatonicosachoron  1
... sidtixhi+dox (?)  1
sifdahihox small fissary dodecahedronary hecatonicosihemihexacosachoron  1
siidcup small icosicosidodecahedral cupoliprism, closer siid atop siid  1.765796
siidip small-icosicosidodecahedron prism  1.792631
sik vipathi small skewverted prismatotriakishecatonicosachoron  2.828427
sik vixathi small skewverted hexacositriakishecatonicosachoro  4.684471
siphado small prismatohexadecadisoctachoron  2.613126
siphatit small diprismatodemitesseractic tetracomb, steric tesseractic tetracomb  
siphidy small prismated hecatonicosadishecatonicosachoron  4.917351
sipthi small prismatotriakishecatonicosachoron  1.878261
sipti small prismatotriakisicositetrachoron  3.498949
sirc small retrotetracontoctachoron  1.847759
sirco aticu expanded axially-octahedral ursachoron, (sirco,tic)-based ursulate  1.806144
sircoa gircotum bistratic cap of prismatorhombated tesseract, rhombicuboctahedral rotunda, (sirco,girco)-based tutschoron, (sirco,girco)-based tutism  2.370932
sircoagirco, sirco || girco (degenerate) small rhombicuboctahedron atop great rhombicuboctahedron ∞   i.e. flat in euclidean space
sircoatic, sirco || tic, K-4.100 small rhombicuboctahedron atop truncated cube, small-rhombicuboctahedral cap of small rhombated tesseract  1.847759
sircoatoe, sirco || toe, K-4.75 small rhombicuboctahedron atop truncated octahedron  1.582890
sircope, K-4.66 small-rhombicuboctahedron prism, medial (cube-first) subsegment of sidpith  1.485633
sirdatady small retroditetrahedral dishecatonicosachoron  2.288246
... sirdatady+1440{5/2}  2.288246
sirdop small rhombidispentachoron  1.183216
sirdtapady small retroditetrahedronary prismatodishecatonicosachoron  2.288246
... sirdtapady+600 2tet (?)  2.288246
sirdtaxady small retroditetrahedronary hexacosidishecatonicosachoron  2.288246
sirfix small rhombated faceted hexacosachoron  4.352502
sirfixthi small retrofrustic hexacositrishecatonicosachoron  2.236068
sirgaghi small rhombated great grand hecatonicosachoron  1.513868
sirgashi small rhombated grand stellated hecatonicosachoron  1.589926
sirgax small rhombated grand hexacosachoron  1.054256
sirghi small rhombated great hecatonicosachoron  3.387054
sirpdo small rhombiprismatodisoctachoron  2.370932
sirpith small rhombiprismated tesseractihexadecachoron  2.613126
sirsashi small rhombated small stellated hecatonicosachoron  3.963358
sirsiddip small-(inverted)-retrosnub-icosicosidodecahedron prism  0.766294
sisdipthi small stellated dipental trishecatonicosachoron  2.497212
sishi small stellated hecatonicosachoron  1
... sishi+gaghi+120did (?)  1
... sishi+gaghi+idhi (?)  1
... sishi+gridixhi (?)  1
... sishi+idhi (?)  1
... sishi+ofiddady (?)  1
... sishi+paphicki+gridaphi (?)  1
sisp small swirlprism  1.618034
sissidadid, sissid || did small stellated dodecahedron atop dodecadodecahedron, small-stellated-dodecahedral cupola  1.064815
sissidagad, sissid || gad small stellated decahedron atop great dodecahedron, sissid antiprism, gad antiprism  1
sissidaraded, sissid || raded small stellated dodecahedron atop rhombidodecadodecahedron, sissid-first cap of padohi  2.497212
sissiddip small-stellated-dodecahedron prism  0.771681
sissidpy small-stellated-dodecahedral pyramid, vertex cap of gofix  0.618034
sistodip square - octagram duoprism  0.890446
sistople (old: stodop) square-octagram plus-prism, octagram diorthoprism, compound of 2 sistodip  1.485633
sit thixady small tritrigonal hecatonicosihexacosidishecatonicosachoron  3.835128
sitphi small tripesic hecatonicosachoron  2.288246
sitpodady small (intersected) tripesic dodecahedronary dishecatonicosachoron  1
sitwadip square - dodecagon duoprism  2.057195
six fipady small hexacosafaceted prismatodishecatonicosachoron  5.236068
sixathi small hexacositriakishecatonicosachoron  2.351141
... six fipady+1200tet (?)  5.236068
sixhidy small hexacosihecatonicosadishecatonicosachoron  2.975584
sixhihy small hexacosihecatonicosihecatonicosachoron  0.763932
sixipady small hexacosiprismatodishecatonicosachoron  6.881910
skiv datapixady small skewverted ditrigonary prismatohexacosadishecatonicosachoron  4.684471
skiviphado small skewverted prismatohexadecadisoctachoron  1.414214
snahi s3s3s5s, snub hecatonicosachoron, non-uniform alternation of gidpixhi ...
snappoth small spinoprismatotesseractihexadecachoron  1.485633
snet s3s3s4s, snub tesseract, non-uniform alternation of gidpith ...
sniccup, K-4.60 snub-cube prism, snub-cuboctahedron prism  1.433724
snico s3s4s3s, (full) snubbed icositetrachoron (but not sadi), non-uniform alternation of gippic ...
sniddip, K-4.110 snub-dodecahedron prism, snub-icosidodecahedron prism  2.213060
snip s3s3s3s, snub pentachoron, non-uniform alternation of gippid ...
soccope small-cubicuboctahedron prism  1.485633
sodip, K-4.70 square - octagon duoprism  1.485633
sophi small prismatohecatonicosachoron  3.077684
sople (old: odop) square-octagon plus-prism, octagonal diorthoprism, compound of 2 sodip  1.485633
spaht small prismated demitesseractic tetracomb, small disicositetrachoric tetracomb  
spapivady small pentagrammal antiprismatoverted dishecatonicosachoron  1.175571
... hexaconta-sphenated id-first deep parabidiminished rahi ...
sphiddix small prismatohecatonicosadishexacosachoron  6.881910
sphihix small prismatohecatonicosahecatonicosahexacosachoron  5.515107
sphixhi small prismatohecatonicosihexacosihecatonicosachoron  4.179968
spic small prismatotetracontoctachoron, runcinated icositetrachoron  1.847759
spict small prismated icositetrachoric tetracomb, small prismatotetracontaoctachoric tetracomb  
spid small prismatodecachoron, runcinated pentachoron, expanded pentachoron, tetaco gyrobicupola, vertex figure of cypit  1
spidrox swirlprismatodiminished rectified hexacosachoron  3.077684
spidy swirlprismattic dishecatonicosachoron, compound of 24 starpedip  1
spixady small prismatohexacosadishecatonicosachoron  8.278950
spixhihy small prismatohexacosihecatonicosihecatonicosachoron  9.744610
... q-laced {3} || gyro trip, vertex figure of srix  0.907485
sporaggix swirlprismatoreplenished rectified grand hexacosachoron  0.726543
sprapivady small pentagonal retroprismatoverted dishecatonicosachoron  3.077684
spriphi small pseudorhombated prismatohecatonicosachoron  6.735034
... spriphi+600 2thah (?)  6.735034
spript small pseudorhombated prismatotesseract  1.847759
... spript+16 2thah (?)  1.847759
spysp small pyramidic swirlprism  1.618034
squacufbil square-cupofastegia biluna, rotunda of quawros, square atop squobcu  
squacupe, K-4.69 square-cupola prism, cube atop octagonal prism  1.485633
squadedip, K-4.97 square - decagon duoprism  1.765796
squaf, K-4.14 square antifastegium, square - squap wedge, {4} || gyro cube, bidiminished octahedral antiprism  0.879465
squappip, K-4.19 square-antiprism prism  0.962692
squappy square-antiprismatical pyramid  0.879465
squapt (line-)square-antiprismatic tegum, square-antiprismatic bipyramid, square-pyramidal antiprism  
squasc (old: squippypy),
4pyr-pyr, K-4.4
square-scalene, square-pyramidal pyramid, line atop fully orthogonal square, 1/4-luna of hex, 4 tet rosette  0.707107
... squashed hexaconta-sphenated id-first deep parabidiminished rahi ...
squicuf, K-4.73 square cupofastegium,
octagon - cube wedge of sidpith, square orthobicupolaic ring, {8} || cube, {4} || squacu, 1/4-luna of quawros
 1.485634
squipdip, K-4.42 square-pentagon duoprism  1.106168
squippia squacu, K-4.109 square pyramid atop square cupola  1.847759
squippiaco, K-4.31 square-pyramid atop cuboctahedron  1
squippiatricu, K-4.32 square-pyramid atop triangular-cupola  1
squippyp, K-4.12 square-pyramidal prism, J1 prism, line || cube, digonal magnabicupolaic ring  0.866025
squipuf, K-4.105 square pucofastegium, square - octagon-prismatic wedge, square magnabicupolaic ring, {4} || op, {8} || squacu, square-cap of srit  1.847759
sradditdahix small retroditetrahedronary dishecatonicosihexacosachoron  2.288246
sraghi small rhombated grand hecatonicosachoron  2.689994
srahi small rhombated hecatonicosachoron, cantellated hecatonicosachoron  6.735034
srawv ditathi small retrosphenoverted ditrigonary triakishecatonicosachoron  3.294556
srawv hidy small retrosphenoverted hecatonicosadishecatonicosachoron  3.387054
srawv hixhi small retrosphenoverted hecatonicosihexacosihecatonicosachoron  6.073594
srawvathi small retrosphenoverted triakishecatonicosachoron  4.352502
srawvixady small retrosphenoverted hexacosadishecatonicosachoron  6.735034
srico small rhombated icositetrachoron, cantellated icositetrachoron  2.613126
sricot small rhombated demitesseractic tetracomb, small prismatodisicositetrachoric tetracomb  
..., xFoFx3ooooo5xofox&#xt  
(F=ff=x+f)
bilunabirotundic rhombicosidodecahedron prism, castellated rhombicosidodecahedral prism  
srida gridtum bistratic srid-cap of prahi, (srid,grid)-based tutsachoron, (srid,grid)-based tutism  8.278950
sridaphi small retroinverted dodecahedronary prismatohecatonicosachoron  1
sridati, srid || ti, K-4.126 small-rhombicosidodecahedron atop truncated-icosahedron  2.485450
sridatid, K-4.159 small rhombicosidodecahedron atop truncated dodecahedron, small-rhombicosidodecahedral cap of small rhombated hecatonicosachoron  6.735034
sridatidu expanded axially-icosahedral ursachoron, (srid,tid)-based ursulate  3.077684
sriddip, K-4.111 small-rhombicosidodecahedron prism  2.288246
sridixhi small retroinverted dodecahedronary hexacosahecatonicosachoron  1
srip small rhombated pentachoron, cantellated pentachoron  1.183216
sriphi small retropental hecatonicosachoron  3.077684
srit small rhombated tesseract, cantellated tesseract  1.847759
srittit small rhombitesseractic tetracomb, cantellated tesseractic tetracomb  
srix small rhombated hexacosachoron, cantellated hexacosachoron  6.073594
stadidip decagram-decagram duoprism  0.874032
stappyp pentagram-pyramidal prism, line || stip  0.771681
stardedip pentagram - decagon duoprism  1.701302
stardip pentagram-pentagram duoprism  0.743496
starodip pentagram - octagon duoprism  1.408368
starpedip (older: stipdip,
oldest: starpendip)
pentagram-pentagon duoprism, stellar (pentagonal) pentagonal diprism  1
stasc (old: stappypy) stellar scalene, pentagram-scalene, pentagram-pyramidal pyramid, line atop fully orthogonal pentagram, 5 tet two-step rosette  0.618034
stastidedip pentagram - decagram duoprism  0.811393
stastodip pentagram - octagram duoprism  0.754511
stawros pentagrammic ({10} || pip-)wedge rosette, bridge cyclopentaaugmented starpedip, ring-augmented starpedip  
sted stellated decachoron, compound of 2 pen  0.632456
stefacoth small tesseractifaceted cubitesseractihexadecachoron  1.485633
steth small tesseractitesseractihexadecachoron  1.485633
stico stellated icositetrachoron, stella tegmata, compound of 3 hex  0.707107
stippy stellated-pentagonal prismatic pyramid, vertex pyramid of the rectified grand hexacosachoron  0.726543
sto small trisoctachoron, small triakisoctachoron  1.224745
... sto+16tet (?)  1.224745
stoc stellated tetracontoctachoron, compound of 2 ico  1
stodatixhi small toroidoditrigonary hexacosihecatonicosachoron  1.732051
stodip octagram-octagram duoprism  0.765367
stoditpix small toroidoditrigonary prismatohexacosichoron  1.732051
stut dixady small tritrigonal dihexacosidihecatonicosachoron  3.835128
stut phiddix small tritrigonal prismatohecatonicosidishexacosachoron  3.835128
stut pixady small tritrigonal prismatohexacosidihecatonicosachoron  3.835128
stut thix small tritrigonal trishecatonicosihexacosachoron  3.835128
stut xethi small tritrigonal hexacositrishecatonicosachoron  3.835128
suti small tetrakisicositetrachoron  1.608038
swav ditathi small sphenoverted ditrigonary triakishecatonicosachoron  2.572554
swavathi small sphenoverted triakishecatonicosachoron  2.093315
swavixady small sphenoverted hexacosadishecatonicosachoron  3.294556
tabene rectified-icositetrachoron dual, trigonal-bipyramidal enneacontahexachoron, surtegmated icositetrachoron  
taggix truncated grand hexacosachoron  1.199039
taghi truncated grand hecatonicosachoron  3.477092
tah tesseractihexadecachoron, bitruncated tesseract, bitruncated hexadecachoron, runcicantic tesseract  2.121320
tahi triakishecatonicosachoron  2
tat truncated tesseract  2.149726
tattit truncated tesseractic tetracomb  
tau ope tetra-augmented ope  
tau tope tetra-augmented tope  
tautipip triaugmented-triangular-prism prism  
tautisdip triaugmented 3,4-duoprism ...
teddi adoe, teddi || doe, K-4.83 tridiminished-icosahedron atop dodecahedron  1.618034
teddi aid, teddi || id, K-4.147 tridiminished icosahedron atop icosidodecahedron  3.077684
teddipe tridiminished-icosahedron prism  1.074481
teddipy, K-4.88 tridiminished-icosahedral pyramid  1.618034
tehipau tuttip hip-wise tetra-augmented tuttip  
telex vertex first tele-elongated hexacosachoron  
tepe, K-4.9
(alt: dycuf)
tetrahedron prism, line || trip, square - square bi-wedge, digonal orthobicupolaic ring, vertex figure of rix, dyadic cupolafastegium  0.790569
teppix (old: dattix) tripesic hexacosachoron, compound of 60 deca  1.414214
tes (alt.: squadip),
K-4.20
tesseract, octachoron, "hypercube", 4D measure-polytope4), 8-cell, geoter(id), square duoprism, vertex figure of icot  1
test tesseractic tetracomb, 4D hypercubical honeycomb4), Voronoi complex of C4 lattice, Delone complex of C4 lattice  
tetaco altut tetrahedron atop cuboctahedron atop inverted truncated tetrahedron ...
tetaco, tet || co, K-4.23 tetrahedron atop cuboctahedron, tetrahedral rotunda of small prismatodecachoron  1
tetacoaoct octahedron atop (pseudo) cuboctahedron atop tetrahedron  1
tetaltut, tet || inv. tut (degenerate) tetrahedron atop inverted truncated tetrahedron, (degenerate) tetrahedron atop alternate truncated tetrahedron ∞   i.e. flat in euclidean space
tetatricu, tet || tricu, K-4.24 tetrahedron atop trigonal cupola, 0.290215-luna of small prismatodecachoron  1
tetatut, K-4.56 tetrahedron atop truncated tetrahedron, tetrahedral cap of rectified tesseract  1.224745
tete (old: tedpy) (line-)tetrahedron-tegum, tetrahedral bipyramid  
tetripau tuttip trip-wise tetra-augmented tuttip  
tetu axially-tetrahedral ursachoron ofx3xoo3ooo&#xt, tet-based ursulate, vertex figure of sadit  1
tewau thawrorh tetra-augmented thawro rhombochoron ...
tex truncated hexacosachoron  4.643523
thahp tetrahemihexahedral prism, vertex figure of rhohid  0.866025
thaquitoth tesseractihexadecaquasitruncated tesseractihexadecachoron  1.338990
thaquitpath tesseractihexadecaquasitruncated prismatotesseractihexadecachoron  2.326846
thatoth tesseractihexadecatruncated tesseractihexadecachoron  1.790840
thatpath tesseractihexadecatruncated prismatotesseractihexadecachoron  1.608038
... thawro pyrite, octa-diminishing of id - srid - F-ike - ti tower ...
thawrorh thawro rhombochoron ...
... thawro-wedged 1/6-luna of hexacosachoron ...
... thawro-wedged 2/6-luna of hexacosachoron ...
... thawro wedge ...
thex truncated hexadecachoron, cantic tesseract  1.581139
thext truncated hexadecachoric tetracomb, truncated demitesseractic tetracomb, cantic tesseractic tetracomb  
thi truncated hecatonicosachoron  8.218334
thiddip, K-4.47 triangle - hexagon duoprism, hexagon - hip wedge  1.154701
tho tesseractihemioctachoron, octahemioctachoron, vertex figure of hehad  0.707107
thoot thibbit tomohexagonal-omnitruncated-trihexagonal duoprismatic tetracomb  
thorahbit tomohexagonal-rhombitrihexagonal duoprismatic tetracomb  
thot thibbit trihexagonal-omnitruncated-trihexagonal duoprismatic tetracomb  
thrathibbit trihexagonal-rhombitrihexagonal duoprismatic tetracomb  
tiatid, ti || tid, K-4.151 truncated icosahedron atop truncated dodecahedron  3.835128
tibbic rectified-hecatonicosachoron dual, triangular-bipyramidal chilliadiacosichoron, surtegmated hexacosachoron  
tibbid (alt.: durap) rectified-pentachoron dual, triangular-bipyramidal decachoron, surtegmated pentachoron  
... expanded augmented axially-octahedral ursachoron ofx3xoo4xxx&#xt  
tica gircobcu ticagirco bicupola  
ticagirco, K-4.128 truncated cube atop great rhombicuboctahedron, truncated-cubical cap of prismatorhombated hexadecachoron, cuboctahedral supra-cap of small rhombated icositetrachoron  2.613126
ticcup, K-4.99 truncated-cube prism  1.847759
tico truncated icositetrachoron, cantitruncated hexadecachoron  2.645751
ticot truncated icositetrachoric tetracomb  
... expanded augmented axially-icosahedral ursachoron ofxo3xooo5xxxx&#xt  
... triaconta-sphenated id-first tristratic sub-cap of rahi ...
tidagrid, tid || grid, K-4.173 truncated dodecahedron atop great rhombicosidodecahedron, truncated-dodecahedral cap of prismatorhombated hexacosichoron  9.744610
tiddip, K-4.130 truncated-dodecahedron prism  3.011250
tidimex (alt.: idimtex) truncated icosidiminished hexacosachoron, icosidiminished truncated hexacosachoron  4.643523
tidox (old: togex) truncated dodecahedronary-hexacosachoron (truncated great hexacosachoron), compound of 25 tico  2.645751
tidtidohi truncated ditrigonal dishecatonicosachoron  2.645751
tiffix truncated faceted hexacosichoron  4.643523
tigaghi truncated great grand hecatonicosachoron  2
tigfix truncated great faceted hexacosichoron  1.199039
tiggidtixhi truncated great ditrigonal hexacosihecatonicosachoron  2.645751
tiggipe truncated-great-icosahedron prism  1.165943
tighi truncated great hecatonicosachoron  3.477092
tigiddip truncated-great-dodecahedron prism  1.942303
tip (alt: tettum) truncated pentachoron, tet-based tutsatope, tet-based tutism  1.264911
tipe, K-4.127 truncated-icosahedron prism  2.527959
tisadi (alt.: idtex) truncated snub icositetrachoron, icositetradiminished truncated hexacosachoron  4.643523
tiscsrix tristratic icosidodecahedron-first cap of small rhombihexacosachoron  6.073594
tisdip, K-4.18 triangle - square duoprism, square - cube wedge, vertex figure of nit  0.912871
tissidtixhi truncated small ditrigonal hexacosihecatonicosachoron  2.645751
tisthit triangular-simotrihexagonal tetracomb  
tistodip triangle - octagram duoprism, octagram - stop wedge  0.791345
titho truncated tesseractihemioctachoron  1.581139
titwadip triangle - dodecagon duoprism, dodecagon - twip wedge  2.016280
toagirco, toe || girco, K-4.149 truncated octahedron atop great rhombicuboctahedron, truncated octahedral cap of prismatorhombated icositetrachoron  3.498949
toagircoatic toe atop girco atop tic  
toatic, toe || tic, K-4.98 truncated octahedron atop truncated cube  1.785406
tobcuatut, tobcu || tut, K-4.49 triangular-orthobicupola atop truncated-tetrahedron  1.183216
todip, K-4.59 triangle - octagon duoprism, octagon - op wedge  1.428440
todithix toroidoditrigonary hecatonicosihexacosichoron  1.732051
todtixhi toroidal ditrigonal hexacosihecatonicosachoron  1.732051
... vertex figure of topax  0.907485
tope, K-4.89 truncated-octahedron prism  1.658312
tosot thibbit tomosquare-omnitruncated-trihexagonal duoprismatic tetracomb  
tracufbil triangular-cupofastegia biluna, {3} || tricu || {3}, 0.419569-luna of gyspid  1
tradedip, K-4.94 triangle - decagon duoprism, decagon - dip wedge  1.717954
traf, K-4.6 triangular antifastegium, triangle oct wedge, {3} || gyro trip, {3} || oct, (vertex-) diminished rap  0.774597
trapedip, K-4.34 triangle - pentagon duoprism, pentagon - pip wedge  1.028076
tribbit triangular duoprismatic tetracomb  
tricuatut, tricu || tut, K-4.50 triangular-cupola atop truncated-tetrahedron  1.183216
tricuf trigonal cupofastegium, hexagon - triangle-prismatic wedge, triangle orthobicupolaic ring, {6} || trip, {3} || tricu, 0.209785-luna of small prismatodecachoron  1
tricupe, K-4.45 triangular-cupola prism, triangular prism atop hexagonal prism  1.118034
triddip, K-4.10 triangle-triangle duoprism, triangle - trip wedge, vertex figure of dot, Delone cell of lattice A2×A2  0.816497
..., trip || gybef triangular prism || gyrobifastegium ...
trippy, K-4.7 trigonal-prismatic pyramid, vertex pyramid of the rectified pentachoron  0.774597
tript trigonal-prismatic (line-)tegum, trigonal-prismatic dipyramid ...
tripuf, K-4.51 trigonal pucofastegium, triangle - hexagon-prismatic wedge, trigonal magnabicupolaic ring, {3} || hip, {6} || tricu  1.183216
tritep (alt: dycufbil) (line-)triangle-tegum prism, triangular-bipyramidal prism, dyadic cupofastegia biluna  
turap two rectified-pentachoron cupolaic blend  0.774597
... expanded augmented axially-tetrahedral ursachoron ofxo3xooo3xxxx&#xt  
tutatobcu tutatoe orthobicupola  
tutatoe gybcu tutatoe gyrobicupola  
tutatoe, tut || toe, K-4.76 truncated tetrahedron atop truncated octahedron, truncated-tetrahedral cap of prismatorhombated pentachoron  1.612452
tutcup (alt.: pabdirit,
tutaltut), tut || inv tut,
K-4.55
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
tuttip, K-4.57 truncated-tetrahedron prism  1.274755
twaddip dodecagonal-dodecagonal duoprism  2.732051
twagy griddip twelve-gyro-augmented great-rhombated-icosidodecahedral prism  
twagy tiddip twelve-gyro-augmented truncated-icosidodecahedral prism  
twau doaid deep mono-diminished rotunda of ex, 12-augmented doe || id  1.618034
twau griddip twelve-(ortho-)augmented great-rhombated-icosidodecahedral prism  
twau iddip twelve-augmented icosidodecahedral-prism  
twau sridati twelve-augmented sridati  
twau sriddip twelve-augmented sriddip  
twau tiddip twelve-(ortho-)augmented truncated-icosidodecahedral prism  
twau tipe twelve-augmented truncated-icosahedral prism  
wavathi sphenoverted triakishecatonicosachoron  1.662508
wavaty sphenoverted triakisicositetrachoron  1.082392
wavdatixady sphenoverted ditrigonal hexacosadishecatonicosachoron  1.258409
wavhiddix sphenoverted hecatonicosadishexacosachoron  5.330704
wavitoth sphenoverted tesseractitesseractihexadecachoron  0.765367
... wx ox3xx4oo&#zx  
... wx ox3xx4xx&#zx  
... hyperbolic order 5 pentachoric tetracomb  0.393076 i
... hyperbolic pentagrammic-order hexacontachoric tetracomb  0.393076 i
... x3o3o5v, variation of small disprismatohexacosihecatonicosachoron  3.835128
... x3o3β4o (?) ...
... x3o3β4x (?) ...
... x3o3β5o (?) ...
... x3o3β5x (?) ...
... hyperbolic order 4 icositetrachoral tetracomb  0 i
... x3o4q3o, variation of small rhombated icositetrachoron  3.316625
... x3o4β3o (?) ...
... hyperbolic order 5 faceted-hexacosichoral tetracomb, hyperbolic order 5 icosahedral-hecatonicosachoral tetracomb  0.393076 i
... x3β3o3o (?) ...
... x3β3o3β (?) ...
... x3β3o3x (?) ...
... x3β3o4o (?) ...
... x3β3o4β (?) ...
... x3β3o4x (?) ...
... x3β3o5o (?) ...
... x3β3o5β (?) ...
... x3β3o5x (?) ...
... x3β3β3x (?) ...
... x3β3β4o (?) ...
... x3β3β4β (?) ...
... x3β3β4x (?) ...
... x3β3β5o (?) ...
... x3β3β5β (?) ...
... x3β3β5x (?) ...
... x3β3x4β (?) ...
... x3β3x5β (?) ...
... x3β4o3o (?) ...
... x3β4o3β (?) ...
... x3β4o3x (?) ...
... x3β4β3x (?) ...
... x3x3β3o (?) ...
... x3x3β4o (?) ...
... x3x3β5o (?) ...
... truncated hyperbolic order 4 icositetrachoral tetracomb  1.414214 i
... x3x4β3o (?) ...
... tesseractic tetracomb  
... hyperbolic order 5 tesseractic tetracomb  0.242934 i
... hyperbolic order 5 hecatonicosachoric tetracomb  0.206652 i
... xAFxx3ooxxF3Fxoxo3ooffx&#zx  
... xFfoo3xoxxF3fxoxo3ooffx&#zx  
... xFfxo3xoxoF3fxooo3oofFx&#zx  
... xfofxxfoFxfxo3ooxxoFxFoxxoo3oxfxFofxxfofx&xt (F=ff=x+f)  
... trigonal mibdi-laced wedge  1
xhi hexacosihecatonicosachoron, bitruncated hecatonicosachoron, bitruncated hexacosachoron  7.579634
xhidy hexacosihecatonicosadishecatonicosachoron  3
xithi hexacositriakishecatonicosachoron  3.872983
... xo3oo3ox&#q, longer variant of tetrahedral antiprism, vertex figure of scad  0.707107
... tetra-augmented axially-octahedral ursachoron xoBo3ofox3xooo&#xt ...
... tetra-augmented axially-tetrahedral ursachoron xofo3ooox3oxoo&#xt ...
... triaugmented trigonal mibdi-laced wedge ...
... xofxxFfooFxfo3xxxoFxxxFoxxx3ofxFoofFxxfox&#xt  
... xoofoox3ofxoxfo5xoxxxox&#xt  
... xooFxxFfooFoofo3xxFooFxxxFooFxx3ofooFoofFxxFoox&#xt  
... xoofxxFfooFxofo3xxFxoFxxxFoxFxx3ofoxFoofFxxfoox&#xt  
... :xoqo:4:xxox:3:oooo:4:oxxx:&##x  
... hexastratic ike-first cap of rectified hexacosachoron  3.077684
... xoxFoFxox3oxoooooxo5ooxofoxoo&#xt  
... xoxFxFxox3oxfoxofxo5xxoxxxoxx&#xt  
... ike atop id atop srid atop ti  
... xoxxFxxox3oxoxoxoxo5ooxoooxoo&#xt  
... decachoron-derived Gévay polychoron ...
... xxfoF3oxxFx3xFxxo3Fofxx&#zx  
... magnaursachoron, cell-expanded tetrahedral ursachoron ...
... xxxFooAFxxAxxFx3oxFxxAxxxFooFxx3xfoxFoofFxxFoox&#xt  
... xxxoooFFFAAA 2 FxfoFfxFofxo 2 xfFFfoFoxxof 2 fFxfoFoxFofx &#zx  
... xxxoooFFFAAABxxxF FxfoFfxFofxooVoof xfFFfoFoxxofooVof FAoFxAxoAxFoxxxBF&#zx  
zucypit schmoozed cyclopentachoric tetracomb, schmoozed pentachoric-dispentachoric tetracomb  

Count of actually available polychora: 1439



top of page

---- 5D ----


Acronym Name Circumradius
... 2firx (?)  0.816497
... 2hehad (?)  0.707107
... 2howoh (?)  1.732051
... 2rhohid (?)  1
3,n-dippip triangle - n-gon duoprismatic prism sqrt[7/12+1/(4 sin2(π/n))]
..., {4} || perp {4} (degenerate) square atop fully orthogonal square ∞   i.e. flat in euclidean space
5,n-dippip pentagon - n-gon duoprismatic prism sqrt[(15+2 sqrt(5))/20+1/(4 sin2(π/n))]
..., {5} || perp {5/2} (degenerate) pentagon atop fully perpendicular pentagram, pentagon-pentagram tegum ∞   i.e. flat in euclidean space
..., {5} || gyro pedip (degenerate) pentagon atop gyrated pedip ∞   i.e. flat in euclidean space
bad biprismatododecateron  0.866025
bend biprismatointercepted dodecateron  0.866025
bidhin bidiminished hemipenteract, oct || hex, tet || rap  0.790569
bidsid pixhi bi-icositetra-diminished small disprismatohexacosihecatonicosachoron  5.236068
bittin bitruncated penteract  2.549510
bittit bitruncated triacontiditeron, Voronoi cell of lattice D5*  2.121320
bittix (old: dittox) bitruncated hexateron  1.554563
brinoh birectified penteractic pentacomb  
cabbix cellibiprismatohexateron  0.866025
caddix cellidishexateron  0.866025
cappin celliprismated penteract, steritruncated pentacross  2.423081
cappix (old: happix) celliprismated hexateron, cellitruncated hexateron, hedratoprismated hexateron, steritruncated hexateron  1.632993
capt celliprismated triacontiditeron, steritruncated penteract  2.878460
captid (old: hiptid) celliprismatotruncated dodecateron, hedratoprismatotruncated dodecateron, steriruncitruncated hexateron  2.236068
captint celliprismatotruncated penteractitriacontiditeron, steriruncitruncated penteract, steriruncitruncated pentacross  3.701317
card (older: scard,
oldest: shard)
(small) cellirhombated dodecateron, small hedratorhombated dodecateron, stericantellated hexateron  1.658312
carnit (old: scarnit) (small) cellirhombated penteractitriacontiditeron, stericantellated penteract, stericantellated pentacross  2.660531
chad cellihemidodecateron  1
coa tutcup, co || tutcup co atop tutcup  1.224745
coahex, co || hex 1/4-lune of rectified triacontiditeron, cuboctahedron atop hexadecachoron  1
cogart (old: gocart) celligreatorhombated triacontiditeron (great cellirhombated triacontiditeron), stericantitruncated pentacross  3.534493
cograx (older: gocrax,
oldest: goharx)
celligreatorhombated hexateron (great cellirhombated hexateron, great hedratorhombated hexateron), stericanitruncated hexateron  2.327373
cogrin (old: gocrin) celligreatorhombated penteract (great cellirhombated penteract), stericantitruncated penteract  3.988340
..., cont || grico (degenerate) cont atop grico ∞   i.e. flat in euclidean space
contip tetracontoctachoron prism, bitruncated-icositetrachoron prism  3.450631
copeatope cope atop tope, coatoe-prism  1.802776
cubasc (degenerate) cubical scalene, line atop fully orthogonal cube ∞   i.e. flat in euclidean space
cytaxh cyclotruncated hexateric honeycomb  
cyxh cyclohexateric honeycomb, Delone complex of lattice A5  
dah dishexadecateron  0.790569
danbitot dispenteractibitruncated triacontaditeron  1.802776
danpit dispenteractiprismated triacontaditeron  2.500000
..., deca || gippid (degenerate) deca atop gippid ∞   i.e. flat in euclidean space
decap decachoron prism  1.500000
dehad dodecahemidodecateron  1
dibhid dodecabiprismatohemidodecateron  1
dihin (alt.: penalrap) (vertex-)diminished hemipenteract, pentachoron atop alternate rectified pentachoron  0.790569
..., doe || ipe (degenerate) doe atop ipe ∞   i.e. flat in euclidean space
dot dodecateron, birectified hexateron, equatorial cross-section of (vertex first) 1/q-ax, rap atop inverted rap, vertex figure of mo  0.866025
... point || hex || gyro hex, Dutour polyteron type A  
exip hexacosachoron prism  1.693527
fawdint frustisphenary dispenteractitriacontaditeron, fastegiverted dispenteractitriacontaditeron  0.914214
fenandoh facetospinopenteractidishexadecateron  1.274755
fidoh facetoinverted decahexadecateron  1.274755
firx facetorectified hexateron  0.816497
..., fix || padohi (degenerate) fix atop padohi ∞   i.e. flat in euclidean space
gabdacan great biprismatodiscellipenteract  1.021221
gacnet great cellated penteractitriacontiditeron, omnitruncated penteract, omnitruncated pentacross  4.829189
gadencorn great dispinocellirhombated penteract  1.192297
gadinnert great dispenteractirhombated triacontaditeron  2.336045
gadtaxhiap grand ditetrahedrary hexacontahecatonicosachoron antiprism  0.951057
gafwan great facetosphenary penteract  0.792893
..., gaghi || gofix (degenerate) gaghi atop gofix, (degenerate) gaghi antiprism, (degenerate) gofix antiprism ∞   i.e. flat in euclidean space
gaghipy, pt || gaghi (degenerate) gaghi pyramid ∞   i.e. flat in euclidean space
gancpan great spinocelliprismated penteract  1.276197
gapcyxh great prismated cyclohexateric honeycomb, Voronoi complex of lattice A5*  
gappip great-antiprism prism  1.693527
gapquinoh great prismated quarterpenteractic pentacomb  
gaqrin great quasirhombated penteract  1.673396
gaquacint great quasicellated penteractitriacontiditeron  3.029675
gaquapan great quasiprismated penteract  2.527061
gaquidpothip great-quasidisprismatotesseractihexadecachoric prism, great-quasiprismated-tesseract prism  2.001839
garcornit great retrocellirhombated penteractitriacontaditeron  1.192297
gart great rhombated triacontiditeron, cantitruncated pentacross  2.645751
garx great rhombated hexateron, cantitruncated hexateron  2
gatopin great pteroprismated penteract  0.914214
getitdin great tesseractitriacontidiadispenteract  1.276197
gibcotdin great biprismatocellitriacontadiadispenteract  2.001839
gibrant great birhombated penteractitriacontiditeron, bicantitruncated penteract  3.391165
gibrid (old: gadrid) great birhombated dodecateron, bicantitruncated hexateron  2.179449
gibtadin great biprismatotriacontadiadispenteract  1.488108
gidpithip great-disprismatotesseractihexadecachoric prism, great-prismated-tesseract prism, central segment of cogart  3.534493
gidtixhipy, pt || gidtixhi (degenerate) gidtixhi pyramid ∞   i.e. flat in euclidean space
giktabacadint great skewtrigonary biprismatocellidispenteractitriacontiditeron  1.500000
ginnont great penteractipenteractitriacontiditeron  1.021221
gipbin great prismated biprismatopenteract  0.914214
giphin great prismated hemipenteract, steriruncicantic penteract  3.259601
gippiccup great-prismatotetracontoctachoron prism, omnitruncated-icositetrachoron prism  5.194028
gippiddip great-prismatodecachoron prism  2.291288
gippin great prismated penteract, runcicantitruncated penteract  4.371952
gippit great prismated triacontiditeron, omnitruncated hemipenteract  3.872983
gippix great prismated hexateron, runcicantitruncated hexateron  2.581989
gircaptint (old: grecaptint) great retrocelliprismatotruncated penteractitriacontaditeron  1.949424
girhin great rhombated hemipenteract, cantitruncated demipenteract, runcicantic penteract  2.761340
girn great rhombated penteract, cantitruncated penteract  3.563671
gloptin great lapidoprismatotruncated penteract  1.416813
gocad (old: gohad) great cellated dodecateron (great hedrated dodecateron), omnitruncated hexateron, Voronoi cell of lattice A5*  2.958040
..., gofix || quipdohi (degenerate) gofix atop quipdohi ∞   i.e. flat in euclidean space
gorcrin great retrocelligreat rhombated penteract  2.143163
grahip (old: grahipe) great-rhombated-hecatonicosachoron prism, cantitruncated-hecatonicosachoron prism 11.263210
..., grico || gippic (degenerate) grico atop gippic ∞   i.e. flat in euclidean space
gricoalgrico great-rhombated-icositetrachoron atop alternate great-rhombated-icositetrachoron  4.311477
gricope (old: gripe) great-rhombated-icositetrachoron prism, cantitruncated-icositetrachoron prism  4.328427
grippip great-rhombated-pentachoron prism  1.910497
grittip truncated-tesseract prism, central segment of prin  3.047217
..., grix || prix (degenerate) grix atop prix ∞   i.e. flat in euclidean space
grixip great-rhombated-hexacosachoron prism  4.776223
haco (old: hicco) hexagon cuboctahedron duoprism  1.414214
hacube (old: hiccube) hexagon cube duoprism  1.322876
hadoe hexagon - dodecahedron duoprism  1.721489
hagirco (old: higgirco) hexagon great-rhombicuboctahedron duoprism  2.524147
hagrid hexagon - great-rhombicosidodecahedron duoprism  3.931692
hahip (old: hiddippip) hexagon hexagonal-prism duoprism, hexagon-hexagon duoprismatic prism  1.500000
han hexadecapenteract  0.790569
haquitco hexagon quasitruncated-cuboctahedron duoprism  1.459000
hasirco (old: hissirco) hexagon small-rhombicuboctahedron duoprism  1.719624
hasrid hexagon - small-rhombicosidodecahedron duoprism  2.446644
hatet (old: hittet) hexagon-tetrahedron duoprism  1.172604
hati hexagon - truncated-icosahedron duoprism  2.672186
hatic (old: hittic) hexagon truncated-cube duoprism  2.040640
hatid hexagon - truncated-dodecahedron duoprism  3.133309
hatoe (old: hittoe) hexagon truncated-octahedron duoprism  1.870829
hatut (old: hittut) hexagon truncatet-tetrahedron duoprism  1.541104
hehad hexadecahemidecateron  0.707107
..., hex || sidpith (degenerate) hex atop sidpith ∞   i.e. flat in euclidean space
..., hex || thex (degenerate) hex atop thex ∞   i.e. flat in euclidean space
hexaico, hex || ico hexadecachoron-first rotunda of rectified triacontiditeron, hexadecachoron atop icositetrachoron  1
hexarit (degenerate) hex atop rit ∞   i.e. flat in euclidean space
hexip hexadecachoron prism, vertex figure of rag  0.866025
hexpy hexadecachoral pyramid, vertex-first rotunda of triacontiditeron  0.707107
hextum hex-based tutsatope, hex-based tutism  1.581139
hexu hexadecachoral-based ursateron ofx3xoo3ooo4ooo&#xt, hex-based ursulate  1.144123
hiarahi, hi || rahi (degenerate) hi atop rahi ∞   i.e. flat in euclidean space
hid hexagon icosidodecahedron duoprism  1.902113
hike hexagon icosahedron duoprism  1.380039
hin hemipenteract, demipenteract, hemitesseractic gyroprism, vertex figure of jak  0.790569
hinoh hemipenteractic pentacomb, Delone complex of lattice D5  
hipe hecatonicosachoron prism  3.736068
hit hexadecateron  0.790569
hix hexateron, 5D simplex5), pyropet(id), pentachoral pyramid, regular tet-scalene, regular triangle-tettene, regular line-pennene, regular (point-)hixene, vertex figure of hop  0.645497
hoct hexagon octahedron duoprism  1.224745
howoh hexadecasphenohexadecateron, cantellated hexadecahemidecateron  1.732051
ica sidpith, ico || sidpith icositetrachoron atop small disprismatotesseractihexadecachoron  1.847759
ica tutcup, ico || tutcup icositetrachoron atop truncated-tetrahedral-cupoliprism  1.224745
icarico (degenerate) ico atop rico ∞   i.e. flat in euclidean space
icarit, ico || rit icositetrachoron atop rectified tesseract, ico-first half of nit  1.224745
icates, ico || tes icositetrachoron atop tesseract  1.050501
..., ico || sadi ico atop sadi ∞   i.e. flat in euclidean space
..., ico || spic (degenerate) ico atop spic ∞   i.e. flat in euclidean space
..., ico || srit (degenerate) ico atop srit ∞   i.e. flat in euclidean space
icoap (alt.: icoalico) icositetrachoral antiprism, icositetrachoron atop dual icositetrachoron  1.050501
icope icositetrachoron prism  1.118034
icopy (degenerate) ico pyramid ∞   i.e. flat in euclidean space
icou icositetrachoral-based ursateron ofx3xoo4ooo3ooo&#xt, ico-based ursulate  1.738546
idprix icositetra-diminished prismatorhombated hexacosachoron  9.744610
idsid pixhi icositetra-diminished small disprismatohexacosihecatonicosachoron  5.236068
idsrahi icositetra-diminished small rhombated hecatonicosachoron  6.735034
idsrix icositetra-diminished small rhombated hexacosachoron  6.073594
..., ike || dope (degenerate) ike atop dope ∞   i.e. flat in euclidean space
irl invertiretrolepidoteron  1.224745
irohlohn invertiretrohexadecalepidohemipenteract  1.224745
kafandoh spikifacetospinodishexadecateron  1.620185
lawx ???-sphenary hexateron  1.290994
..., line||ope octahedron-prismatic wedge, line atop ope, half of hexip  0.866025
mibdinit metabidiminished nit, rectified bidhin  1.224745
n,co-dip n-gon - cuboctahedron duoprism sqrt[1+1/(4 sin2(π/n))]
n,cube-dip n-gon - cube duoprism sqrt[3/4+1/(4 sin2(π/n))]
n,doe-dip n-gon - dodecahedron duoprism sqrt[(9+3 sqrt(5))/8+1/(4 sin2(π/n))]
n,girco-dip n-gon - great-rhombicuboctahedron duoprism sqrt[(13+6 sqrt(2))/4+1/(4 sin2(π/n))]
n,grid-dip n-gon - great-rhombicosidodecahedron duoprism sqrt[(31+12 sqrt(5))/4+1/(4 sin2(π/n))]
n,id-dip n-gon - icosidodecahedron duoprism sqrt[(3+sqrt(5))/2+1/(4 sin2(π/n))]
n,ike-dip n-gon - icosahedron duoprism sqrt[(5+sqrt(5))/8+1/(4 sin2(π/n))]
n,k-dippip n-gon - k-gon duoprismatic prism sqrt[1/4+1/(4 sin2(π/n))+1/(4 sin2(π/k))]
n,m-dafup (n,m)-duoantifastegiaprism, (n,m)-dip atop bidual (n,m)-dip sqrt([2+1/(1-cos(pi/n))+1/(1-cos(pi/m))]/8)
n,n-dippip n-gon - n-gon duoprismatic prism sqrt[1/4+1/(2 sin2(π/n))]
n,oct-dip n-gon - octahedron duoprism sqrt[1/2+1/(4 sin2(π/n))]
n,sirco-dip n-gon small-rhombicuboctahedron duoprism sqrt[(5+2 sqrt(2))/4+1/(4 sin2(π/n))]
n,srid-dip n-gon - small-rhombicosidodecahedron duoprism sqrt[sqrt(5)+11/4+1/(4 sin2(π/n))]
n,tet-dip n-gon - tetrahedron duoprism sqrt[3/8+1/(4 sin2(π/n))]
n,tic-dip n-gon - truncated-cube duoprism sqrt[sqrt(2)+7/4+1/(4 sin2(π/n))]
n,tid-dip n-gon - truncated-dodecahedron duoprism sqrt[(37+15 sqrt(5))/8+1/(4 sin2(π/n))]
n,ti-dip n-gon - truncated-icosahedron duoprism sqrt[(29+9 sqrt(5))/8+1/(4 sin2(π/n))]
n,toe-dip n-gon truncated-octahedron duoprism sqrt[5/2+1/(4 sin2(π/n))]
n,tut-dip n-gon - truncated-tetrahedron duoprism sqrt[11/8+1/(4 sin2(π/n))]
n/d,2n/d-dipcup n/d,2n/d-dip cupoliprism sqrt([7+4 cos(π d/n)-2 cos2(π d/n)]/[8-8 cos2(π d/n)])
n/d-daf n/d-duoantifastegium, n/d-p atop bidual n/d-p sqrt([3+1/(1-cos(pi d/n))]/8)
naquiptant penteractiquasiprismatotruncated penteractitriacontaditeron  1.621320
naquitant penteractiquasitruncated penteractitriacontaditeron  1.354911
narptint penteractiretroprismatotruncated penteractitriacontaditeron  2.621320
nat spinotriacontaditeron  1.224745
nippant penteractiprismated penteractitriacontaditeron  3.505073
niptant penteractiprismatotruncated penteractitriacontaditeron  2.621320
nit penteractitriacontiditeron, birectified penteract, birectified triacontiditeron, birectified pentacross  1.224745
noqrant penteractiquasirhombated penteractitriacontaditeron  1.849749
noqraptant penteractiquasiretroprismatotruncated penteractitriacontaditeron  1.621320
noquapant penteractiquasiprismated penteractitriacontaditeron  2.283521
nottant penteractitruncated penteractitriacontaditeron  2.159679
nurrant penteractirhombated penteractitriacontaditeron  3.013043
... dodecateron dual  0.790569
oco (old: occo) octagon cuboctahedron duoprism  1.645329
octa tutcup, oct || tutcup oct atop tutcup  1.274755
octasc octahedral scalene, octahedron-pyramid pyramid, line atop fully orthogonal octahedron, 1/4-lune of triacontiditeron  0.707107
octatepe oct atop tepe  0.816497
ocube octagon - cube duoprism  1.567516
odoe octagon - dodecahedron duoprism  1.915889
..., ofx3xoo4ooo&#xt || o3o4x cube atop (oct,co)-ursachoron, (oct,co)-ursachoron based wedge  1.994779
ogirco octagon - great-rhombicuboctahedron duoprism  2.660531
ogrid octagon - great-rhombicosidodecahedron duoprism  4.020611
oid octagon-icosidodecahedron duoprism  2.079697
oike octagon-icosahedron duoprism  1.453140
opepy octahedral-prismatic pyramid, vertex pyramid of rectified triacontiditeron  1
osirco octagon small-rhombicuboctahedron duoprism  1.914214
osrid octagon - small-rhombicosidodecahedron duoprism  2.587117
otet octagon-tetrahedron duoprism  1.442951
oti octagon - truncated-icosahedron duoprism  2.801372
otic (old: ottic) octagon - truncated-cube duoprism  2.207107
otid octagon - truncated-dodecahedron duoprism  3.244185
otoe (old: otto) octagon truncated-octahedron duoprism  2.051123
otut octagon - truncated-tetrahedron duoprism  1.755593
owoct octagon octahedron duoprism  1.485633
pabdinit (alt: sripalsrip) parabidiminished nit, small rhombated pentachoron atop inverted small rhombated pentachoron, equatorial segment of nit  1.224745
pabex hix (alt.: thiddipcup) partially bi-expanded hexateron, thiddip cupoliprism  1.190238
..., padohi || rofix (degenerate) padohi atop rofix ∞   i.e. flat in euclidean space
pattin prismatotruncated penteract, runcitruncated penteract  3.239235
pattit prismatotruncated triacontiditeron, runcitruncated pentacross  2.738613
pattix prismatotruncated hexateron, runcitruncated hexateron  1.848423
peco pentagon-cuboctahedron duoprism  1.312862
pecube pentagon-cube duoprism  1.213922
pedoe pentagon-dodecahedron duoprism  1.639247
..., pen || inv srip (degenerate) pen atop inverted srip ∞   i.e. flat in euclidean space
penaspid pentachoron atop small prismated decachoron, pen-first rotunda of scad  1
pendpy pentachoral dipyramid  
penp pentachoron prism, vertex figure of ril  0.806226
pent penteract, decateron, 5D measure-polytope5), geopet(id)  1.118034
penth (alt.: stenoh) penteractic pentacomb, 5D hypercubical honeycomb5), (alt.: small terated penteractic pentacomb)  
penu pentachoral-based ursateron ofx3xoo3ooo3ooo&#xt, pen-based ursulate  1.029086
petet pentagon-tetrahedron duoprism  1.048144
pexhix partially expanded hexateron  1.172604
pid pentagon - icosidodecahedron duoprism  1.828016
pike pentagon-icosahedron duoprism  1.275976
pirhin prismatorhombated hemipenteract, runcicantellated demipenteract, steriruncic penteract  2.150581
pirt prismatorhombated triacontiditeron, runcicantellated pentacross  3
pirx prismatorhombated hexateron, runcicantellated hexateron  1.914854
pithin prismatotruncated hemipenteract, runcitruncated demipenteract, stericantic penteract  2.371708
poct pentagon - octahedron duoprism  1.106168
..., prahi || grix (degenerate) prahi atop grix ∞   i.e. flat in euclidean space
prahip (old: prahipe) prismatorhombated-hexacosachoron prism, runcitruncated-hexacosachoron prism  8.294035
praquinoh prismatorhombated quarterpenteractic pentacomb  
..., prico || gyro grico (degenerate) prico atop gyrated grico ∞   i.e. flat in euclidean space
pricoalprico prismatorhombated-icositetrachoron atop alternate prismatorhombated-icositetrachoron  3.522336
pricope (old: pripe) prismatorhombated-icositetrachoron prism, runcitruncated-icositetrachoron prism  3.534493
prin prismatorhombated penteract, runcicantellated penteract  3.047217
pripagrip prip atop grip  1.870829
pripalgrip prip atop alternate grip  1.848423
prippip prismatorhombated-pentachoron prism  1.688194
pripro prip-first rotunda of captid  2.236068
..., prit || grit (degenerate) prit atop grit ∞   i.e. flat in euclidean space
prittip prismatorhombated-tesseract prism, prismatotruncated-hexadecachoron prism, runcitruncated-hexadecachoron prism, central segment of cappin  2.423081
..., proh || gidpith (degenerate) proh atop gidpith ∞   i.e. flat in euclidean space
prohp prismatorhombated-hexadecachoron prism, prismatotruncated-tesseract prism, runcitruncated-tesseract prism, central segment of carnit  2.660531
... q x3o3o3o, variation of pentachoron prism, vertex figure of rectified hexeract  0.948683
quacant quasicellated penteractitriacontiditeron  1.021221
quacgarn quasicelligreatorhombated penteract  2.143163
quacpot quasicelliprismated triacontiditeron  1.102028
quicgrat (old: cogqrit) quasicelligreat rhombated triacontiditeron, (celligreat quasirhombated triacontiditeron)  2.001839
quicpatint quasicelliprismatotruncated penteractitriacontiditeron  1.949424
quiprin quasiprismatorhombated penteract  1.488108
quiptin quasiprismatotruncated penteract  1.416813
quititip quasitruncated-tesseract prism  0.792893
quittin quasitruncated penteract  0.649286
rabird retrobirhombidodecateron  1.414214
raccoth retrocellitriacontadiahexadecateron  1.224745
radah retrodishexadecateron  0.790569
..., ragaghi || tigaghi (degenerate) ragaghi atop tigaghi ∞   i.e. flat in euclidean space
..., rahi || tex (degenerate) rahi atop tex ∞   i.e. flat in euclidean space
rahia sidpixhi (degenerate) rahi atop sidpixhi ∞   i.e. flat in euclidean space
rahipe rectified-hecatonicosachoron prism  4.562051
..., rap || inv tip (degenerate) rap atop inverted tip ∞   i.e. flat in euclidean space
..., rap || prip (degenerate) rap atop prip ∞   i.e. flat in euclidean space
rapaspid rectified pentachoron atop small prismated decachoron, rap-first half of rat  1
rapasrip rectified pentachoron atop small rhombated pentachoron, rap-first cap of nit  1.224745
rapirx retroprismatorhombated hexateron  1.914854
rappip rectified-pentachoron prism, vertex figure of rojak  0.921954
rappy rectified-pentachoric pyramid, vertex cap of hin  0.790569
rapt rectified-pentachoric (line-)tegum, rectified-pentachoric dipyramid ...
raptum rap-first bistratic cap of thin, rap-based tutsatope, rap-based tutism  1.903943
rapu rectified-pentachoral-based ursateron xoo3ofx3xoo3ooo&#xt, rap-based ursulate  1.258489
rat rectified triacontiditeron, rectified pentacross, vertex figure of hinoh  1
ratchet retrotriacontidicellihemitriacontaditeron  1
rawcax (old: rawvdipdopdix) retrosphenary cellihexateron, (retrosphenoverted disprismatoduoprismatodiakishexateron)  1.290994
rawcbinant (old: recarnit) retrosphenary cellibiprismatopenteractipenteractitriacontaditeron, retrocellirhombated penteractitriacontaditeron  2.660531
rawn (old: rawvanant) retrosphenary penteract  2.207107
rawx retrosphenary hexateron  1.290994
recaptid retrocelliprismatotruncated dodecateron  2.236068
repirt retroprismatorhombated triacontiditeron  3
rhohid rectified hexadecahemidecateron  1
ricasrit, rico || srit rectified-icositetrachoron atop small-rhombated-tesseract  1.847759
..., rico || gyro srico (degenerate) rico atop gyrated srico ∞   i.e. flat in euclidean space
..., rico || proh (degenerate) rico atop proh ∞   i.e. flat in euclidean space
..., rico || sadi rico atop sadi  1.738546
ricoalrico, rico || gyro rico rectified icositetrachoron atop gyrated rectified icositetrachoron  1.778824
ricoaspic rectified icositetrachoron atop small prismated icositetrachoron  1.847759
ricoatico (degenerate) rico atop tico ∞   i.e. flat in euclidean space
ricope rectified-icositetrachoron prism  1.802776
..., rigfix || quipdohi (degenerate) rigfix atop quipdohi ∞   i.e. flat in euclidean space
..., rigfix || sirgaghi (degenerate) rigfix atop sirgaghi ∞   i.e. flat in euclidean space
rin rectified penteract  1.414214
rinah retropenteractihexadecateron  0.790569
rinoh rectified penteractic pentacomb  
rippix retroprismated hexateron  1.190238
..., rit || tah (degenerate) rit atop tah ∞   i.e. flat in euclidean space
..., rit || tat (degenerate) rit atop tat ∞   i.e. flat in euclidean space
..., rit || thex (degenerate) rit atop thex ∞   i.e. flat in euclidean space
rita sidpith, rit || sidpith rectified-tesseract atop small-disprismated-tesseractihexadecachoron  1.502958
ritag rit, rit || gyro rit rit atop gyro rit  1.274755
ritarico rectified-tesseract atop rectified-icositetrachoron, rectified-tesseract-first segment of small-prismated-triacontiditeron  1.870829
ritasrit, rit || srit rectified-tesseract atop small-rhombated-tesseract  2.632865
rittip rectified-tesseract prism  1.322876
rix rectified hexateron, vertex figure of hax  0.816497
rocgrax retrocelligreat rhombated hexateron  2.327373
..., rofix || sirsashi (degenerate) rofix atop sirsashi ∞   i.e. flat in euclidean space
roxahi, rox || hi (degenerate) rox atop hi ∞   i.e. flat in euclidean space
roxip rectified-hexacosachoron prism  3.118034
sadinnert small dispenteractirhombated triacontaditeron  2.010695
sadip snub-icositetrachoron prism, snub-disicositetrachoron prism, semistruncated-icositetrachoron prism  1.693527
sart small rhombated triacontiditeron, cantellated pentacross  1.732051
sarx small rhombated hexateron, cantellated hexateron  1.290994
scad (old: shad) small cellated dodecateron, small hedrated dodecateron, stericated hexateron, expanded hexateron, vertex figure of cyxh  1
scant small cellated penteractitriacontiditeron, stericated penteract, stericated pentacross  1.567516
setitdin small tesseractitriacontidiadispenteract  2.423081
sibcotdin small biprismatocellitriacontadiadispenteract  3.534493
sibrant small birhombated penteractitriacontiditeron, bicantellated penteract, bicantellated pentacross  2.236068
sibrid (old: sadrid) small birhombated dodecateron, bicantellated hexateron  1.414214
sibtadin small biprismatotriacontadiadispenteract  3.047217
sicrax small retrocellirhombated hexateron  1.658312
..., sidpith || prit (degenerate) sidpith atop prit ∞   i.e. flat in euclidean space
..., sidpith || tat (degenerate) sidpith atop tat ∞   i.e. flat in euclidean space
sidpithip small-disprismatotesseractihexadecachoron prism, runcinated-tesseract prism, small-prismated-tesseract prism, central segment of scant  1.567516
..., sidpixhi || srix (degenerate) sidpixhi atop srix ∞   i.e. flat in euclidean space
sidpixhip small-disprismatohexacosihecatonicosachoron prism, runcinated-hecatonicosachoron prism, runcinated-hexacosachoron prism  5.259887
sidtaxhiap small ditetrahedrary hexacontahecatonicosachoron antiprism  2.321762
sidtixhipy, pt || sidtixhi (degenerate) sidtixhi pyramid ∞   i.e. flat in euclidean space
sinnont small penteractipenteractitriacontiditeron  1.567516
siphin small prismated hemipenteract, runcinated demipenteract, steric penteract  1.274755
sircaptint (old: srecaptint) small retrocelliprismatotruncated penteractitriacontaditeron  3.701317
sirhin small rhombated hemipenteract, cantellated demipenteract, runcic penteract  1.620185
sirn small rhombated penteract, cantellated penteract  2.207107
sirpin small retroprismated penteract  1.914214
..., sishi || fix (degenerate) sishi atop fix, (degenerate) sishi antiprism, (degenerate) fix antiprism ∞   i.e. flat in euclidean space
sishipy, pt || sishi (degenerate) sishi pyramid ∞   i.e. flat in euclidean space
skatbacadint small skewtrigonary biprismatocellidispenteractitriacontiditeron  1.500000
span small prismated penteract, runcinated penteract  1.914214
spaquinoh small prismated quarterpenteractic pentacomb  
spat small prismated triacontiditeron, runcinated pentacross  1.870829
..., spic || srico (degenerate) spic atop srico ∞   i.e. flat in euclidean space
spiccup small-prismatotetracontoctachoron prism, runcinated-icositetrachoron prism  1.914214
..., spid || deca (degenerate) spid atop deca ∞   i.e. flat in euclidean space
spidaprip spid atop prip, spid-first monostratic cap of spat  1.870829
spidatip small-prismate-pentachoron atop alternate truncated-pentachoron  1.274755
spiddip small-prismatodecachoron prism  1.118034
spidpy (degenerate) spid pyramid ∞   i.e. flat in euclidean space
... vertex figure of spil  0.924211
spix small prismated hexateron, runcinated hexateron  1.190238
squaco square-cuboctahedron duoprism  1.224745
squadoe square-dodecahedron duoprism  1.569562
squagirco square great-rhombicuboctahedron duoprism  2.423081
squagrid square - great-rhombicosidodecahedron duoprism  3.867584
... squap - square duoprism, {4}-wedge of tessap  1.050501
squasirco square - small-rhombicuboctahedron duoprism  1.567516
squasnic square - snub-cube duoprism  1.518409
squasnid square - snub-dodecahedron duoprism  2.268840
squasrid square - small-rhombicosidodecahedron duoprism  2.342236
squatet square-tetrahedron duoprism, 2,4-duoprism cupoliprism, vertex figure of brox  0.935414
squati square - truncated-icosahedron duoprism  2.576932
squatic square - truncated-cube duoprism  1.914214
squatid square - truncated-dodecahedron duoprism  3.052479
squatoe (old: squato) square - truncated-octahedron duoprism  1.732051
squatut square - truncated-tetrahedron duoprism  1.369306
squete square-pyramidal pyramid pyramid, square-tettene, 1/8 of the triacontiditeron  0.707107
squid square-icosidodecahedron duoprism  1.765796
squiddaf square duoantifastegium, square prism atop bidual square prism  0.895420
squike square-icosahedron duoprism  1.185120
squoct square-octahedron duoprism, vertex figure of brinoh  1
..., srahi || xhi (degenerate) srahi atop xhi ∞   i.e. flat in euclidean space
srahip (old: srahipe) small-rhombated-hecatonicosachoron prism  6.753568
..., srico || cont (degenerate) srico atop cont ∞   i.e. flat in euclidean space
..., srico || prico (degenerate) srico atop prico ∞   i.e. flat in euclidean space
sricoalsrico, srico || gyro srico small-rhombated-icositetrachoron atop gyrated small-rhombated-icositetrachoron  2.632865
sricope (old: sripe) small-rhombated-icositetrachoron prism, cantellated-icositetrachoron prism  2.660531
..., srip || inv grip (degenerate) srip atop inverted grip ∞   i.e. flat in euclidean space
sripa gippidtum srip-first bistratic cap of pithin, (srip,gippid)-based tutsateron, (srip,gippid)-based tutism  2.371708
sripadecu (srip,deca)-based ursateron  1.514954
sripal pripu (srip,inv.prip)-based ursateron  1.637956
srippip small-rhombated-pentachoron prism  1.284523
..., srit || proh (degenerate) srit atop proh ∞   i.e. flat in euclidean space
srittip small-rhombated-tesseract prism  1.914214
srixasrahi (degenerate) srix atop srahi ∞   i.e. flat in euclidean space
srixip small-rhombated-hexacosachoron prism, cantellated-hexacosachoron prism  6.094140
srocgrin small retrocelligreat rhombated penteract  3.988340
stade stellated dodecateron, compound of 2 hix  0.645497
starpedippy, pt || starpedip (degenerate) starpedip pyramid ∞   i.e. flat in euclidean space
stotet octagram-tetrahedron duoprism  0.817247
stotoe octagram truncated-octahedron duoprism, star-octagon truncated-octahedron duoprism  1.671195
tac triacontiditeron, pentacross5), aeropet(id), pentachoral antiprism, vertex figure of gee  0.707107
..., tah || grit (degenerate) tah atop grit ∞   i.e. flat in euclidean space
tahagtah, tah || gyro tah tah atop gyro tah  2.150581
tahp tesseractihexadecachoron prism, bitruncated-tesseract prism, bitruncated-hexadecachoron prism  2.179449
tan truncated penteract  2.465447
tanoh truncated penteractic pentacomb  
..., tat || grit (degenerate) tat atop grit ∞   i.e. flat in euclidean space
..., tat || prit (degenerate) tat atop prit ∞   i.e. flat in euclidean space
tattip truncated-tesseract prism  2.207107
tedrix tridiminished rectified hexateron, lace simplex of 3 mutually orthogonal squares  0.816497
tepeatuttip tepe atop tuttip, tetatut-prism  1.322876
tepepy tetrahedral-prismatic pyramid, vertex pyramid of rectified hexateron  0.816497
..., tes || sadi tes atop sadi ∞   i.e. flat in euclidean space
..., tes || srit (degenerate) tes atop srit ∞   i.e. flat in euclidean space
tespy (degenerate) tes pyramid ∞   i.e. flat in euclidean space
tessap tesseract antiprism, hexadecachoron antiprism  1.050501
tessarit tesseract atop rectified tesseract  1.227160
tetaf (alt.: tetaltepe),
tet || inv tepe
tetrahedral antifastegium, tet atop inverted tepe, tet-first rotunda of hin  0.790569
..., tex || sidpixhi (degenerate) tex atop sidpixhi ∞   i.e. flat in euclidean space
texip truncated-hexacosachoron prism  4.749980
..., thex || prit (degenerate) thex atop prit ∞   i.e. flat in euclidean space
..., thex || tah (degenerate) thex atop tah ∞   i.e. flat in euclidean space
thexag thex, thex || gyro thex thex atop gyro thex, equatorial segment of sirhin  1.620185
thexip truncated-hexadecachoron prism  1.658312
thin truncated hemipenteract, cantic penteract  1.903943
thinoh truncated hemipenteractic pentacomb  
thipe truncated-hecatonicosachoron prism  4.670365
..., tico || gidpith (degenerate) tico atop gidpith ∞   i.e. flat in euclidean space
..., tico || gyro prico (degenerate) tico atop gyrated prico ∞   i.e. flat in euclidean space
..., tico || prissi tico atop prissi  2.647378
ticope truncated-icositetrachoron prism  2.692582
tin triacontadipenteract  1.414214
..., tip || inv prip (degenerate) tip atop inverted prip ∞   i.e. flat in euclidean space
tipadeca tip atop deca, 2nd segment of rin in pen-first orientation  1.414214
tippip truncated-pentachoron prism  1.360147
titanoh tritruncated penteractic pentacomb, Voronoi complex of body-centered penteractic lattice (lattice D5*)  
tix (alt.: pentum) truncated hexateron, pen-based tutism  1.322876
toa tutcup, toe || tutcup toe atop tutcup  1.620185
topax ???  1.190238
tot truncated triacontiditeron, truncated pentacross  1.581139
traco triangle - cuboctahedron duoprism  1.154701
tracube triangle - cube duoprism  1.040833
tradoe triangle - dodecahedron duoprism  1.515539
tragirco triangle - great-rhombicuboctahedron duoprism  2.388442
tragrid triangle - great-rhombicosidodecahedron duoprism  3.845977
traltisdip triangle atop gyrated tisdip  1
trapip (old: trapedippip) triangle pentagonal-prism duoprism, triangle-pentagon duoprismatic prism  1.143215
traquith triangle quasitruncated-cube duoprism  0.817997
trasirco triangle small-rhombicuboctahedron duoprism  1.513420
trasnic triangle - snub-cube duoprism  1.462497
trasnid triangle - snub-dodecahedron duoprism  2.231808
trasrid triangle - small-rhombicosidodecahedron duoprism  2.306383
tratet triangle - tetrahedron duoprism, vertex figure of bril  0.841625
trati triangle - truncated-icosahedron duoprism  2.544388
tratic triangle truncated-cube duoprism  1.870173
tratid triangle - truncated-dodecahedron duoprism  3.025056
tratoe triangle truncated-octahedron duoprism  1.683251
tratrip (old: triddippip) triangle triangular-prism duoprism, triangle-triangle duoprismatic prism, vertex figure of ram  0.957427
tratut triangle truncated-tetrahedron duoprism  1.307032
trial triddip {3} atop gyrated triddip, {3}-first cap of rix  0.816497
trid triangle - icosidodecahedron duoprism  1.717954
tridafup triangular duoantifastegiaprism, triddip atop bidual triddip, central segment of vertex first dot  0.866025
triddaf triangular duoantifastegium, trip atop bidual trip  0.790569
triddippy trigonal-duoprismatic pyramid, vertex pyramid of the dodecateron  0.866025
trike triangle - icosahedron duoprism  1.112583
trippasc triangular-prismatic scalene, triangular-prismatic-pyramid pyramid, line atop fully orthogonal triangular-prism  0.790569
troct triangle-octahedron duoprism, vertex figure of brag  0.912871
wacbinant sphenary cellibiprismatopenteractipenteractitriacontaditeron  1.192297
wavinant sphenoverted penteractipenteractitriacontaditeron  0.792893
..., xhi || thi (degenerate) xhi atop thi ∞   i.e. flat in euclidean space
xhip hexacosihecatonicosachoron prism, bitruncated-hecatonicosachoron prism, bitruncated-hexacosachoron prism  7.596108

Count of actually available polytera: 473



top of page

---- 6D ----


Acronym Name Circumradius
3,3,4-tip triangle-triangle-square triprism  1.080123
4,n,m-tip square - n-gon - m-gon - triprism  
4,n,n-tip square - n-gon - n-gon - triprism sqrt[1/2+1/(2 sin2(π/n))]
ax (old: hexe) hexeract, dodecapeton, 6D measure-polytope6), geoex(id)  1.224745
axh hexeractic pentacomb, 6D hypercubical honeycomb6)  
bapril biprismatorhombated heptapeton, biruncitruncated heptapeton  2.203893
barm (older: scram,
even older: bram, again older: remak,
oldest kram)
birectified pentacontitetrapeton (small centrorhombated pentacontitetrapeton)  2.449490
batal bitruncated heptapeton  1.647509
bitem (older: gacram,
even older: botam, oldest: kobtam)
bitruncated pentacontitetrapeton (great centrorhombated pentacontitetrapeton, heptacontidia-bitruncated pentacontitetrapeton)  4.123106
bittixalbittix bitruncated-hexateron atop inverted bitruncated-hexateron  1.581139
boprax biprismatorhombated hexeract, biruncitruncated hexacross  3.464102
botag bitruncated hexacontatetrapeton, bitruncated hexacross  2.121320
botajik bitruncated icosiheptaheptacontidipeton  2.943920
botox bitruncated hexeract  2.915476
brag (old: dric) birectified hexacontitetrapeton, Voronoi cell of lattice D6*  1.224745
bril (old: driss) birectified heptapeton, vertex figure of lin  0.925820
brox (old: drax) birectified hexeract  1.414214
cagral (old: gacral) celligreatorhombated heptapeton, stericantitruncated heptapeton  2.618615
cappixalcappix cappix atop alternate cappix  1.658312
captal celliprismatotruncated heptapeton, steriruncitruncated heptapeton  2.591194
catal cellitruncated heptapeton, steritruncated heptapeton  1.851640
catax cellitruncated hexeract  3.456841
catog cellitruncated hexacontatetrapeton, steritruncated hexacross  2.828427
cocube cuboctahedron-cube duoprism  1.322876
codip cuboctahedron-cuboctahedron duoprism  1.414214
codoe cuboctahedron-dodecahedron duoprism  1.721489
cograxalcograx cograx atop alternate cograx  2.345208
coid cuboctahedron-icosidodecahedron duoprism  1.902113
coike cuboctahedron-icosahedron duoprism  1.380039
copal celliprismated heptapeton, steriruncinated heptapeton  1.963961
copog celliprismated hexacontatetrapeton, steriruncinated hexacross  3.316625
copox celliprismated hexeract, steriruncinated hexeract  3.087966
copril celliprismatorhombated heptapeton, steriruncicantellated heptapeton  2.725541
crag (old: scrag) cellirhombated hexacontatetrapeton, stericantellated hexacross  3.082207
cral (old: scral) cellirhombated heptapeton, stericantellated heptapeton  1.927248
crax (old: scrax) (small) cellirhombated hexeract, stericantellated hexeract  3.277597
crohax (old: scrohax) (small) cellirhombated hemihexeract, pentiruncinated demihexeract, pentiruncic hexeract  2.397916
cubedoe cube-dodecahedron duoprism  1.647278
cubid cube-icosidodecahedron duoprism  1.835220
cubike cube-icosahedron duoprism  1.286277
cyloh cycloheptapetic honeycomb, Delone complex of lattice A6  
dijak (alt.: taccahin) (mono-)diminished icosiheptaheptacontidipeton, tac atop hin  0.816497
dodoe dodecahedron-dodecahedron duoprism  1.981679
dotip dodecateron prism  1
dotpy dodecateron pyramid, vertex pyramid of mo  1
dottascad dodecateron atop small cellated dodecateron  1
dotum dot-first bistratic cap of tim, dot-based tutsatope, dot-based tutism  2.645751
endjak ennea-diminished jak  0.816497
fe tetradecapeton, tritruncated heptapeton, equatorial cross-section of (vertex first) q-hept  1.732051
gaborg great birhombihexacontatetrapeton, bicantitruncated hexacross  3.391165
gabril great birhombated heptapeton, bicantitruncated heptapeton  2.390457
gacal great cellated heptapeton, steriruncicantitruncated heptapeton  3.380617
gapil great prismated heptapeton, runcicantitruncated heptapeton  2.803060
gaqrox great quasirhombihexeract  1.906840
gaquitxog great quasiterated hexeractihexacontatetrapeton  4.288753
gee (old: xic) hexacontitetrapeton, hexacross6), aeroex(id), hexateral antiprism, vertex figure of zee  0.707107
gibpof great biprismated tetradecapeton, biruncicantitruncated heptapeton  3
gippitip great-prismated-triacontiditeron prism  3.905125
girhax great rhombated hemihexeract, cantitruncated demihexeract, runcicantic hexeract  3.278719
gocadip great-cellated-hexateron prism  3
gocog great cellated hexacontatetrapeton, omnitruncated hemihexeract  5.244044
gopam (older: gakpam) great prismated pentacontitetrapeton (great heptaheptacontidiprismated pentacontitetrapeton)  6.244998
gotaf great terated tetradecapeton, omnitruncated heptapeton, Voronoi cell of lattice A6*  3.741657
gotaxog great terated hexeractihexacontatetrapeton  6.293378
gril great rhombated heptapeton, cantitruncated heptapeton  2.104417
grog great rhombihexacontatetrapeton, cantitruncated hexacross  2.645751
grox great rhombihexeract, cantitruncated hexeract  4.045239
hagippid hexagon - great-prismated-pentachoron duoprism  2.449490
harjak (old: trojak) demirectified icosiheptaheptacontidipeton (trirectified icosiheptaheptacontidipeton)  2.160247
hatope hexagon - truncated-octahedron duoprismatic prism  1.936492
hax hemihexeract, vertex figure of laq  0.866025
haxh hemihexeractic pentacomb, Delone complex of lattice D6  
hejak demified icosiheptaheptacontidipeton  1.632993
hexaf, hex || gyro hexip hexadecachoral antifastegium, hex atop gyrated hexip, hex-first rotunda of hax  0.866025
hexasc hexadecachoric scalene, hexadecachoron-pyramid pyramid, line atop fully orthogonal hexadecachoron, 1/4-lune of hexacontatetrapeton  0.707107
hinnip hemipenteractic prism, vertex figure of ranq  0.935414
hinpy demipenteractic pyramid, vertex pyramid of jak  0.816497
hinro (alt.: hinarat) demipenteractic rotunda, hin-first half of mo, hin atop rat  1
hint demipenteractic (line-)tegum, demipenteractic dipyramid ...
hixadot hexateron atop dodecateron, hix-first half of hax  0.866025
hixalrix hexateron atop inverted rectified hexateron, hix-first rotunda of jak  0.816497
hixascad hexateron atop small cellated decateron, hix-first rotunda of small terated tetradecapeton  1
hixip hexateron prism, vertex figure of roc  0.816497
hop (old: hep) heptapeton, 6D simplex6), pyroex(id), hexateral pyramid, vertex figure of oca  0.654654
iddoe icosidodecahedron-dodecahedron duoprism  2.140458
idodip icosidodecahedron-icosidodecahedron duoprism  2.288246
ikedip icosahedron-icosahedron duoprism  1.344997
ikedoe icosahedron-dodecahedron duoprism  1.693527
ikid icosahedron-icosidodecahedron duoprism  1.876844
jak icosiheptaheptacontidipeton, Gosset polypeton 22,1, vertex figure of naq, Delone cell of lattice E6  0.816497
jakoh icosiheptaheptacontidipetic hexacomb, Gosset hexacomb 22,2, Delone complex of lattice E6  
madek pentacontatetradisheptacontadipeton, compound of 2 jak  0.816497
mo pentacontitetrapeton, Gosset polypeton 12,2, vertex figure of jakoh, E6 polytope (span of its roots)  1
n,co-dippip n-gon - cuboctahedron duoprismatic prism  
n,doe-dippip n-gon - dodecahedron duoprismatic prism  
n,ex-dip n-gon - hexacosachoron duoprism  
n,hex-dip n-gon - hexadecachoron duoprism  
n,hi-dip n-gon - hecatonicosachoron duoprism  
n,ico-dip n-gon - icositetrachoron duoprism  
n,id-dippip n-gon - icosidodecahedron duoprismatic prism  
n,ike-dippip n-gon - icosahedron duoprismatic prism  
n,m,k-tip n-gon - m-gon - k-gon - triprism sqrt[1/(4 sin2(π/n))+1/(4 sin2(π/m))+1/(4 sin2(π/k))]
n,n,k-tip n-gon - n-gon - k-gon - triprism sqrt[1/(2 sin2(π/n))+1/(4 sin2(π/k))]
n,n,n-tip n-gon - n-gon - n-gon - triprism sqrt[3/(4 sin2(π/n))]
n,oct-dippip n-gon - octahedron duoprismatic prism  
n,pen-dip n-gon - pentachoron duoprism  
n,rahi-dip n-gon - rectified-hecatonicosachoron duoprism  
n,rap-dip n-gon - rectified-pentachoron duoprism  
n,rico-dip n-gon - rectified-icositetrachoron duoprism  
n,rit-dip n-gon - rectified-tesseract duoprism  
n,rox-dip n-gon - rectified-hexacosachoron duoprism  
n,tes-dip n-gon - tesseract duoprism  
n,tet-dippip n-gon - tetrahedron duoprismatic prism  
nitarin nit atop rin, nit-first rotunda of brox  1.414214
nitip penteractitriacontiditeron prism  1.322876
... tetradecapeton dual  0.774597
... pentacontitetrapeton dual, convex hull of medak  0.816497
octatratet oct atop tratet, oct-first cap of ril  0.845154
octco octahedron-cuboctahedron duoprism  1.224745
octcube octahedron-cube duoprism  1.118034
octdip octahedron-octahedron duoprism, dual of Delone cell of lattice D6*, vertex figure of traxh  1
octdoe octahedron-dodecahedron duoprism  1.569562
octete octahedral tettene, octahedral-pyramid pyramid pyramid, triangle atop fully orthogonal octahedron  0.707107
octid octahedron-icosidodecahedron duoprism  1.765796
octike octahedron-icosahedron duoprism  1.185120
oddimo octadeca-diminished mo  1
... (mono) tetal tratet augmented tetdip  0.866025
pabdihax (alt.: rixalrix) parabidiminished demihexeract, rectified hexateron atop inverted rectified hexateron  0.866025
pabdimo, dot||scad||dot parabidiminished mo, dodecateron atop pseudo small cellated dodecateron atop dodecateron  1
patal prismatotruncated heptapeton, runcitruncated heptapeton  2
penppy penp pyramid, vertex-pyramid of ril  0.845154
pentanit pent atop nit  1.228783
pentarin tesseract atop rectified tesseract  1.418705
potag prismatotruncated hexacontatetrapeton, runcitruncated hexacross  2.738613
pril prismatorhombated heptapeton, runcicantellated heptapeton  2.104417
prog prismatorhombated hexacontatetrapeton, runcicantellated hexacross  3
quotacog quasitericellated hexacontatetrapeton  1.121320
quotox quasitruncated hexeract  0.681517
rag (old: ric) rectified hexacontitetrapeton  1
ram rectified pentacontitetrapeton, Gosset polypeton 02,2,1, Voronoi cell of lattice E6*  1.732051
ramoh rectified-pentacontitetrapetic hexacomb, Gosset hexacomb 02,2,2, Voronoi complex of lattice E6*  
rapa penp rap atop penp, rap-first cap of ril  0.845154
rapesc rectified-pentachoric scalene, rectified-pentachoron-pyramid pyramid, line atop fully orthogonal rectified pentachoron  0.816497
ratanit rectified triacontaditeron atop penteractitriacontiditeron, rat-first rotunda of brag  1.224745
ratasiphin rat atop siphin, rat-first cap of rojak  1.290994
ratip rectified-triacontiditeron prism  1.118034
rax rectified hexeract, rectified dodecapeton  1.581139
raxh rectified hexeractic pentacomb  
ril (old: riss) rectified heptapeton, vertex figure of hesa  0.845154
rinnip rectified-penteract prism  1.500000
ritgyt rectified-tesseractic gyrotrigonism  1.290994
rixasarx rectified hexateron atop small rhombated hexateron, rix-first cap of brox  1.414214
rixip rectified-hexateron prism, vertex figure of rolaq  0.957427
rixpy rectified-hexateronal pyramid, vertex pyramid of demihexeract  0.866025
rojak rectified icosiheptaheptacontidipeton  1.290994
saborx small birhombated hexeract, bicantellated hexeract  2.645751
sabril small birhombated heptapeton, bicantellated heptapeton  1.558387
sabrim (older: pirm,
even older: sirmak, oldest: skorm)
small birhombated pentacontitetrapeton (prismatorectified pentacontitetrapeton, small rhombated pentacontitetraheptacontidipeton, small heptacontidirhombated pentacontitetrapeton)  3
sarxasibrid small rhombated hexateron atop small birhombated dodecateron, rix-first subsegment of brox  1.414214
scag small cellihexacontatetrapeton, stericated hexacross  2
scal small cellated heptapeton, stericated heptapeton  1.195229
scox small cellihexeract, stericated hexeract  1.978437
shopjak small demiprismated icosiheptaheptacontidipeton  1.914854
siborg small birhombated hexacontatetrapeton, bicantellated hexacross  2.236068
sibpof small biprismated tetradecapeton, biruncinated heptapeton  1.414214
sirhax small rhombated hemihexeract, cantellated demihexeract, runcic hexeract  1.936492
sirjak small rhombated icosiheptaheptacontidipeton  2.380476
sobpoxog small biprismated hexeractihexacontatetrapeton, biruncinated hexeract, biruncinated hexacross  2.345208
sochax small cellated hemihexeract, stericated demihexeract, pentic hexaract  1.322876
sophax small prismated hemihexeract, runcinated demihexeract  1.658312
spam (old: skopam) small prismated pentacontitetrapeton (small hebdomecontadiaprismated pentacontitetrapeton)  2.236068
spil small prismated heptapeton, runcinated heptapeton  1.309307
spixip small-prismated-hexateron prism  1.290994
spog small prismatohexacontatetrapeton, runcinated hexacross  1.870829
spox small prismated hexeract, runcinated hexeract  2.263033
squahex square-hexadecachoron duoprism  1
squahi square-hecatonicosachoron duoprism  3.769377
squapen square-pentachoron duoprism, vertex figure of bersa  0.948683
squarahi square - rectified-hecatonicosachoron duoprism  4.589369
squarap square - rectified-pentachoron duoprism  1.048809
squarico square - rectified-icositetrachoron duoprism  1.870829
squarit square - rectified-tesseract duoprism  1.414214
squarox square - rectified-hexacosachoron duoprism  3.157869
squepe square pennene  0.707107
squex square-hexacosachoron duoprism  1.765796
squico square-icositetrachoron duoprism  1.224745
sram (older: skobram,
oldest skabram)
small rhombated pentacontitetrapeton (small hebdomecontadiabirhombated pentacontitetrapeton)  3.316625
sril small rhombated heptapeton, cantellated heptapeton  1.362770
srog small rhombihexacontatetrapeton, cantellated hexacross  1.732051
srox small rhombated hexeract, cantellated hexeract  2.515637
staf (interim: stef) small terated tetradecapeton, pentellated heptapeton, expanded heptapeton  1
stef stellated tetradecapeton, compound of 2 hop  0.654654
stoxog small terated hexeractihexacontatetrapeton, pentellated hexeract, pentellated hexacross  1.645329
taccarat triacontaditeron atop rectified triacontaditeron, tac-first rotunda of rectified hexacontitetrapeton  1
taccup triacontiditeron prism, vertex figure of rez  0.866025
tacog tericellated hexacontatetrapeton, pentitruncated hexeract  3.121320
tacogral (old: gatocral) tericelligreatorhombated heptapeton, pentistericantitruncated heptapeton  2.976095
tacox tericellated hexeract, pentitruncated hexacross  2.474130
tacpy triacontaditeric pyramid, vertex-first rotunda of gee  0.707107
tactaf tericellitruncated tetradecapeton, pentisteritruncated heptapeton  2.236068
tag truncated hexacontatetrapeton  1.581139
tagopal (old: gatopal) terigreatoprismated heptapeton, pentiruncicantitruncated heptapeton  3.116775
tahgyt tesseractihexadecachoric gyrotrigonism  2.160247
taporf (old: staporf) teriprismatorhombitetradecapeton, pentiruncicantellated heptapeton  2.449490
tapox (old: stapox) teriprismated hexeract, penticantellated hexacross  2.707107
tedjak (alt.: hexgyt) tridiminished icosiheptaheptacontidipeton, tridiminished 22,1, hexadecachoral gyrotrigonism  0.816497
tepasc tetrahedral-prismatic scalene, tetrahedron-prism-pyramid pyramid, line atop fully orthogonal tetrahedron prism  0.866025
tetal tratet tetrahedron atop alternate triangle,tetrahedron-duoprism  0.866025
tetco tetrahedron-cuboctahedron duoprism  1.172604
tetcube tetrahedron - cube duoprism  1.060660
tetdip tetrahedron-tetrahedron duoprism, vertex figure of he  0.866025
tetdoe tetrahedron-dodecahedron duoprism  1.529224
tetid tetrahedron-icosidodecahedron duoprism  1.730039
tetike tetrahedron-icosahedron duoprism  1.131154
tetoct tetrahedron-octahedron duoprism, vertex figure of sez  0.935414
thax truncated hemihexeract  1.581139
thexgyt (alt.: pex tedjak) truncated-hexadecachoral gyrotrigonism, partially expanded tridiminished icosiheptaheptacontidipeton, partially expanded tridiminished 21,2  1.632993
til truncated heptapeton  1.362771
tim truncated pentacontitetrapeton  2.645751
titam (older: cacram,
totam, tomak,
katom)
tritruncated pentacontitetrapeton (centrocellirhombated pentacontitetrapeton, trunkated pentacontitetraheptacontidipeton, heptacontiditruncated pentacontitetrapeton)  3.741657
tocal teracellated heptapeton, pentitruncated heptapeton  1.647509
tocral (old: stocral) tericellirhombated heptapeton, pentiruncitruncated heptapeton  2.329929
togral (old: gotral) terigreatorhombated heptapeton, penticantitruncated heptapeton  2.390457
tojak truncated icosiheptaheptacontidipeton  2
topag (old: stopag) teriprismated hexacontatetrapeton, penticantellated hexeract  2.921564
topal (old: stopal) teriprismated heptapeton, penticantellated heptapeton  1.690309
tox truncated hexeract  2.745093
tracope triangle-cuboctahedron duoprismatic prism  1.258306
tradope triangle-dodecahedron duoprismatic prism  1.595888
trahex triangle - hexadecachoron duoprism, vertex figure of barz  0.912871
trahi triangle - hecatonicosachoron duoprism  3.747204
trapen triangle - pentachoron duoprism, vertex figure of broc  0.856349
trarahi triangle - rectified-hecatonicosachoron duoprism  4.571175
trarap triangle - rectified-pentachoron duoprism, vertex figure of branq  0.966092
trarico triangle - rectified-icositetrachoron duoprism  1.825742
trarit triangle - rectified-tesseract duoprism  1.354006
trarox triangle - rectified-hexacosachoron duoprism  3.131369
traspid triangle - small-prismated-pentachoron duoprism  1.154701
tratepe triangle-tetrahedron-duoprism prism, vertex figure of rolin  0.978945
tratess triangle - tesseract duoprism  1.154701
tratetpy (triangle,tetrahedron)-duoprism pyramid, vertex-pyramid of bril  0.925820
traxh tri-rectified hexeractic pentacomb, Voronoi complex of body-centered hexeractic lattice (lattice D6*)  
trex triangle - hexacosachoron duoprism  1.717954
trial tratet triangle atop dual tratet, triangle-first cap of ril  0.845154
trico triangle - icositetrachoron duoprism  1.154701
triddipabl tratrip triddip atop bidual tratrip  1
tridep triangle-icosidodecahedron duoprismatic prism  1.789237
trikep triangle-icosahedron duoprismatic prism  1.219771
trim (older: cacam,
even older: tram, oldest: mak)
trirectified pentacontitetrapeton (centrocellated pentacontitetrapeton, pentacontitetraheptacontidipeton)  1.414214
trittip triangle-triangle-triangle-triprism, vertex figure of ramoh  1
trope (old: troctip) triangle-octahedron duoprismatic prism  1.040833
xog hexeractihexacontatetrapeton, tritruncated hexeract, tritruncated hexacross  2.549510

Count of actually available polypeta: 252



top of page

---- 7D ----


Acronym Name Circumradius
barz (old: drhio) birectified hecatonicosoctaexon  1.224745
berlin (old: shabrilq) birhombated pentacontihexahecatonicosihexaexon (small demibirhombated pentacontihexapentacosiheptacontihexaexon)  3.570714
bersa (old: dars) birectified hepteract  1.581139
bittoc bitruncated octaexon  1.713914
bragabrox brag atop brox, brag-first rotunda of sez  1.414214
bragasochax brag atop sochax, 2nd subsegment of lin in hax-first orientation  1.322876
branq (old: dranq) birectified hecatonicosihexapentacosiheptacontihexaexon  1.936492
brillip birectified - heptapeton prism  1.052209
brilpy birectified-heptapetonal pyramid, vertex pyramid of pentacontihexahecatonicosihexaexon  1.322876
broc (old: droc) birectified octaexon, duorectified octaexon, vertex figure of bif  0.968246
copen cuboctahedron - pentachoron duoprism  1.183216
... point || pseudo hax || gee, Dutour polyexon type A  
gahax gee atop hax, gee-first segment of naq  0.866025
garag gee atop rag, gee-first rotunda of rez  1
geep hexacontitetrapeton prism, hexacross prism, vertex figure of rek  0.866025
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
haxabrag hax-first monostratic cap of lin, hax atop brag  1.322876
haxip hemihexeractic prism, vertex figure of rinquoh  1.060660
haxpy hemihexeractic pyramid, vertex pyramid of laq  1
haxt demihexeractic (line-)tegum, demihexeractic bipyramid ...
he (old: ache) hexadecaexon, trirectified octaexon, equatorial cross-section of (vertex first) 1/q-octo  1
hept hepteract, tetradecaexon, 7D measure-polytope7), geozett(id)  1.322876
hesa (old: hiss) hemihepteract, vertex figure of bay  0.935414
hexete hexadecachoric tettene, hexadecachoron-pyramid pyramid-pyramid, triangle atop fully orthogonal hexadecachoron  0.707107
hinsc demipenteractic scalene, demipenteractic-pyramid pyramid, line atop fully orthogonal demipenteract  0.866025
hopabril heptapeton atop birectified heptapeton, hop-first monostratic cap of hesa  0.935414
hopalbril hop atop inverted bril, hop-first cap of laq  1
hopalril hop atop inverted ril, hop-first cap of naq  0.866025
hopip heptapeton prism, vertex figure of rene  0.823754
jakaljak jak atop inverted jak, medial segment of naq  0.866025
jakip icosihepta-heptacontidi-peton prism, vertex figure of riffy  0.957427
jakpy icosihepta-heptacontidi-peton pyramid, vertex-first cap of naq  0.866025
laq pentacontihexapentacosiheptacontihexaexon, Gosset polyexon 21,3, vertex figure of naquoh  1
lin pentacontihexahecatonicosihexaexon, Gosset polyexon 12,3, Voronoi cell of lattice E7*  1.322876
linoh pentacontihexahecatonicosihexaexic heptacomb, Gosset heptacomb 13,3, Voronoi complex of lattice E7*  
moarojak mo-first monostratic cap of lin, mo atop rojak  1.322876
n,hix-dip n-gon - hexateron duoprism sqrt[5/12 + 1/(2 sin(π/n))2]
n,n,n-tippip n-gon - n-gon - n-gon - triprismatic prism sqrt[1/4+3/(4 sin2(π/n))]
naq hecatonicosihexapentacosiheptacontihexaexon, Gosset polyexon 32,1, vertex figure of fy, (one of the) Delone cell(s) of lattice E7  0.866025
naquoh hecatonicosihexapentacosiheptacontihexaexic heptacomb, Gosset heptacomb 33,1, Delone complex of lattice E7  
oca (old: oc) octaexon, 7D simplex7), pyrozett(id), heptapetal pyramid, vertex figure of ene, (one of the) Delone cell(s) of lattice E7  0.661438
octepe octahedral pennene  0.707107
octico octahedron - icositetrachoron duoprism  1.224745
octpen octahedron - pentachoron duoprism, vertex figure of tro  0.948683
octrap octahedron - rectified-pentachoron duoprism  1.048809
puph petaprismated hexadecaexon  1.732051
ragabrag rag atop brag, rag-first rotunda of barz  1.224745
ranq rectified hecatonicosihexapentacosiheptacontihexaexon  1.414214
rapete rap tettene  0.866025
rasa (old: ras) rectified hepteract  1.732051
rez (old: rhio) rectified hecatonicosoctaexon  1
rilalbril rectified heptapeton atop inverted birectified heptapeton, equatorial monostratic segment of demihepteract  0.935414
rilalril rectified heptapeton atop inverted rectified heptapeton, medial segment of naq  0.866025
rilastaf ril atop staf, ril-first rotunda of rez  1
rillip rectified-heptapeton prism, vertex figure of robay  0.981981
rilpy rectified-heptapetonal pyramid, vertex pyramid of demihepteract  0.935414
rixasc rectified-hexateronal scalene, rectified-hexateronal-pyramid pyramid, line atop fully orthogonal rectified-hexateron  1
roc rectified octaexon, vertex figure of hocto  0.866025
rojaka hejak rojak atop hejak, rojak-first cap of rolaq  1.732051
rojakalrojak (alt.: pabdilin) parabidiminished lin, rojak atop alternate rojak  1.322876
rolaq rectified pentacontihexapentacosiheptacontihexaexon  1.732051
rolin (old: lanq) rectified pentacontihexahecatonicosihexaexon, pentacontihexahecatonicosihexapentacosiheptacontihexaexon  2.449490
rolinoh rectified pentacontihexahecatonicosihexaexic heptacomb, Gosset heptacomb 03,3,1  
sabach small bicellated hexadecaexon, bistericated octaexon  1.414214
sabro small birhombated octaexon, bicantellated octaexon  1.658312
saro small rhombated octaexon, cantellated octaexon  1.414214
sarz small rhombated hecatonicosoctaexon, cantellated heptacross  1.732051
sco small cellated octaexon, stericated octaexon  1.322876
sersa small rhombated hepteract, cantellated hepteract  2.790257
seto small terated octaexon, pentellated octaexon  1.198958
sez (old: shio) hepteractihecatonicosoctaexon  1.414214
shilq small demified pentacontihexapentacosiheptacontihexaexon  2.179449
sibpo small biprismated octaexon, biruncinated octaexon  1.561250
sirhesa small rhombated hemihepteract, cantellated demihepteract  2.207940
spaz small prismated hecatonicosoctaexon, runcinated heptacross  1.870829
spo small prismated octaexon, runcinated octaexon  1.391941
squahix square - hexateron duoprism, vertex figure of bro  0.957427
suph small petated hexadecaexon, hexicated octaexon, expanded octaexon  1
tacpy triacontaditeric pyramid, vertex-first rotunda of gee  0.707107
talq truncated pentacontihexapentacosiheptacontihexaexon  2.645751
tanq truncated hecatonicosihexapentacosiheptacontihexaexon  2.179449
tasa truncated hepteract  2.998773
tattoc tritruncated octaexon  1.854050
taz truncated hecatonicosoctaexon, truncated heptacross  1.581139
tethex tetrahedron - hexadecachoron duoprism, vertex figure of tark  0.935414
tetpen tetrahedron-pentachoron duoprism, vertex figure of trene  0.880341
tetrap tetrahedron - rectified-pentachoron duoprism, vertex figure of torfy  0.987421
tettepe tetrahedron-tetrahedron duoprismatic prism, vertex figure of 03,3,1  1
thesa truncated demihepteract  2.423840
toc truncated octaexon  1.391941
trahin triangle - hemipenteract duoprism, vertex figure of borfy  0.978945
trahix triangle - hexateron duoprism, vertex figure of brene  0.866025
tratac triangle - triacontiditeron duoprism, vertex figure of bark  1.154701
tratratrip triangle - triangle - triangle - triprismatic prism  1.118034
trippen triangle - pentachoron duoprism-prism, vertex figure of buffy  0.991632
zee (old: hio) hecatonicosoctaexon, heptacross7), aerozett(id), heptapetal antiprism, vertex figure of ek  0.707107

Count of actually available polyexa: 96



top of page

---- 8D ----


Acronym Name Circumradius
bark birectified diacosipentacontahexazetton  1.224745
bay diacositetracont-myriaheptachiliadiacosioctaconta-zetton, Gosset polyzetton 24,1  1.414214
bayoh diacositetracont-myriaheptachiliadiacosioctaconta-zettic octacomb, Gosset octacomb 25,1  
be octadecazetton, enneaenneazetton, bi-enneazetton, quadritruncated enneazetton, equatorial cross-section of (vertex first) q-enne  2
bif diacositetracont-dischiliahectohexaconta-zetton, Gosset polyzetton 14,2  2
bifoh diacositetracont-dischiliahectohexaconta-zettic octacomb, Gosset octacomb 15,2  
borfy birectified dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton, t2(41,2)  2.449490
brene birectified enneazetton  1
bro birectified octeract, birectified hexadecazetton  1.732051
brocalbroc broc atop inverted broc, central segment of hocto  1
buffy diacositetracont-dischiliahectohexacont-myriaheptachiliadiacosioctaconta-zetton; rectified bif,  t1(12,4); birectified bay,  t2(21,4); tetrarectified fy,  t4(41,2)  3.872983
... point || pseudo hesa || zee, Dutour polyzetton type A  
ek diacosipentacontahexazetton, octacross8), aeroyott(id), octaexal antiprism, vertex figure of vee, (one of the) Delone cell(s) of lattice E8  0.707107
ene enneazetton, 8D simplex8), pyroyott(id), octaexal pyramid, vertex figure of day, (one of the) Delone cell(s) of lattice E8  0.666667
fy dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton, Gosset polyzetton 41,2, Witting polytope, vertex figure of goh  1
goh Gosset octacomb 52,1, Delone complex of lattice E8  
hauhocto hexadeca-augmented hemiocteract ...
haxesc (degenerate) demihexaractic scalene, line atop fully orthogonal demihexaract ∞   i.e. flat in euclidean space
hesapy hemihepteractic pyramid, vertex pyramid of bay  1.414214
hocto hemiocteract  1
kadify heptacontadia-diminished dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton, tegum sum of two mutually inverted birectified enneazetta  1
n,n,n,n-quip n-gon - n-gon - n-gon - n-gon - tetraprism (or: -quadprism) sqrt[1/sin2(π/n)]
naqpe naq prism, prism of Gosset polyexon 32,1  1
ocalroc oca atop inverted roc, oca-first cap of fy  1
ocpe octaexon prism, vertex figure of reday  0.829156
octo octeract, hexadecazetton, 8D measure-polytope8), geoyott(id)  1.414214
pendip pentachoron duoprism, vertex figure of icoy  1.054093
recto rectified octeract, rectified hexadecazetton  1.224745
rek rectified diacosipentacontahexazetton  1
rene rectified enneazetton, vertex figure of henne  0.881917
ribfoh rectified diacositetracont-dischiliahectohexaconta-zettic octacomb, Gosset heptacomb 05,2,1  
riffy rectified dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton, t1(41,2)  1.732051
robay rectified diacositetracont-myriaheptachiliadiacosioctaconta-zetton, t1(21,4)  2.645751
rocalbroc roc atop inverted broc, oca-first subsegment of fy  1
rocpy rectified-octaexonal pyramid, vertex pyramid of demiocteract  1
satpeb small triprismated bi-enneazetton, triruncinated enneazetton  1.732051
soro small rhombated octeract, cantellated octeract  3.040171
soxeb small exiated bi-enneazetton, heptellated enneazetton, expanded enneazetton  1
spene small prismated enneazetton, runcinated enneazetton  1.452966
spuho small petated hemiocteract  1.414214
squahop square - heptapenton duoprism, vertex figure of barn  0.963624
srek small rhombated diacosipentacontahexazetton, cantellated octacross  1.732051
srene small rhombated enneazetton, cantellated enneazetton  1.452966
tark trirectified diacosipentacontahexazetton  1.414214
tek truncated diacosipentacontahexazetton, truncated octacross  1.581139
tene truncated enneazetton  1.414214
tethix tetrahedron-hexateron duoprism, vertex figure of treday  0.889757
tettac tetrahedron-triacontiditeron duoprism, vertex figure of tarv  0.935414
thocto truncated hemiocteract  2.645751
tiffy truncated dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton  2.645751
toby (old: tobay) truncated diacositetracont-myriaheptachiliadiacosioctaconta-zetton  4
tocto truncated octeract  3.232607
torfy trirectified dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton, t3(41,2)  3.162278
trene trirectified enneazetton  1.054093
trigee triangle - hexacontitetrapeton duoprism, vertex figure of brav  0.912871
trihop triangle - heptapenton duoprism, vertex figure of breday  0.872872
triphix triangle - hexateron duoprismatic prism, vertex figure of ribfoh  1
triquip triangle-triangle-triangle-triangle-tetraprism (or: -quadprism)  1.154701
tro trirectified octeract, trirectified hexadecazetton  1.581139
zeep hecatonicosoctaexon prism, vertex figure of riv  0.866025
zeepy zee pyramid, heptacross pyramid, vertex pyramid of ek  0.707107

Count of actually available polyzetta: 61



top of page

---- 9D ----


Acronym Name Circumradius
barn birectified enneract, birectified octadecayotton  1.870829
brav birectified pentacosidodecayotton  1.224745
breday birectified decayotton  1.024695
day decayotton, 9D simplex9), pyroxenn(id), enneazettal pyramid, vertex figure of ux  0.670820
ekip diacosipentacontahexazetton prism, vertex figure of rake  0.866025
enep enneazetton prism, vertex figure of ru  0.833333
enne enneract, octadecayotton, 9D measure-polytope9), geoxenn(id)  1.500000
henne demi-enneract  1.060660
icoy icosayotton, quadrirectified decayotton, equatorial cross-section of (vertex first) 1/q-deker  1.118034
reday rectified decayotton, vertex figure of hede  0.894427
ren rectified enneract, rectified octadecayotton  2
riv rectified pentacosidodecayotton  1
squoc square - octaexon duoprism, vertex figure of brade  0.968246
tarv trirectified pentacosidodecayotton  1.414214
treday trirectified decayotton  1.095445
vee pentacosidodecayotton, enneacross9), aeroxenn(id), enneazettal antiprism, vertex figure of ka  0.707107

Count of actually available polyyotta: 16



top of page

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


Acronym Name Circumradius
brade birectified dekeract, birectified icosaxennon  2
deker dekeract, icosaxennon, 10D measure-polytope10), geodak(id)  1.581139
hede demi-dekeract  1.118034
ka chilliaicositetraxennon, decacross10), aerodak(id), decayottal antiprism  0.707107
rade rectified dekeract, rectified icosaxennon  2.121320
rake rectified chilliaicositetraxennon  1
ru rectified hendecaxennon, rectified undecaxennon  0.904534
ux hendecaxennon, undecaxennon, 10D simplex10), pyrodak(id), decayottal pyramid  0.674200

Count of actually available polyxenna: 8



© 2004-2018
top of page