List of uniform polychora

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This list of uniform polychora is sorted based on Jonathan Bowers' Polychoron Site. Currently, 2191 uniform polychora are known, plus two infinite families: the polygonal duoprisms and polygonal-antiprismatic prisms. At least 305 fissary polychora (plus an unknown number in the last three categories) are excluded from the main count.

Category A: Duoprisms (infinite)[edit | edit source]

These are prism products of two polygons. A subset of these are the prisms of 3-dimensional prisms. They have either tetragonal disphenoid (for n,n-duoprisms) or digonal disphenoid (m,n-duoprisms) vertex figures.

Name OBSA Picture Coxeter diagram Vertex figure Cells Army Regiment Company Symmetry
Triangular duoprism Triddip Tetragonal disphenoid 6 trip Triddip
9 vertices
Triddip
18 edges
A2≀S2
Triangular-square duoprism Tisdip Digonal disphenoid 4 trip
3 cube
Tisdip
12 vertices
Tisdip
24 edges
A2×B2
Triangular-pentagonal duoprism Trapedip Digonal disphenoid 5 trip
3 pip
Trapedip
15 vertices
Trapedip
30 edges
A2×H2
Triangular-pentagrammic duoprism Tistadip Digonal disphenoid 5 trip
3 stip
Semiuniform

Trapedip

Tistadip
30 edges
A2×H2
Square-pentagonal duoprism Squipdip Digonal disphenoid 5 cube
4 pip
Squipdip
20 vertices
Squipdip
40 edges
B2×H2
Square-pentagrammic duoprism Sistadip Digonal disphenoid 5 cube
4 stip
Semiuniform

Squipdip

Sistadip
40 edges
B2×H2
Pentagonal duoprism Pedip Tetragonal disphenoid 10 pip Pedip
25 vertices
Pedip
50 edges
H2≀S2
Pentagonal-pentagrammic duoprism Starpedip Digonal disphenoid 5 pip
5 stip
Semiuniform

Pedip

Starpedip
50 edges
H2×H2
Pentagrammic duoprism Stardip Tetragonal disphenoid 10 stip Pedip Stardip
50 edges
H2≀S2

Category B: Antiduoprisms (infinite)[edit | edit source]

These are prisms of 3-dimensional antiprisms. Their vertex figures are isosceles trapezoidal pyramids or crossed isosceles trapezoidal pyramids.

Name OBSA Picture Coxeter diagram Vertex figure Cells Army Regiment Company Symmetry
Square antiprismatic prism Squappip Isosceles trapezoidal pyramid 8 trip
2 cube
2 squap
Squappip
16 vertices
Squappip
40 edges
(I2(8)×A1)+×A1
Pentagonal antiprismatic prism Pappip Isosceles trapezoidal pyramid 10 trip
2 pip
2 pap
Pappip
20 vertices
Pappip
50 edges
(I2(10)×A1)+×A1
Pentagrammic antiprismatic prism Stappip Isosceles trapezoidal pyramid 10 trip
2 stip
2 stap
Semiuniform

Squipdip
20 vertices

Pappip
50 edges
H2×A1×A1
Hexagonal antiprismatic prism Happip Isosceles trapezoidal pyramid 12 trip
2 hip
2 hap
Happip
24 vertices
Happip
60 edges
(I2(12)×A1)+×A1
Heptagonal antiprismatic prism Heappip Isosceles trapezoidal pyramid 14 trip
2 hep
2 heap
Heappip
28 vertices
Heappip
70 edges
(I2(14)×A1)+×A1
Heptagrammic antiprismatic prism Shappip Isosceles trapezoidal pyramid 14 trip
2 ship
2 shap
Semiuniform

Squahedip
28 vertices

Shappip
70 edges
I2(7)×A1×A1
Great heptagrammic antiprismatic prism Gishappip Isosceles trapezoidal pyramid 14 trip
2 giship
2 gishap
Semiuniform

Heappip

Gishappip
70 edges
(I2(14)×A1)+×A1
Octagonal antiprismatic prism Oappip Isosceles trapezoidal pyramid 16 trip
2 op
2 oap
Oappip
32 vertices
Oappip
80 edges
(I2(16)×A1)+×A1
Octagrammic antiprismatic prism Stoappip Isosceles trapezoidal pyramid 16 trip
2 stop
2 stoap
Semiuniform

Oappip

Stoappip
80 edges
(I2(16)×A1)+×A1

Category 1: Regulars + 1 (#1-17)[edit | edit source]

These are the flag-transitive uniform polychora. There are 6 convex regulars and 10 nonconvex regulars. One quasiregular polychoron is included here for lack of a better placement.

Index Name OBSA Picture Coxeter diagram Vertex figure Cells Army Regiment Company Symmetry
1 Pentachoron Pen Tetrahedron 5 tet Pen
5 vertices
Pen
10 edges
Pen A4
2 Tesseract Tes Tetrahedron 8 cube Tes
16 vertices
Tes
32 edges
Tes B4
3 Hexadecachoron Hex Octahedron 16 tet Hex
8 vertices
Hex
24 edges
Hex B4
4 Icositetrachoron Ico Cube 24 oct Ico
24 vertices
Ico
96 edges
Ico F4
5 Hecatonicosachoron Hi Tetrahedron 120 doe Hi
600 vertices
Hi
1200 edges
Hi H4
6 Hexacosichoron Ex Icosahedron 600 tet Ex
120 vertices
Ex
720 edges
Ex H4
7 Faceted hexacosichoron Fix Great dodecahedron 120 ike Ex Ex Ex H4
8 Great hecatonicosachoron Gohi Small stellated dodecahedron 120 gad Ex Ex Gohi H4
9 Grand hecatonicosachoron Gahi Great icosahedron 120 doe Ex Ex Gohi H4
10 Small stellated hecatonicosachoron Sishi Dodecahedron 120 sissid Ex Sishi
1200 edges
Sishi H4
11 Great grand hecatonicosachoron Gaghi Great stellated dodecahedron 120 gad Ex Sishi Gaghi H4
12 Great stellated hecatonicosachoron Gishi Icosahedron 120 gissid Ex Gishi
720 edges
Gishi H4
13 Grand stellated hecatonicosachoron Gashi Great dodecahedron 120 sissid Ex Gishi Gishi H4
14 Great faceted hexacosichoron Gofix Small stellated dodecahedron 120 gike Ex Gishi Gofix H4
15 Grand hexacosichoron Gax Great icosahedron 600 tet Ex Gishi Gofix H4
16 Great grand stellated hecatonicosachoron Gogishi Tetrahedron 120 gissid Hi Gogishi
1200 edges
Gogishi H4
17 Tesseractihemioctachoron Tho /2 Tetrahemihexahedron 8 tet
4 oct
Hex Hex Hex D4

Category 2: Truncates (#18-38)[edit | edit source]

These are the truncations and quasitruncations of the regular polychora and other non-rectates with uniform vertex figures. Their vertex figures are pyramids of the original edge figures.

Index Name OBSA Picture Coxeter diagram Vertex figure Cells Army Regiment Company Symmetry
18 Truncated pentachoron Tip Triangular pyramid 5 tet
5 tut
Tip
20 vertices
Tip
40 edges
Tip A4
19 Truncated tesseract Tat Triangular pyramid 16 tet
8 tic
Tat
64 vertices
Tat
128 edges
Tat B4
20 Truncated hexadecachoron Thex Square pyramid 8 oct
16 tut
Thex
48 vertices
Thex
120 edges
Thex B4
21 Truncated icositetrachoron Tico Triangular pyramid 24 cube
24 toe
Tico
192 vertices
Tico
384 edges
Tico F4
22 Truncated hecatonicosachoron Thi Triangular pyramid 600 tet
120 tid
Thi
2400 vertices
Thi
4800 edges
Thi H4
23 Truncated hexacosichoron Tex Pentagonal pyramid 120 ike
600 tut
Tex
1440 vertices
Tex
4320 edges
Tex H4
24 Truncated faceted hexacosichoron Tiffix Pentagrammic pyramid 120 gad
120 ti
Tex Tex Tiffix H4
25 Truncated great hecatonicosachoron Tighi Pentagonal pyramid 120 sissid
120 tigid
Semiuniform

Tex

Tighi
4320 edges
Tighi H4
26 Truncated grand hecatonicosachoron Taghi Pentagrammic pyramid 120 gike
120 tid
Semiuniform

Tex

Tighi Taghi H4
27 Truncated great grand hecatonicosachoron Tigaghi Triangular pyramid 120 gissid
120 tigid
Sidpixhi
2400 vertices
Tigaghi
4800 edges
Tigaghi H4
28 Truncated great faceted hexacosichoron Tigfix Pentagonal pyramid 120 sissid
120 tiggy
Semiuniform

Tex

Tigfix
4320 edges
Tigfix H4
29 Truncated grand hexacosichoron Taggix Pentagrammic pyramid 120 gike
600 tut
Semiuniform

Tex

Tigfix Taggix H4
30 Truncated tesseractihemioctachoron Titho /2 Bowtie pyramid 8 thah
8 tut
4 toe
Thex Thex Titho D4
31 Truncated small ditrigonary hexacosihecatonicosachoron Tissidtixhi Ditrigonal pyramid 120 sidtid
600 tut
120 tiggy
Semiuniform

Sidpixhi

Tissidtixhi
8400 edges
Tissidtixhi H4
33 Truncated great ditrigonary hexacosihecatonicosachoron Tiggidtixhi Tripod pyramid 120 gidtid
600 tut
120 ti
Semiuniform

Sidpixhi

Tissidtixhi Tiggidtixhi H4
32 Truncated ditrigonary dishecatonicosachoron Tidtidohi Propeller tripod pyramid 120 ditdid
120 ti
120 tiggy
Semiuniform

Sidpixhi

Tissidtixhi Tidtidohi H4
34 Quasitruncated tesseract Quitit Triangular pyramid 16 tet
8 quith
Sidpith
64 vertices
Quitit
128 edges
Quitit B4
35 Quasitruncated small stellated hecatonicosachoron Quit sishi Triangular pyramid 120 doe
120 quit sissid
Tissidtixhi
2400 vertices
Quit sishi
4800 edges
Quit sishi H4
36 Quasitruncated great stellated hecatonicosachoron Quit gishi Pentagonal pyramid 120 ike
120 quit gissid
Semiuniform

Tex

Quit gishi
4320 edges
Quit gishi H4
37 Quasitruncated grand stellated hecatonicosachoron Quit gashi Pentagrammic pyramid 120 gad
120 quit sissid
Semiuniform

Tex

Quit gishi Quit gashi H4
38 Quasitruncated great grand stellated hecatonicosachoron Quit gogishi Triangular pyramid 600 tet
120 quit gissid
Semiuniform

Sidpixhi

Quit gogishi
4800 edges
Quit gogishi H4

Category 3: Triangular Rectates (#39-59)[edit | edit source]

These are the rectifications of regular polychora where three cells meet at an edge, and their facetings. There are 7 regiments which have 3 members in this category each (two of them have more members in other categories). Their vertex figures are triangular prisms, triangular retroprisms and triangular toroprisms, one of each in each regiment.

Index Name OBSA Picture Coxeter diagram Vertex figure Cells Army Regiment Company Symmetry
39 Rectified pentachoron Rap Triangular prism 5 tet
5 oct
Rap
10 vertices
Rap
30 edges
A4
40 Faceted rectified pentachoron Firp /2 Triangular retroprism 5 tet
10 trip
Rap Rap A4
41 Prismatointercepted pentachoron Pinnip Triangular toroprism 5 oct
10 trip
Rap Rap A4
42 Rectified tesseract Rit Triangular prism 16 tet
8 co
Rit
32 vertices
Rit
96 edges
B4
43 Faceted rectified tesseract Firt Triangular retroprism 16 tet
16 tut
Rit Rit B4
44 Hexadecintercepted tesseract Hinnit Triangular toroprism 8 co
16 tut
Rit Rit B4
45 Rectified icositetrachoron Rico Triangular prism 24 cube
24 co
Rico
96 vertices
Rico
288 edges
F4
46 Faceted rectified icositetrachoron Frico /2 Triangular retroprism 24 cube
24 toe
Rico Rico F4
47 Icositetrintercepted icositetrachoron Ini Triangular toroprism 24 co
24 toe
Rico Rico F4
48 Rectified hecatonicosachoron Rahi Triangular prism 600 tet
120 id
Rahi
1200 vertices
Rahi
3600 edges
H4
49 Faceted rectified hecatonicosachoron Fry /2 Triangular retroprism 600 tet
120 tid
Rahi Rahi H4
50 Small hecatonicosintercepted hecatonicosachoron Shinhi Triangular toroprism 120 id
120 tid
Rahi Rahi H4
51 Rectified small stellated hecatonicosachoron Rasishi Triangular prism 120 doe
120 did
Rahi Rasishi
3600 edges
H4
52 Faceted rectified small stellated hecatonicosachoron Firsashi /2 Triangular retroprism 120 doe
120 ti
Rahi Rasishi H4
53 Hecatonicosintercepted hecatonicosachoron Hinhi Triangular toroprism 120 did
120 ti
Rahi Rasishi H4
54 Rectified great grand hecatonicosachoron Ragaghi Triangular prism 120 gissid
120 did
Rahi Ragaghi
3600 edges
H4
55 Faceted rectified great grand hecatonicosachoron Firgaghi /2 Triangular retroprism 120 gissid
120 tiggy
Rahi Ragaghi H4
56 Medial hecatonicosintercepted hecatonicosachoron Mohiny Triangular toroprism 120 did
120 tiggy
Rahi Ragaghi H4
57 Rectified great grand stellated hecatonicosachoron Rigogishi Triangular prism 600 tet
120 gid
Rahi Rigogishi
3600 edges
H4
58 Faceted rectified great grand stellated hecatonicosachoron Firgogishi /2 Triangular retroprism 600 tet
120 quit gissid
Rahi Rigogishi H4
59 Great hecatonicosintercepted hecatonicosachoron Gohiny Triangular toroprism 120 gid
120 quit gissid
Rahi Rigogishi H4

Category 4: Ico Regiment (#60-72)[edit | edit source]

The icositetrachoron is regular and is also the rectified hexadecachoron and the rectified demitesseract. This category contains all the members of its regiment except ico itself. There are 13 members in this category with three different types of symmetry. Their vertex figures are semi-uniform facetings of a cube. They could also be called the "square rectates."

Index Name OBSA Picture Coxeter diagram Vertex figure Cells Army Regiment Company Symmetry
60 Icositetrahemiicositetrachoron Ihi 24 thah
12 co
Ico
24 vertices
Ico
96 edges
F4/2
61 Octahemihexadecachoron Oh /2 Crossed square prism 8 oct
8 oho
Ico Ico B4
62 Small hexadecahemihexadecachoron Shahoh Inverted square prism 16 oct
8 oho
Ico Ico B4
63 Hexadecahemihexadecachoron Huhoh 16 thah
8 cho
Ico Ico B4
64 Hexadecaoctahemihexadecachoron Hohoh 8 oct
16 thah
8 cho
Ico Ico B4
65 Octahexadecahemihexadecachoron Ohuhoh 8 oct
16 thah
8 co
Ico Ico B4
66 Great hexadecahemihexadecachoron Ghahoh 16 thah
8 co
Ico Ico B4
67 Rectified tesseractihemioctachoron Ratho /2 8 oct
8 thah
4 co
Ico Ico D4
68 Octadishemioctachoron Odho 8 thah
4 oho
4 cho
Ico Ico D4
69 Hexadecaoctadishemioctachoron Hodho 16 oct
8 thah
4 oho
4 cho
Ico Ico D4
70 Hexadecaocta-hemihexadecintercepted hemioctachoron Hoh honho 24 thah
8 cho
4 co
Ico Ico D4
71 Disocta-dishemioctintercepted hemioctachoron Dod honho 16 thah
4 oho
4 cho
4 co
Ico Ico D4
72 Disocta-hemihexadecintercepted hemioctachoron Doh honho 8 oct
8 thah
4 co
8 oho
Ico Ico D4

Category 5: Pentagonal Rectates (#73-132)[edit | edit source]

These are the rectifications of the regular polychora where five cells meet at an edge. There are four regiments with 2 rectates and 13 faceted rectates each. Their vertex figures are pentagonal prisms and their facetings.

Index Name OBSA Picture Coxeter diagram Vertex figure Cells Army Regiment Company Symmetry
73 Rectified hexacosichoron Rox Pentagonal prism 120 ike
600 oct
Rox
720 vertices
Rox
3600 vertices
H4
74 Rectified faceted hexacosichoron Rofix Pentagrammic prism 120 gad
120 id
Rox Rox H4
75 Small prismatohecatonicosachoron Sophi /2 Pentagrammic antiprism 120 gad
720 pip
Rox Rox H4
76 Small pentagonal retroprismatoverted dishecatonicosachoron Sprapivady /2 Pentagonal retroprism 120 ike
120 tid
Rox Rox H4
77 Faceted rectified hexacosichoron Frox Pentagrammic toroprism 120 id
720 pip
Rox Rox H4
78 Retroinverted hexacosihecatonicosachoron Rixhi Pentagonal toroprism 120 tid
600 oct
Rox Rox H4
79 Small retropental hecatonicosachoron Sriphi Pentagonal stephanoid 120 sird Rox Rox H4
80 Invertipental hexacosidishecatonicosachoron Ipixady 120 gad
120 saddid
600 oct
Rox Rox H4
81 Polar facetopental prismatohexacosihecatonicosachoron Lifpipixhi 120 saddid
600 oct
720 pip
Rox Rox H4
82 Intercepted invertipental hexacosidishecatonicosachoron Nipixady 120 gad
120 srid
600 oct
Rox Rox H4
83 Small omnicircumfacetopental trishecatonicosachoron Som fapathi 120 ike
120 id
120 srid
Rox Rox H4
84 Small omnifacetopental trishecatonicosachoron Sofapathi 120 id
120 tid
120 srid
Rox Rox H4
85 Small circumfacetopental trishecatonicosachoron Smiffipathi 120 ike
120 id
120 saddid
Rox Rox H4
86 Pental prismatohecatonicosintercepted hecatonicosachoron Paphiny 120 ike
120 saddid
720 pip
Rox Rox H4
87 Small inverted retropental hecatonicosintercepted dishecatonicosachoron Sirphinady 120 gad
120 tid
120 srid
Rox Rox H4
88 Rectified great hecatonicosachoron Righi Pentagonal prism 120 sissid
120 did
Rox Righi
3600 vertices
H4
89 Rectified grand hecatonicosachoron Raghi Pentagrammic prism 120 gike
600 id
Rox Righi H4
90 Pentagrammal antiprismatoverted hexacosihecatonicosachoron Papvixhi /2 Pentagrammic antiprism 120 gike
600 tut
Rox Righi H4
91 Great pentagonal retroprismatoverted dishecatonicosachoron Giprapivady /2 Pentagonal retroprism 120 sissid
120 tigid
Rox Righi H4
92 Faceted rectified great hecatonicosachoron Froghi Pentagrammic toroprism 120 id
600 tut
Rox Righi H4
93 Retroinverted dishecatonicosachoron Ridhi Pentagonal toroprism 120 did
120 tigid
Rox Righi H4
94 Medial retropental hecatonicosachoron Mriphi Pentagonal stephanoid 120 siddy Rox Righi H4
95 Small invertipental trishecatonicosachoron Sipathi 120 gike
120 sidditdid
120 did
Rox Righi H4
96 Polar facetopental hexacosidishecatonicosachoron Lifpixady 120 sidditdid
120 did
600 tut
Rox Righi H4
97 Small intercepted invertipental trishecatonicosachoron Snipathi 120 gike
120 siid
120 did
Rox Righi H4
98 Medial omnicircumfacetopental trishecatonicosachoron Mom fapathi 120 sissid
120 id
120 siid
Rox Righi H4
99 Great omnifacetopental trishecatonicosachoron Gofapathi 120 id
120 tigid
120 siid
Rox Righi H4
100 Medial circumfacetopental trishecatonicosachoron Mim fipathi 120 sissid
120 id
120 sidditdid
Rox Righi H4
101 Pental hexacosihecatonicosintercepted hecatonicosachoron Pixhiny 120 sissid
120 sidditdid
600 tut
Rox Righi H4
102 Great inverted retropental hecatonicosintercepted dishecatonicosachoron Girphinady 120 gike
120 tigid
120 siid
Rox Righi H4
103 Rectified great stellated hecatonicosachoron Ragishi Pentagonal prism 120 ike
120 gid
Rox Ragishi
3600 vertices
H4
104 Rectified grand stellated hecatonicosachoron Ragashi Pentagrammic prism 120 gad
120 did
Rox Ragishi H4
105 Small pentagrammal antiprismatoverted dishecatonicosachoron Spapivady /2 Pentagrammic antiprism 120 gad
120 quit sissid
Rox Ragishi H4
106 Pentagonal retroprismatoverted hexacosihecatonicosachoron Prap vixhi /2 Pentagonal retroprism 120 ike
600 tut
Rox Ragishi H4
107 Faceted rectified great stellated hecatonicosachoron Frogshi Pentagrammic toroprism 120 did
120 quit sissid
Rox Ragishi H4
108 Retroinverted hecatonicosihexacosichoron Rihix Pentagonal toroprism 120 gid
600 tut
Rox Ragishi H4
109 Great retropental hecatonicosachoron Griphi Pentagonal stephanoid 120 giddy Rox Ragishi H4
110 Medial invertipental trishecatonicosachoron Mipathi 120 gad
120 giid
120 gid
Rox Ragishi H4
111 Small polar facetopental trishecatonicosachoron Sliffipathi 120 giid
120 gid
120 quit sissid
Rox Ragishi H4
112 Medial intercepted invertipental trishecatonicosachoron Minnipathi 120 gad
120 gidditdid
120 gid
Rox Ragishi H4
113 Great omnicircumfacetopental trishecatonicosachoron Gom fapathi 120 ike
120 did
120 gidditdid
Rox Ragishi H4
114 Omnifacetopental hexacosidishecatonicosachoron Ofapaxady 120 did
600 tut
120 gidditdid
Rox Ragishi H4
115 Great circumfacetopental trishecatonicosachoron Gam fipathi 120 ike
120 did
120 giid
Rox Ragishi H4
116 Small pental dishecatonicosintercepted hecatonicosachoron Spidhiny 120 ike
120 giid
120 quit sissid
Rox Ragishi H4
117 Inverted retropental hexacosintercepted dishecatonicosachoron Irp xanady 120 gad
600 tut
120 gidditdid
Rox Ragishi H4
118 Rectified great faceted hexacosichoron Rigfix Pentagonal prism 120 sissid
120 gid
Rox Rigfix
3600 vertices
H4
119 Rectified grand hexacosichoron Raggix Pentagrammic prism 120 gike
600 oct
Rox Rigfix H4
120 Great pentagrammal antiprismatoverted dishecatonicosachoron Gippapivady /2 Pentagrammic antiprism 120 gike
120 quit gissid
Rox Rigfix H4
121 Quasiprismatohecatonicosachoron Quiphi /2 Pentagonal retroprism 120 sissid
720 stip
Rox Rigfix H4
122 Faceted rectified great faceted hexacosichoron Frogfix Pentagrammic toroprism 600 oct
120 quit gissid
Rox Rigfix H4
123 Retroinverted prismatohecatonicosachoron Ripahi Pentagonal toroprism 120 gid
720 stip
Rox Rigfix H4
124 Grand retropental hecatonicosachoron Graphi Pentagonal stephanoid 120 gird Rox Rigfix H4
125 Great invertipental trishecatonicosachoron Gipathi 120 gike
120 qrid
120 gid
Rox Rigfix H4
126 Great polar facetopental trishecatonicosachoron Gliffipathi 120 qrid
120 gid
120 quit gissid
Rox Rigfix H4
127 Great intercepted invertipental trishecatonicosachoron Ganipathi 120 gike
120 gaddid
120 gid
Rox Rigfix H4
128 Omnicircumfacetopental hexacosidishecatonicosachoron Omfapaxady 120 sissid
600 oct
120 gaddid
Rox Rigfix H4
129 Omnifacetopental prismatohexacosihecatonicosachoron Ofpipixhi 600 oct
720 stip
120 gaddid
Rox Rigfix H4
130 Circumfacetopental hexacosidishecatonicosachoron Mif pixady 120 sissid
600 oct
120 qrid
Rox Rigfix H4
131 Great pental dishecatonicosintercepted hecatonicosachoron Gipdohiny 120 sissid
120 qrid
120 quit gissid
Rox Rigfix H4
132 Inverted retropental prismatointercepted dishecatonicosachoron Irp panady 120 gike
720 stip
120 gaddid
Rox Rigfix H4

Category 6: Sphenoverts (#133-297)[edit | edit source]

This category includes the cantellated polychora, all polychora with wedge vertex figures, and their facetings. There are 24 regiments with 7 members each, although the rico regiment contains 3 members counted previously.

Index Name OBSA Picture Coxeter diagram Vertex figure Cells Army Regiment Company Symmetry
133 Small rhombated pentachoron Srip Wedge 5 oct
5 co
10 trip
Srip
30 vertices
Srip
90 edges
A4
134 Retrosphenoverted trispentachoron Rawvtip Crossed wedge 5 oct
5 oho
5 tut
Srip Srip A4
135 Small rhombic dispentachoron Sirdop 5 tut
5 cho
10 trip
Srip Srip A4
136 Pseudorhombic prismatopentachoron Pirpop 5 tut
10 trip
10 hip
Srip Srip A4
137 Grand rhombic prismatopentachoron Garpop 5 cho
10 hip
Srip Srip A4
138 Prismatopentintercepted dispentachoron Pippindip Inverted wedge 5 oct
5 co
5 tut
10 hip
Srip Srip A4
139 Prismatointercepted prismatodispentachoron Pinnipdip 5 oct
5 oho
10 trip
10 hip
Srip Srip A4
140 Small rhombated tesseract Srit Wedge 16 oct
8 sirco
32 trip
Srit
96 vertices
Srit
288 edges
B4
141 Retrosphenoverted tesseractitesseractihexadecachoron Rawvatoth Crossed wedge 16 oct
8 socco
8 tic
Srit Srit B4
142 Small rhombic disoctachoron Sirdo 8 tic
8 sroh
32 trip
Srit Srit B4
143 Small pseudorhombic prismatotesseract Spript 8 tic
32 trip
24 op
Srit Srit B4
144 Grand rhombic prismatotesseract Garpit 8 sroh
24 op
Srit Srit B4
145 Prismatotesseractintercepted tesseractihexadecachoron Pattinoth Inverted wedge 16 oct
8 sirco
8 tic
24 op
Srit Srit B4
146 Prismatointercepted prismatotesseractihexadecachoron Pinpith 16 oct
8 socco
32 trip
24 op
Srit Srit B4
147 Retrosphenoverted hexadecatesseractioctachoron Rawvhitto Crossed wedge 8 co
16 oho
8 toe
Rico
96 vertices
Rico
288 edges
B4
148 Small rhombic tesseractihexadecachoron Sirth 8 toe
16 cho
24 cube
Rico Rico B4
149 Grand rhombic dishexadecachoron Gardoh 16 cho
16 toe
Rico Rico B4
150 Hexadecintercepted prismatotesseractihexadecachoron Hinpith 8 co
16 oho
24 cube
16 toe
Rico Rico B4
151 Small rhombated icositetrachoron Srico Wedge 24 co
24 sirco
96 trip
Srico
288 vertices
Srico
864 edges
F4
152 Retrosphenoverted trisicositetrachoron Rawvaty Crossed wedge 24 co
24 socco
24 tic
Srico Srico F4
153 Small rhombic disicositetrachoron Sirdi 24 tic
24 sroh
96 trip
Srico Srico F4
154 Small pseudorhombic disicositetrachoron Spirdy 24 tic
96 trip
24 girco
Srico Srico F4
155 Grand rhombic disicositetrachoron Gardi 24 sroh
24 girco
Srico Srico F4
156 Disicositetrintercepted disicositetrachoron Dindi Inverted wedge 24 co
24 sirco
24 tic
24 girco
Srico Srico F4
157 Icositetrintercepted prismatodisicositetrachoron Inipdi 24 co
24 socco
96 trip
24 girco
Srico Srico F4
158 Small rhombated hecatonicosachoron Srahi Wedge 600 oct
120 srid
1200 trip
Srahi
3600 vertices
Srahi
10800 edges
H4
159 Small retrosphenoverted hexacosidishecatonicosachoron Srawvixady Crossed wedge 600 oct
120 saddid
120 tid
Srahi Srahi H4
160 Small rhombic dishecatonicosachoron Sirdhi 120 tid
120 sird
1200 trip
Srahi Srahi H4
161 Small pseudorhombic prismatohecatonicosachoron Spriphi 120 tid
1200 trip
720 dip
Srahi Srahi H4
162 Grand rhombic prismatohecatonicosachoron Garphi 120 sird
720 dip
Srahi Srahi H4
163 Prismatohecatonicosintercepted hexacosihecatonicosachoron Phinxhi Inverted wedge 600 oct
120 srid
120 tid
720 dip
Srahi Srahi H4
164 Prismatointercepted prismatohexacosihecatonicosachoron Pinpixhi 600 oct
120 saddid
1200 trip
720 dip
Srahi Srahi H4
165 Small rhombated hexacosichoron Srix Wedge 120 id
600 co
720 pip
Srix
3600 vertices
Srix
10800 edges
H4
166 Small retrosphenoverted hecatonicosihexacosihecatonicosachoron Srawv hixhi Crossed wedge 120 id
600 oho
120 ti
Srix Srix H4
167 Rhombic small hexacosihecatonicosachoron Rassixhi 120 ti
600 cho
720 pip
Srix Srix H4
168 Pseudorhombic small dishecatonicosachoron Pirsady 120 ti
720 pip
120 grid
Srix Srix H4
169 Grand rhombic small hexacosihecatonicosachoron Garsixhi 600 cho
120 grid
Srix Srix H4
170 Small dishecatonicosintercepted hexacosihecatonicosachoron Sid hinxhi Inverted wedge 120 id
600 co
120 ti
120 grid
Srix Srix H4
171 Hecatonicosintercepted prismatohexacosihecatonicosachoron Hinpixhi 120 id
600 oho
720 pip
120 grid
Srix Srix H4
172 Small rhombated faceted hexacosichoron Sirfix Wedge 120 did
120 srid
720 stip
Semiuniform

Srix

Sirfix
10800 edges
H4
173 Small retrosphenoverted trishecatonicosachoron Srawvathi Crossed wedge 120 did
120 saddid
120 tigid
Semiuniform

Srix

Sirfix H4
174 Rhombic small hecatonicosihecatonicosachoron Rashihy 120 tigid
120 sird
720 stip
Semiuniform

Srix

Sirfix H4
175 Small pseudorhombic hecatonicosihecatonicosachoron Sprahihy 120 tigid
720 stip
120 grid
Semiuniform

Srix

Sirfix H4
176 Grand rhombic dishecatonicosachoron Garady 120 sird
120 grid
Semiuniform

Srix

Sirfix H4
177 Small dishecatonicosintercepted dishecatonicosachoron Sid hinady Inverted wedge 120 did
120 srid
120 tigid
120 grid
Semiuniform

Srix

Sirfix H4
178 Hecatonicosintercepted prismatodishecatonicosachoron Hinipady 120 did
120 saddid
720 stip
120 grid
Semiuniform

Srix

Sirfix H4
179 Small rhombated small stellated hecatonicosachoron Sirsashi Wedge 120 id
120 raded
1200 trip
Semiuniform

Xhi
3600 vertices

Sirsashi
10800 edges
H4
180 Medial retrosphenoverted hecatonicosihexacosihecatonicosachoron Mrawv hixhi Crossed wedge 120 id
120 ided
600 tut
Semiuniform

Xhi

Sirsashi H4
181 Rhombic small hecatonicosihexacosichoron Rashix 600 tut
120 ri
1200 trip
Semiuniform

Xhi

Sirsashi H4
182 Pseudorhombic small hexacosihecatonicosachoron Pirsixhi 600 tut
1200 trip
120 grid
Semiuniform

Xhi

Sirsashi H4
183 Grand rhombic small dishecatonicosachoron Garsady 120 ri
120 grid
Semiuniform

Xhi

Sirsashi H4
184 Small hexacosihecatonicosintercepted dishecatonicosachoron Sixhinady Inverted wedge 120 id
120 raded
600 tut
120 grid
Semiuniform

Xhi

Sirsashi H4
185 Small hecatonicosintercepted prismatodishecatonicosachoron Shinipady 120 id
120 ided
1200 trip
120 grid
Semiuniform

Xhi

Sirsashi H4
186 Small rhombated great hecatonicosachoron Sirghi Wedge 120 did
120 raded
720 pip
Semiuniform

Srix

Sirghi
10800 edges
H4
187 Small retrosphenoverted hecatonicosidishecatonicosachoron Srawv hidy Crossed wedge 120 did
120 ided
120 ti
Semiuniform

Srix

Sirghi H4
188 Rhombic small dishecatonicosachoron Rassady 120 ti
120 ri
720 pip
Semiuniform

Srix

Sirghi H4
189 Pseudorhombic small hecatonicosihexacosichoron Pirshix 120 ti
720 pip
600 toe
Semiuniform

Srix

Sirghi H4
190 Grand rhombic small hecatonicosihexacosichoron Garshix 120 ri
600 toe
Semiuniform

Srix

Sirghi H4
191 Small hecatonicosihexacosintercepted dishecatonicosachoron Shixanady Inverted wedge 120 did
120 raded
120 ti
600 toe
Semiuniform

Srix

Sirghi H4
192 Small hexacosintercepted prismatodishecatonicosachoron Sixnapady 120 did
120 ided
720 pip
600 toe
Semiuniform

Srix

Sirghi H4
193 Small rhombated grand hecatonicosachoron Sraghi Wedge 120 gid
120 srid
720 stip
Semiuniform

Srix

Sraghi
10800 edges
H4
194 Retrosphenoverted trishecatonicosachoron Rawvathi Crossed wedge 120 gid
120 saddid
120 tigid
Semiuniform

Srix

Sraghi H4
195 Small rhombic hecatonicosihecatonicosachoron Sirhihy 120 tigid
120 sird
720 stip
Semiuniform

Srix

Sraghi H4
196 Pseudorhombic dishecatonicosachoron Pirdy 120 tigid
720 stip
120 quitdid
Semiuniform

Srix

Sraghi H4
197 Grand rhombic hecatonicosihecatonicosachoron Garhihy 120 sird
120 quitdid
Semiuniform

Srix

Sraghi H4
198 Dishecatonicosintercepted dishecatonicosachoron Dohinady Inverted wedge 120 gid
120 srid
120 tigid
120 quitdid
Semiuniform

Srix

Sraghi H4
199 Hecatonicosintercepted hecatonicosiprismatohecatonicosachoron Hinhiphi 120 gid
120 saddid
720 stip
120 quitdid
Semiuniform

Srix

Sraghi H4
200 Small rhombated great grand hecatonicosachoron Sirgaghi Wedge 120 gid
120 raded
1200 trip
Semiuniform

Xhi

Sirgaghi
10800 edges
H4
201 Great retrosphenoverted hecatonicosihexacosihecatonicosachoron Grawv hixhi Crossed wedge 120 gid
120 ided
600 tut
Semiuniform

Xhi

Sirgaghi H4
202 Rhombic great hecatonicosihexacosichoron Raghix 600 tut
120 ri
1200 trip
Semiuniform

Xhi

Sirgaghi H4
203 Pseudorhombic great hexacosihecatonicosachoron Pirgixhi 600 tut
1200 trip
120 gaquatid
Semiuniform

Xhi

Sirgaghi H4
204 Grand rhombic great dishecatonicosachoron Gargady 120 ri
120 gaquatid
Semiuniform

Xhi

Sirgaghi H4
205 Great hexacosihecatonicosintercepted dishecatonicosachoron Gixhinady Inverted wedge 120 gid
120 raded
600 tut
120 gaquatid
Semiuniform

Xhi

Sirgaghi H4
206 Great hecatonicosintercepted prismatodishecatonicosachoron Ghinipady 120 gid
120 ided
1200 trip
120 gaquatid
Semiuniform

Xhi

Sirgaghi H4
207 Small rhombated grand stellated hecatonicosachoron Sirgashi Wedge 120 did
120 raded
720 stip
Srahi Sirgashi
10800 edges
H4
208 Great retrosphenoverted hecatonicosidishecatonicosachoron Grawv hidy Crossed wedge 120 did
120 ided
120 tiggy
Srahi Sirgashi H4
209 Rhombic great dishecatonicosachoron Raggady 120 tiggy
120 ri
720 stip
Srahi Sirgashi H4
210 Pseudorhombic great hecatonicosihexacosichoron Pirghix 120 tiggy
720 stip
600 toe
Srahi Sirgashi H4
211 Grand rhombic great hecatonicosihexacosichoron Garghix 120 ri
600 toe
Srahi Sirgashi H4
212 Great hecatonicosihexacosintercepted dishecatonicosachoron Ghixanady Inverted wedge 120 did
120 raded
120 tiggy
600 toe
Srahi Sirgashi H4
213 Great hexacosintercepted prismatodishecatonicosachoron Gixnapady 120 did
120 ided
720 stip
600 toe
Srahi Sirgashi H4
214 Small rhombated grand hexacosichoron Sirgax Wedge 120 gid
600 co
720 stip
Semiuniform

Srahi

Sirgax
10800 edges
H4
215 Grand retrosphenoverted hecatonicosihexacosihecatonicosachoron Garawv hixhi Crossed wedge 120 gid
600 oho
120 tiggy
Semiuniform

Srahi

Sirgax H4
216 Rhombic great hexacosihecatonicosachoron Raggixhi 120 tiggy
600 cho
720 stip
Semiuniform

Srahi

Sirgax H4
217 Pseudorhombic great dishecatonicosachoron Pirgady 120 tiggy
720 stip
120 gaquatid
Semiuniform

Srahi

Sirgax H4
218 Grand rhombic great hexacosihecatonicosachoron Gargixhi 600 cho
120 gaquatid
Semiuniform

Srahi

Sirgax H4
219 Great dishecatonicosintercepted hexacosihecatonicosachoron Gid hinxhi Inverted wedge 120 gid
600 co
120 tiggy
120 gaquatid
Semiuniform

Srahi

Sirgax H4
220 Hecatonicosintercepted prismatohecatonicosihexacosichoron Hin phix 120 gid
600 oho
720 stip
120 gaquatid
Semiuniform

Srahi

Sirgax H4
221 Sphenoverted tesseractitesseractihexadecachoron Wavitoth Wedge 16 oct
8 gocco
8 quith
Srit Wavitoth
288 edges
B4
222 Quasirhombated tesseract Qrit Crossed wedge 16 oct
8 querco
32 trip
Srit Wavitoth B4
223 Great rhombic disoctachoron Girdo 8 quith
8 groh
32 trip
Srit Wavitoth B4
224 Great pseudorhombic prismatotesseract Gapript 8 quith
32 trip
24 stop
Srit Wavitoth B4
225 Grand quasirhombic prismatotesseract Gaqript 8 groh
24 stop
Srit Wavitoth B4
226 Disprismatointercepted tesseractihexadecachoron Dippanoth Inverted wedge 16 oct
8 gocco
32 trip
24 stop
Srit Wavitoth B4
227 Prismatointercepted tesseractitesseractihexadecachoron Pinnatoth 16 oct
8 querco
8 quith
24 stop
Srit Wavitoth B4
228 Sphenoverted trisicositetrachoron Wavaty Wedge 24 co
24 gocco
24 quith
Srico Wavaty
864 edges
F4
229 Quasirhombated icositetrachoron Qrico Crossed wedge 24 co
24 querco
96 trip
Srico Wavaty F4
230 Great rhombic disicositetrachoron Girdi 24 quith
24 groh
96 trip
Srico Wavaty F4
231 Great pseudorhombic disicositetrachoron Gapirdy 24 quith
96 trip
24 quitco
Srico Wavaty F4
232 Grand quasirhombic disicositetrachoron Gaquerdy 24 groh
24 quitco
Srico Wavaty F4
233 Prismatoicositetrintercepted disicositetrachoron Pindi Inverted wedge 24 co
24 gocco
96 trip
24 quitco
Srico Wavaty F4
234 Icositetrintercepted trisicositetrachoron Inti 24 co
24 querco
24 quith
24 quitco
Srico Wavaty F4
235 Small sphenoverted ditrigonal trishecatonicosachoron Swav ditathi Wedge 120 id
120 gidditdid
120 quit sissid
Srahi Swav ditathi
10800 edges
H4
236 Great retrosphenoverted trishecatonicosachoron Grawvathi Crossed wedge 120 id
120 giid
120 ti
Srahi Swav ditathi H4
237 Small hecatonicosidishecatonicosachoron Shidy 120 quit sissid
120 giddy
120 ti
Srahi Swav ditathi H4
238 Small retrotrishecatonicosachoron Sirthi 120 quit sissid
120 ti
120 idtid
Srahi Swav ditathi H4
239 Small small dishecatonicosachoron Sisady 120 giddy
120 idtid
Srahi Swav ditathi H4
240 Dishecatonicosintercepted ditrigonal dishecatonicosachoron Dohine dattidy Inverted wedge 120 id
120 gidditdid
120 ti
120 idtid
Srahi Swav ditathi H4
241 Small hecatonicosintercepted trishecatonicosachoron Shinathi 120 id
120 giid
120 quit sissid
120 idtid
Srahi Swav ditathi H4
242 Sphenoverted hecatonicosidishexacosichoron Wavhiddix Wedge 600 oct
120 siid
600 tut
Semiuniform

Srahi

Wavhiddix
10800 edges
H4
243 Retrosphenoverted ditrigonal hexacosidishecatonicosachoron Rawvid tixady Crossed wedge 600 oct
120 sidditdid
120 tid
Semiuniform

Srahi

Wavhiddix H4
244 Small hecatonicosihexacosihecatonicosachoron Shixhi 600 tut
120 siddy
120 tid
Semiuniform

Srahi

Wavhiddix H4
245 Small retrohexacosidishecatonicosachoron Sirxady 600 tut
120 tid
120 grid
Semiuniform

Srahi

Wavhiddix H4
246 Small dishecatonicosachoron Sidahi 120 siddy
120 grid
Semiuniform

Srahi

Wavhiddix H4
247 Dishecatonicosintercepted hecatonicosihexacosichoron Dohinahix Inverted wedge 600 oct
120 siid
120 tid
120 grid
Semiuniform

Srahi

Wavhiddix H4
248 Hecatonicosintercepted hecatonicosidishexacosichoron Hin hiddix 600 oct
120 sidditdid
600 tut
120 grid
Semiuniform

Srahi

Wavhiddix H4
249 Great sphenoverted ditrigonal trishecatonicosachoron Gwav ditathi Wedge 120 id
120 gidditdid
120 quit gissid
Semiuniform

Srahi

Gwav ditathi
10800 edges
H4
250 Great retrosphenoverted hexacosidishecatonicosachoron Grawvixady Crossed wedge 120 id
120 giid
600 tut
Semiuniform

Srahi

Gwav ditathi H4
251 Great hexacosidishecatonicosachoron Gixady 120 quit gissid
120 giddy
600 tut
Semiuniform

Srahi

Gwav ditathi H4
252 Great retrohecatonicosihexacosihecatonicosachoron Girhixhi 120 quit gissid
600 tut
120 idtid
Semiuniform

Srahi

Gwav ditathi H4
253 Great great dishecatonicosachoron Gigady 120 giddy
120 idtid
Semiuniform

Srahi

Gwav ditathi H4
254 Hexacosihecatonicosintercepted ditrigonal dishecatonicosachoron Xhin dattidy Inverted wedge 120 id
120 gidditdid
600 tut
120 idtid
Semiuniform

Srahi

Gwav ditathi H4
255 Medial hecatonicosintercepted trishecatonicosachoron Mohinathi 120 id
120 giid
120 quit gissid
120 idtid
Semiuniform

Srahi

Gwav ditathi H4
256 Small sphenoverted hexacosidishecatonicosachoron Swavixady Wedge 120 gid
120 siid
600 tut
Semiuniform

Srix

Swavixady
10800 edges
H4
257 Small retrosphenoverted ditrigonal trishecatonicosachoron Srawv ditathi Crossed wedge 120 gid
120 sidditdid
120 tid
Semiuniform

Srix

Swavixady H4
258 Small hexacosidishecatonicosachoron Sixady 120 tid
120 siddy
600 tut
Semiuniform

Srix

Swavixady H4
259 Small retrohecatonicosihexacosihecatonicosachoron Sirhixhi 120 tid
600 tut
120 idtid
Semiuniform

Srix

Swavixady H4
260 Small great dishecatonicosachoron Sigady 120 siddy
120 idtid
Semiuniform

Srix

Swavixady H4
261 Great dishecatonicosintercepted dishecatonicosachoron Gid hinady Inverted wedge 120 gid
120 siid
120 tid
120 idtid
Semiuniform

Srix

Swavixady H4
262 Hecatonicosintercepted ditrigonal hexacosidishecatonicosachoron Hind tixady 120 gid
120 sidditdid
600 tut
120 idtid
Semiuniform

Srix

Swavixady H4
263 Sphenoverted ditrigonal hexacosidishecatonicosachoron Wavdatixady Wedge 600 oct
120 gidditdid
120 quit gissid
Semiuniform

Srix

Wavdatixady
10800 edges
H4
264 Retrosphenoverted hecatonicosidishexacosichoron Rawvhiddix Crossed wedge 600 oct
120 giid
600 tut
Semiuniform

Srix

Wavdatixady H4
265 Great hecatonicosihexacosihecatonicosachoron Ghixhi 120 quit gissid
120 giddy
600 tut
Semiuniform

Srix

Wavdatixady H4
266 Great retrohexacosidishecatonicosachoron Girxady 120 quit gissid
600 tut
120 gaquatid
Semiuniform

Srix

Wavdatixady H4
267 Great dishecatonicosachoron Gidahi 120 giddy
120 gaquatid
Semiuniform

Srix

Wavdatixady H4
268 Great hexacosihecatonicosintercepted hexacosihecatonicosachoron Gixhinxhi Inverted wedge 600 oct
120 gidditdid
600 tut
120 gaquatid
Semiuniform

Srix

Wavdatixady H4
269 Hecatonicosintercepted hexacosidishecatonicosachoron Hinxady 600 oct
120 giid
120 quit gissid
120 gaquatid
Semiuniform

Srix

Wavdatixady H4
270 Small sphenoverted trishecatonicosachoron Swavathi Wedge 120 gid
120 siid
120 tiggy
Semiuniform

Srix

Swavathi
10800 edges
H4
271 Great retrosphenoverted ditrigonal trishecatonicosachoron Grawv ditathi Crossed wedge 120 gid
120 sidditdid
120 tigid
Semiuniform

Srix

Swavathi H4
272 Great hecatonicosidishecatonicosachoron Ghidy 120 tiggy
120 siddy
120 tigid
Semiuniform

Srix

Swavathi H4
273 Great retrotrishecatonicosachoron Girthi 120 tiggy
120 tigid
120 idtid
Semiuniform

Srix

Swavathi H4
274 Great small dishecatonicosachoron Gisady 120 siddy
120 idtid
Semiuniform

Srix

Swavathi H4
275 Grand dishecatonicosintercepted dishecatonicosachoron Gad hinady Inverted wedge 120 gid
120 siid
120 tigid
120 idtid
Semiuniform

Srix

Swavathi H4
276 Hecatonicosintercepted ditrigonal trishecatonicosachoron Hind tathi 120 gid
120 sidditdid
120 tiggy
120 idtid
Semiuniform

Srix

Swavathi H4
277 Sphenoverted trishecatonicosachoron Wavathi Wedge 120 id
120 gaddid
120 quit sissid
Semiuniform

Srix

Wavathi
10800 edges
H4
278 Quasirhombated great stellated hecatonicosachoron Qragishi Crossed wedge 120 id
120 qrid
720 pip
Semiuniform

Srix

Wavathi H4
279 Great rhombic hecatonicosihecatonicosachoron Girhihy 120 quit sissid
120 gird
720 pip
Semiuniform

Srix

Wavathi H4
280 Pseudorhombic hecatonicosihecatonicosachoron Pirhihy 120 quit sissid
720 pip
120 quitdid
Semiuniform

Srix

Wavathi H4
281 Grand quasirhombic hecatonicosihecatonicosachoron Gaqrahihy 120 gird
120 quitdid
Semiuniform

Srix

Wavathi H4
282 Small prismatohecatonicosintercepted dishecatonicosachoron Sophinady Inverted wedge 120 id
120 gaddid
720 pip
120 quitdid
Semiuniform

Srix

Wavathi H4
283 Great hecatonicosintercepted trishecatonicosachoron Ghinathi 120 id
120 qrid
120 quit sissid
120 quitdid
Semiuniform

Srix

Wavathi H4
284 Great sphenoverted hexacosidishecatonicosachoron Gwavixady Wedge 600 oct
120 gaddid
120 quit gissid
Semiuniform

Srix

Gwavixady
10800 edges
H4
285 Quasirhombated great grand stellated hecatonicosachoron Qrigogishi Crossed wedge 600 oct
120 qrid
1200 trip
Semiuniform

Srix

Gwavixady H4
286 Great rhombic dishecatonicosachoron Girdhi 120 quit gissid
120 gird
1200 trip
Semiuniform

Srix

Gwavixady H4
287 Great pseudorhombic prismatohecatonicosachoron Gipriphi 120 quit gissid
1200 trip
720 stiddip
Semiuniform

Srix

Gwavixady H4
288 Grand quasirhombic prismatohecatonicosachoron Gaqriphi 120 gird
720 stiddip
Semiuniform

Srix

Gwavixady H4
289 Disprismatointercepted hexacosihecatonicosachoron Dapinxhi Inverted wedge 600 oct
120 gaddid
1200 trip
720 stiddip
Semiuniform

Srix

Gwavixady H4
290 Prismatointercepted hexacosidishecatonicosachoron Pinxady 600 oct
120 qrid
120 quit gissid
720 stiddip
Semiuniform

Srix

Gwavixady H4
291 Great sphenoverted trishecatonicosachoron Gwavathi Wedge 120 did
120 gaddid
120 quit sissid
Semiuniform

Srix

Gwavathi
10800 edges
H4
292 Quasirhombated great faceted hexacosichoron Qrigfix Crossed wedge 120 did
120 qrid
720 pip
Semiuniform

Srix

Gwavathi H4
293 Rhombic great hecatonicosihecatonicosachoron Raghihy 120 quit sissid
120 gird
720 pip
Semiuniform

Srix

Gwavathi H4
294 Great pseudorhombic hecatonicosihecatonicosachoron Gaprahihy 120 quit sissid
720 pip
120 gaquatid
Semiuniform

Srix

Gwavathi H4
295 Grand quasirhombic dishecatonicosachoron Gaqrady 120 gird
120 gaquatid
Semiuniform

Srix

Gwavathi H4
296 Great prismatohecatonicosintercepted dishecatonicosachoron Gophinady Inverted wedge 120 did
120 gaddid
720 pip
120 gaquatid
Semiuniform

Srix

Gwavathi H4
297 Grand hecatonicosintercepted trishecatonicosachoron Gahinathi 120 did
120 qrid
120 quit sissid
120 gaquatid
Semiuniform

Srix

Gwavathi H4

Category 7: Bitruncates (#298-306, F1-F2)[edit | edit source]

These are the bitruncations and biquasitruncations of the regular polychora. They have either tetragonal disphenoid (for doubled symmetry) or digonal disphenoid vertex figures. Two of them are fissary due to coinciding vertices and are generated as double covers.

Index Name OBSA Picture Coxeter diagram Vertex figure Cells Army Regiment Company Symmetry
298 Decachoron Deca Tetragonal disphenoid 10 tut Deca
30 vertices
Deca
60 edges
A4×2
299 Tesseractihexadecachoron Tah Digonal disphenoid 8 toe
16 tut
Tah
96 vertices
Tah
192 edges
B4
300 Tetracontoctachoron Cont Tetragonal disphenoid 48 tic Cont
288 vertices
Cont
576 edges
F4×2
301 Hexacosihecatonicosachoron Xhi Digonal disphenoid 120 ti
600 tut
Xhi
3600 vertices
Xhi
7200 edges
H4
302 Small hecatonicosihecatonicosachoron Shihi Digonal disphenoid 120 tigid
120 tid
Semiuniform

Xhi

Shihi
7200 edges
H4
303 Dishecatonicosachoron Dahi Digonal disphenoid 120 tiggy
120 ti
Semiuniform

Srahi
3600 vertices

Dahi
7200 edges
H4
304 Great hexacosihecatonicosachoron Gixhi Digonal disphenoid 120 tiggy
600 tut
Semiuniform

Srix
3600 vertices

Gixhi
7200 edges
H4
305 Great tetracontoctachoron Gic Tetragonal disphenoid 48 quith Cont Gic
576 edges
F4×2
306 Great hecatonicosihecatonicosachoron Ghihi Digonal disphenoid 120 quit sissid
120 quit gissid
Semiuniform

Xhi

Ghihi
7200 edges
H4
F1 Small tripesic hecatonicosachoron Sitphi /2 Compound of 3 tetragonal disphenoids 120 tigid Hi
600 vertices
Sidtaxhi
3600 edges
H4
F2 Great tripesic hecatonicosachoron Gitphi (o5x5/3x5o)/2 Compound of 3 tetragonal disphenoids 120 quit sissid Hi Gadtaxady
3600 edges
H4

Category 8: Great Rhombates (#307-329)[edit | edit source]

These polychora, which include the cantitruncated polychora, have sphenoid vertex figures.

Index Name OBSA Picture Coxeter diagram Vertex figure Cells Army Regiment Company Symmetry
307 Great rhombated pentachoron Grip Sphenoid 5 toe
5 tut
10 trip
Grip
60 vertices
Grip
120 edges
A4
308 Great rhombated tesseract Grit Sphenoid 8 girco
16 tut
32 trip
Grit
192 vertices
Grit
384 edges
B4
309 Great rhombated icositetrachoron Grico Sphenoid 24 girco
24 tic
96 trip
Grico
576 vertices
Grico
1152 edges
F4
310 Great rhombated hecatonicosachoron Grahi Sphenoid 120 grid
600 tut
1200 trip
Grahi
7200 vertices
Grahi
14400 edges
H4
311 Great rhombated hexacosichoron Grix Sphenoid 600 toe
120 ti
720 pip
Grix
7200 vertices
Grix
14400 edges
H4
312 Great rhombated faceted hexacosichoron Girfix Sphenoid 720 stip
120 tigid
120 grid
Semiuniform Grix Girfix
14400 edges
H4
313 Great rhombated grand hecatonicosachoron Graghi Sphenoid 720 stip
120 tiggy
120 grid
Semiuniform Prahi
7200 vertices
Graghi
14400 edges
H4
314 Great rhombated grand hexacosichoron Graggix Sphenoid 720 stip
600 toe
120 tiggy
Semiuniform Prahi Graggix
14400 edges
H4
315 Great quasirhombated tesseract Gaqrit Sphenoid 32 trip
16 tut
8 quitco
Semiuniform Grit Gaqrit
384 edges
B4
316 Great quasirhombated icositetrachoron Gaqri Sphenoid 96 trip
24 quith
24 quitco
Semiuniform Prico
576 vertices
Gaqri
1152 edges
F4
317 Great quasirhombated great grand hecatonicosachoron Gaqrigaghi Sphenoid 1200 trip
120 quit gissid
120 quitdid
Semiuniform Prahi Gaqrigaghi
14400 edges
H4
318 Great quasirhombated great faceted hexacosichoron Gaqrigafix Sphenoid 720 pip
120 quit sissid
120 gaquatid
Semiuniform Grix Gaqrigafix
14400 edges
H4
319 Great quasirhombated small stellated hecatonicosachoron Gaqrisashi Sphenoid 1200 trip
120 tid
120 quitdid
Semiuniform Grahi Gaqrisashi
14400 edges
H4
320 Great quasirhombated great grand stellated hecatonicosachoron Gaqrigagishi Sphenoid 1200 trip
600 tut
120 gaquatid
Semiuniform Grix Gaqrigagishi
14400 edges
H4
321 Great quasirhombated great stellated hecatonicosachoron Gaqrigashi Sphenoid 720 pip
120 ti
120 gaquatid
Semiuniform Prix Gaqrigashi
14400 edges
H4
322 Tesseractihexadecatruncated tesseractihexadecachoron Thatoth Sphenoid 16 tut
8 tic
8 cotco
Semiuniform Grit Thatoth
384 edges
B4
323 Tesseractihexadecaquasitruncated tesseractihexadecachoron Thaquitoth Sphenoid 16 tut
8 quith
8 cotco
Semiuniform Prit
192 vertices
Thaquitoth
384 edges
B4
324 Icositetraquasitruncated tetracontoctachoron Iquatoc Sphenoid 24 tic
24 quith
24 cotco
Semiuniform Prico Iquatoc
1152 edges
F4
325 Hecatonicosihexacositruncated hecatonicosihexacosichoron Hixthix Sphenoid 600 tut
120 tid
120 idtid
Semiuniform Grahi Hixthix
14400 edges
H4
326 Dishecatonicosatruncated dishecatonicosachoron Dahitady Sphenoid 120 tigid
120 tiggy
120 idtid
Semiuniform Prix
7200 vertices
Dahitady
14400 edges
H4
327 Hecatonicosihecatonicosaquasitruncated dishecatonicosachoron Hihiquatady Sphenoid 120 tid
120 quit gissid
120 idtid
Semiuniform Prahi Hihiquatady
14400 edges
H4
328 Dishecatonicosaquasitruncated dishecatonicosachoron Dahiquatady Sphenoid 120 quit sissid
120 ti
120 idtid
Semiuniform Prahi Dahiquatady
14400 edges
H4
329 Hecatonicosihexacosiquasitruncated hecatonicosihexacosichoron Hixquathix Sphenoid 600 tut
120 quit gissid
120 idtid
Semiuniform Prahi Hixquathix
14400 edges
H4

Category 9: Omnitruncates (#330-351)[edit | edit source]

These polychora are represented by Coxeter-Dynkin diagrams with all nodes ringed. This includes the omnitruncates of regular polychora. Their vertex figures are either phyllic disphenoids (if they have doubled symmetry) or irregular tetrahedra.

Index Name OBSA Picture Coxeter diagram Vertex figure Cells Army Regiment Company Symmetry
330 Great prismatodecachoron Gippid Phyllic disphenoid 20 hip
10 toe
Gippid
120 vertices
Gippid
240 edges
A4×2
331 Great disprismatotesseractihexadecachoron Gidpith Irregular tetrahedron 32 hip
24 op
16 toe
8 girco
Gidpith
384 vertices
Gidpith
768 edges
B4
332 Great prismatotetracontoctachoron Gippic Phyllic disphenoid 192 hip
48 girco
Gippic
1152 vertices
Gippic
2304 edges
F4×2
333 Great disprismatohexacosihecatonicosachoron Gidpixhi Irregular tetrahedron 1200 hip
720 dip
600 toe
120 grid
Gidpixhi
28800 vertices
Gidpixhi
14400 edges
H4
334 Great quasidisprismatotesseractihexadecachoron Gaquidpoth Irregular tetrahedron 32 hip
24 stop
16 toe
8 quitco
Semiuniform

Gidpith

Gaquidpoth
768 edges
B4
335 Great quasiprismatotetracontoctachoron Gaquapac Phyllic disphenoid 192 hip
48 quitco
Semiuniform

Gippic

Gaquapac
2304 edges
F4×2
336 Grand quasidisprismatodishecatonicosachoron Gaquidipdy Irregular tetrahedron 1200 hip
720 dip
120 quitdid
120 gaquatid
Semiuniform

Gidpixhi

Giquidipdy
14400 edges
H4
337 Great quasidisprismatodishecatonicosachoron Goquidipdy Irregular tetrahedron 1200 hip
720 stiddip
120 quitdid
120 grid
Semiuniform

Gidpixhi

Goquidipdy
14400 edges
H4
338 Great quasidisprismatohecatonicosihecatonicosachoron Gaquidphihi Irregular tetrahedron 720 dip
720 stiddip
120 grid
120 gaquatid
Semiuniform

Gidpixhi

Gaquidphihi
14400 edges
H4
339 Great quasidisprismatohexacosihecatonicosachoron Gaquidapixhi Irregular tetrahedron 1200 hip
720 stiddip
600 toe
120 gaquatid
Semiuniform

Gidpixhi

Gaquidapixhi
14400 edges
H4
340 Tesseractihexadecatruncated prismatotesseractihexadecachoron Thatpath Irregular tetrahedron 24 stop
16 toe
8 girco
8 cotco
Semiuniform

Gidpith

Thatpath
768 edges
B4
341 Tesseractihexadecaquasitruncated prismatotesseractihexadecachoron Thaquitpath Irregular tetrahedron 24 op
16 toe
8 quitco
8 cotco
Semiuniform

Gidpith

Thaquitpath
768 edges
B4
342 Icositetraquasitruncated prismatotetracontoctachoron Iquatpic Irregular tetrahedron 96 hip
24 girco
24 quitco
24 cotco
Semiuniform

Gippic

Iquatpic
2304 edges
F4×2
343 Hecatonicosihexacositruncated prismatohecatonicosihexacosichoron Hixtaphix Irregular tetrahedron 720 dip
600 toe
120 grid
120 idtid
Semiuniform

Gidpixhi

Hixtaphix
14400 edges
H4
344 Dishecatonicosatruncated prismatodishecatonicosachoron Dohitipady Irregular tetrahedron 1200 hip
120 grid
120 gaquatid
120 idtid
Semiuniform

Gidpixhi

Dohitipady
14400 edges
H4
345 Hecatonicosihexacosiquasitruncated prismatohecatonicosihexacosichoron Hixquitphix Irregular tetrahedron 720 dip
600 toe
120 gaquatid
120 idtid
Semiuniform

Gidpixhi

Hixquitphix
14400 edges
H4
346 Small dishecatonicosaquasitruncated prismatodishecatonicosachoron Sidhiquit paddy Irregular tetrahedron 720 dip
120 grid
120 quitdid
120 idtid
Semiuniform

Gidpixhi

Sidhiquit paddy
14400 edges
H4
347 Great dishecatonicosaquasitruncated prismatodishecatonicosachoron Gidhiquit paddy Irregular tetrahedron 720 stiddip
120 gaquatid
120 quitdid
120 idtid
Semiuniform

Gidpixhi

Gidhiquit paddy
14400 edges
H4
348 Distetracontoctachoron Doc Phyllic disphenoid 48 girco
48 quitco
Semiuniform

Gippic

Doc
2304 edges
F4×2
349 Tetracontoctarhombated tetracontoctachoron Croc Phyllic disphenoid 48 girco
48 cotco
Semiuniform

Gippic

Croc
2304 edges
F4×2
350 Tetracontoctaquasirhombated tetracontoctachoron Coqroc Phyllic disphenoid 48 quitco
48 cotco
Semiuniform

Gippic

Coqroc
2304 edges
F4×2
351 Hexacositrishecatonicosachoron Xithi Irregular tetrahedron 600 toe
120 quitdid
120 grid
120 gaquatid
Semiuniform

Gidpixhi

Xithi
14400 edges
H4

Category 10: Prismatorhombates (#352-441)[edit | edit source]

These are polychora with isosceles trapezoidal pyramid or skewed rectangular pyramid vertex figures and their facetings, including runcitruncations of the regular polychora. There are 30 regiments of 3.

Index Name OBSA Picture Coxeter diagram Vertex figure Cells Army Regiment Company Symmetry
352 Prismatorhombated pentachoron Prip 10 trip
10 hip
5 tut
5 co
Prip
60 vertices
Prip
150 edges
A4
353 Prismatotrispentachoron Pittip 10 trip
5 tut
5 oho
5 toe
Prip Prip A4
354 Rhombiprismic dispentachoron Ripdip 5 cho
5 toe
10 hip
Prip Prip A4
355 Prismatorhombated tesseract Prit 24 cube
32 hip
16 tut
8 sirco
Prit
192 vertices
Prit
480 edges
B4
356 Small cubihexadecadisoctachoron Sichado 24 cube
16 tut
8 sirco
8 girco
Prit Prit B4
357 Small rhombiprismic disoctachoron Sirpdo 8 sroh
8 girco
32 hip
Prit Prit B4
358 Prismatorhombated hexadecachoron Proh 32 trip
24 op
16 co
8 tic
Proh
192 vertices
Proh
480 edges
B4
359 Small prismatohexadecadisoctachoron Siphado 32 trip
16 oho
8 tic
8 girco
Proh Proh B4
360 Small rhombiprismic tesseractihexadecachoron Sirpith 16 cho
24 op
8 girco
Proh Proh B4
361 Prismatorhombated icositetrachoron Prico 96 trip
96 hip
24 toe
24 sirco
Prico
576 vertices
Prico
1440 edges
F4
362 Small prismatotrisicositetrachoron Sipti 96 trip
24 toe
24 socco
24 girco
Prico Prico F4
363 Small rhombiprismic disicosatetrachoron Sirpdi 24 sroh
24 girco
96 hip
Prico Prico F4
364 Prismatorhombated hecatonicosachoron Prahi 720 pip
1200 hip
600 toe
120 srid
Prahi
7200 vertices
Prahi
18000 edges
H4
365 Small prismatohexacosidishecatonicosachoron Spixady 720 pip
600 toe
120 saddid
120 grid
Prahi Prahi H4
366 Small rhombiprismic dishecatonicosachoron Sripady 120 sird
120 grid
1200 hip
Prahi Prahi H4
367 Prismatorhombated hexacosichoron Prix 1200 trip
720 dip
600 co
120 tid
Prix
7200 vertices
Prix
18000 edges
H4
368 Small prismatohexacosihecatonicosihecatonicosachoron Spixhihy 1200 trip
600 oho
120 tid
120 grid
Prix Prix H4
369 Small rhombiprismic hexacosihecatonicosachoron Sirpaxhi 600 cho
120 grid
720 dip
Prix Prix H4
370 Prismatorhombated stellated hecatonicosachoron Pirshi 720 stip
1200 hip
120 ti
120 raded
Semiuniform

Grix
7200 vertices

Pirshi
18000 edges
H4
371 Small prismatohecatonicosihecatonicosihexacosichoron Sphihix 720 stip
600 toe
120 ti
120 ided
Semiuniform

Grix

Pirshi H4
372 Small rhombiprismatohecatonicosihexacosichoron Sriphix 120 ri
600 toe
1200 hip
Semiuniform

Grix

Pirshi H4
373 Prismatorhombated great hecatonicosachoron Pirghi 720 pip
720 dip
120 tigid
120 raded
Semiuniform

Grix

Pirghi
18000 edges
H4
374 Small prismatohecatonicosidishecatonicosachoron Siphidy 720 pip
120 tigid
120 ided
120 grid
Semiuniform

Grix

Pirghi H4
375 Small rhombiprismic hecatonicosihecatonicosachoron Sirphihy 120 ri
720 dip
120 grid
Semiuniform

Grix

Pirghi H4
376 Prismatorhombated great grand hecatonicosachoron Pirgaghi 720 pip
1200 hip
120 tiggy
120 raded
Semiuniform

Prix

Pirgaghi
18000 edges
H4
377 Great prismatohecatonicosihecatonicosihexacosichoron Giphihix 720 pip
600 toe
120 tiggy
120 ided
Semiuniform

Prix

Pirgaghi H4
378 Great rhombiprismic hecatonicosihexacosichoron Griphix 120 ri
1200 hip
600 toe
Semiuniform

Prix

Pirgaghi H4
379 Quasiprismatorhombated hexadecachoron Quiproh 32 trip
24 stop
16 co
8 quith
Semiuniform

Prit

Quiproh
480 edges
B4
380 Great prismatohexadecadisoctachoron Giphado 32 trip
16 oho
8 quith
8 quitco
Semiuniform

Prit

Quiproh B4
381 Great rhombiprismic tesseractihexadecachoron Girpith 16 cho
24 stop
8 quitco
Semiuniform

Prit

Quiproh B4
382 Quasiprismatorhombated faceted hexacosichoron Quippirfix 1200 trip
720 stiddip
120 quit sissid
120 srid
Semiuniform

Prahi

Quippirfix
18000 edges
H4
383 Great prismatotrishecatonicosachoron Gipthi 1200 trip
120 quit sissid
120 saddid
120 quitdid
Semiuniform

Prahi

Quippirfix H4
384 Rhombiprismic dishecatonicosachoron Rappady 120 sird
720 stiddip
120 quitdid
Semiuniform

Prahi

Quippirfix H4
385 Quasiprismatorhombated grand stellated hecatonicosachoron Quippirgashi 720 stip
720 stiddip
120 quit gissid
120 raded
Semiuniform

Prahi

Quippirgashi
18000 edges
H4
386 Great prismatohecatonicosidishecatonicosachoron Giphidy 720 stip
120 quit sissid
120 ided
120 gaquatid
Semiuniform

Prahi

Quippirgashi H4
387 Great rhombiprismic hecatonicosihecatonicosachoron Girphihy 120 ri
720 stiddip
120 gaquatid
Semiuniform

Prahi

Quippirgashi H4
388 Quasiprismatorhombated grand hecatonicosachoron Quippirghi 720 pip
720 stiddip
120 quit gissid
120 srid
Semiuniform

Prahi

Quippirghi
18000 edges
H4
389 Grand prismatotrishecatonicosachoron Gapthi 720 pip
120 quit gissid
120 saddid
120 quitdid
Semiuniform

Prahi

Quippirghi H4
390 Rhombiprismic hecatonicosihecatonicosachoron Raphihy 120 sird
720 stiddip
120 quitdid
Semiuniform

Prahi

Quippirghi H4
391 Quasiprismatorhombated grand hexacosichoron Quippirgax 1200 trip
720 stiddip
600 co
120 quit gissid
Semiuniform

Prahi

Quippirgax
18000 edges
H4
392 Great prismatohexacosihecatonicosihecatonicosachoron Gippixhihy 1200 trip
600 oho
120 quit gissid
120 gaquatid
Semiuniform

Prahi

Quippirgax H4
393 Great rhombiprismic hexacosihecatonicosachoron Girpixhi 600 cho
720 stiddip
120 gaquatid
Semiuniform

Prahi

Quippirgax H4
394 Great cubihexadecadisoctachoron Gichado 24 cube
16 tut
8 gocco
8 quitco
Semiuniform

Proh

Gichado
480 edges
B4
395 Prismatoquasirhombated tesseract Paqrit 24 cube
32 hip
16 tut
8 querco
Semiuniform

Proh

Gichado B4
396 Great rhombiprismic disoctachoron Girpdo 8 groh
8 quitco
32 hip
Semiuniform

Proh

Gichado B4
397 Great prismatotrisicositetrachoron Gipti 96 trip
24 toe
24 gocco
24 quitco
Semiuniform

Grico
576 vertices

Gipti
1440 edges
F4
398 Prismatoquasirhombated icositetrachoron Paqri 96 trip
96 hip
24 toe
24 querco
Semiuniform

Grico

Gipti F4
399 Great rhombiprismic disicositetrachoron Girpdi 24 groh
24 quitco
96 hip
Semiuniform

Grico

Gipti F4
400 Medial prismatotrishecatonicosachoron Mipthi 720 stip
120 tid
120 gaddid
120 quitdid
Semiuniform

Grix

Mipthi
18000 edges
H4
401 Prismatoquasirhombated great stellated hecatonicosachoron Paqrigshi 720 stip
720 dip
120 tid
120 qrid
Semiuniform

Grix

Mipthi H4
402 Medial rhombiprismic hecatonicosihecatonicosachoron Marphihy 120 gird
720 dip
120 quitdid
Semiuniform

Grix

Mipthi H4
403 Small prismatotrishecatonicosachoron Sipthi 1200 trip
120 tigid
120 gaddid
120 quitdid
Semiuniform

Grix

Sipthi
18000 edges
H4
404 Prismatoquasirhombated great faceted hexacosichoron Paqrigafix 1200 trip
720 dip
120 tigid
120 qrid
Semiuniform

Grix

Sipthi H4
405 Medial rhombiprismic dishecatonicosachoron Mirpady 120 gird
720 dip
120 quitdid
Semiuniform

Grix

Sipthi H4
406 Great prismatohexacosidishecatonicosachoron Gippixady 720 stip
600 tut
120 gaddid
120 gaquatid
Semiuniform

Prahi

Gippixady
18000 edges
H4
407 Prismatoquasirhombated great grand stellated hecatonicosachoron Paqrigagishi 720 stip
1200 hip
600 tut
120 qrid
Semiuniform

Prahi

Gippixady H4
408 Great rhombiprismic dishecatonicosachoron Gripady 120 gird
120 gaquatid
1200 hip
Semiuniform

Prahi

Gippixady H4
409 Small tetrisicositetrachoron Suti 24 toe
24 quith
24 sirco
24 quitco
Semiuniform

Prico

Suti
1440 edges
F4
410 Disicositetraquasitruncated disicositetrachoron Diquitdi 24 toe
24 quith
24 socco
24 cotco
Semiuniform

Prico

Suti F4
411 Small rhombic trisicosatetrachoron Sirti 24 sroh
24 quitco
24 cotco
Semiuniform

Prico

Suti F4
412 Disicositetratruncated disicositetrachoron Ditdi 24 toe
24 tic
24 gocco
24 cotco
Semiuniform

Grico

Ditdi
1440 edges
F4
413 Great tetrisicositetrachoron Guti 24 toe
24 tic
24 querco
24 girco
Semiuniform

Grico

Ditdi F4
414 Great rhombic trisicositetrachoron Girti 24 groh
24 cotco
24 girco
Semiuniform

Grico

Ditdi F4
415 Hecatonicosihexacositruncated hexacosihecatonicosachoron Hixtixhi x3x5x5/2o3*a5/3*c 600 tut
120 tigid
120 gaddid
120 idtid
Semiuniform

Grix

Hixtixhi
18000 edges
H4
416 Great hexacositrishecatonicosachoron Gixathi 600 tut
120 tigid
120 qrid
120 grid
Semiuniform

Grix

Hixtixhi H4
417 Great rhombic trishecatonicosachoron Grithi 120 gird
120 idtid
120 grid
Semiuniform

Grix

Hixtixhi H4
418 Hecatonicosihexacosidishecatonicosachoron Hixady 600 co
120 tid
120 quit gissid
120 quitdid
Semiuniform

Prahi

Hixady
18000 edges
H4
419 Hexacosihecatonicosidishecatonicosachoron Xhidy x3o3/2x5x5/3*a3*c 600 oho
120 tid
120 quit gissid
120 idtid
Semiuniform

Prahi

Hixady H4
420 Rhombic hexacosidishecatonicosachoron Rixady 600 cho
120 quitdid
120 idtid
Semiuniform

Prahi

Hixady H4
421 Small hexacositrishecatonicosachoron Sixathi 600 tut
120 quit sissid
120 srid
120 gaquatid
Semiuniform

Prahi

Sixathi
18000 edges
H4
422 Hecatonicosihexacosiquasitruncated hexacosihecatonicosachoron Hixquitixhi x3/2o5x5/3x3*a5*c 600 tut
120 quit sissid
120 saddid
120 idtid
Semiuniform

Prahi

Sixathi H4
423 Small rhombic trishecatonicosachoron Srithi 120 sird
120 gaquatid
120 idtid
Semiuniform

Prahi

Sixathi H4
424 Great ditrigonal prismatotrishecatonicosachoron Gid tipathi 1200 trip
120 ti
120 gidditdid
120 gaquatid
Semiuniform

Grahi
7200 vertices

Gid tipathi
18000 edges
H4
425 Great prismatohecatonicosihexacosihecatonicosachoron Giphixhi 1200 trip
600 toe
120 ti
120 giid
Semiuniform

Grahi

Gid tipathi H4
426 Great small hexacosidishecatonicosachoron Gasixady 120 giddy
120 gaquatid
600 toe
Semiuniform

Grahi

Gid tipathi H4
427 Great ditrigonal hecatonicosiprismatodishecatonicosachoron Gid thipady 720 pip
120 tid
120 gidditdid
120 quitdid
Semiuniform

Prix

Gid thipady
18000 edges
H4
428 Great hecatonicosiprismatodishecatonicosachoron Ghipady 720 pip
120 tid
120 giid
120 grid
Semiuniform

Prix

Gid thipady H4
429 Great hecatonicosihecatonicosihecatonicosachoron Ghiyay 120 giddy
120 quitdid
120 grid
Semiuniform

Prix

Gid thipady H4
430 Great hexacosiprismatodishecatonicosachoron Gixipady 720 pip
600 tut
120 gidditdid
120 gaquatid
Semiuniform

Prix

Gixipady
18000 edges
H4
431 Great prismatohecatonicosidishexacosichoron Giphiddix 720 pip
600 tut
600 toe
120 giid
Semiuniform

Prix

Gixipady H4
432 Great great hexacosidishecatonicosachoron Gigixady 120 giddy
600 toe
120 gaquatid
Semiuniform

Prix

Gixipady H4
433 Small prismatohecatonicosihexacosihecatonicosachoron Sphixhi 1200 trip
600 toe
120 tiggy
120 siid
Semiuniform

Prahi

Sphixhi
18000 edges
H3●I2(10)
434 Small ditrigonal prismatotrishecatonicosachoron Sid tipathi 1200 trip
120 tiggy
120 sidditdid
120 grid
Semiuniform

Prahi

Sphixhi H4
435 Small great hexacosidishecatonicosachoron Sigixady 120 siddy
120 grid
600 toe
Semiuniform

Prahi

Sphixhi H4
436 Small hecatonicosiprismatodishecatonicosachoron Shipady 720 stip
120 quit gissid
120 siid
120 gaquatid
Semiuniform

Prahi

Shipady
18000 edges
H4
437 Small ditrigonal hecatonicosiprismatodishecatonicosachoron Sid thipady 720 stip
120 quit gissid
120 sidditdid
120 quitdid
Semiuniform

Prahi

Shipady H4
438 Small hecatonicosihecatonicosihecatonicosachoron Shiyay 120 siddy
120 quitdid
120 gaquatid
Semiuniform

Prahi

Shipady H4
439 Small prismatohecatonicosidishexacosichoron Sphiddix 720 stip
600 tut
600 toe
120 siid
Semiuniform

Prahi

Sphiddix
18000 edges
H4
440 Small hexacosiprismatodishecatonicosachoron Sixipady 720 stip
600 tut
120 sidditdid
120 grid
Semiuniform

Prahi

Sphiddix H4
441 Small small hexacosidishecatonicosachoron Sasixady 120 siddy
600 toe
120 grid
Semiuniform

Prahi

Sphiddix H4

Category 11: Antipodiumverts (#442-481)[edit | edit source]

These are the uniform polychora with triangular antipodium (or triangular antiprism) vertex figures and their facetings. This includes the runcinations of regular polychora. There are 6 regiments, one which has 5 members and five with 7.

Index Name OBSA Picture Coxeter diagram Vertex figure Cells Army Regiment Company Symmetry
442 Small prismatodecachoron Spid Triangular antiprism 10 tet
20 trip
Spid
20 vertices
Spid
60 edges
A4×2
443 Prismatopentahemidecachoron Piphid Tetrahemihexahedron 5 tet
10 trip
5 co
Spid Spid A4
444 Decahemidecachoron Duhd Crossed triangular prism 10 tet
5 oho
Spid Spid A4×2
445 Prismatohemidecachoron Phud Inverted triangular antiprism 20 trip
5 oho
Spid Spid A4×2
446 Spinoprismatodispentachoron Nipdip 5 tet
10 trip
5 cho
Spid Spid A4
447 Small disprismatotesseractihexadecachoron Sidpith Triangular antipodium 8+24 cube
16 tet
32 trip
Sidpith
64 vertices
Sidpith
192 edges
B4
448 Small tesseractifaceted cubitesseractihexadecachoron Stefacoth Triangular hemiantipodium 16 tet
24 cube
8 sirco
Sidpith Sidpith B4
449 Small hexadecafaceted prismatotesseractioctachoron Shafipto Triangular hemiantipodium 8 cube
32 trip
8 sirco
Sidpith Sidpith B4
450 Small tesseractitesseractihexadecachoron Steth Crossed triangular frustrum 8 cube
16 tet
8 socco
Sidpith Sidpith B4
451 Diprismatotesseract Dippit Inverted triangular antipodium 32 trip
24 cube
8 socco
Sidpith Sidpith B4
452 Small spinoprismatotesseractihexadecachoron Snappoth 16 tet
32 trip
8 sroh
Sidpith Sidpith B4
453 Small spinoprismatotesseractioctachoron Snipto 8 cube
24 cube
8 sroh
Sidpith Sidpith B4
454 Small disprismatohexacosihecatonicosachoron Sidpixhi Triangular antipodium 120 doe
600 tet
720 pip
1200 trip
Sidpixhi
2400 vertices
Sidpixhi
7200 edges
H4
455 Small hecatonicosafaceted prismatohecatonicosihexacosichoron Shif phix Triangular hemiantipodium 600 tet
720 pip
120 srid
Sidpixhi Sidpixhi H4
456 Small hexacosifaceted prismatodishecatonicosachoron Six fipady Triangular hemiantipodium 120 doe
1200 trip
120 srid
Sidpixhi Sidpixhi H4
457 Small hexacosihecatonicosihecatonicosachoron Sixhihy Crossed triangular frustrum 120 doe
600 tet
120 saddid
Sidpixhi Sidpixhi H4
458 Prismatoprismatohecatonicosachoron Paphi Inverted triangular antipodium 720 pip
1200 trip
120 saddid
Sidpixhi Sidpixhi H4
459 Small spinoprismatohexacosihecatonicosachoron Snapaxhi 600 tet
1200 trip
120 sird
Sidpixhi Sidpixhi H4
460 Small spinoprismatodishecatonicosachoron Snappady 120 doe
720 pip
120 sird
Sidpixhi Sidpixhi H4
461 Small disprismatodishecatonicosachoron Siddapady Triangular antipodium 120 gissid
120 doe
720 stip
720 pip
Sidpixhi Siddapady
7200 edges
H4
462 Hecatonicosafaceted prismatodishecatonicosachoron Hi fipady Triangular hemiantipodium 120 gissid
720 pip
120 raded
Sidpixhi Siddapady H4
463 Medial hecatonicosafaceted prismatodishecatonicosachoron Mohi fipady Triangular hemiantipodium 120 doe
720 stip
120 raded
Sidpixhi Siddapady H4
464 Trishecatonicosachoron Tahi Crossed triangular frustrum 120 gissid
120 doe
120 ided
Sidpixhi Siddapady H4
465 Disprismatohecatonicosachoron Daphi Inverted triangular antipodium 720 stip
720 pip
120 ided
Sidpixhi Siddapady H4
466 Small spinoprismatohecatonicosihecatonicosachoron Snaphihy 120 gissid
720 stip
120 ri
Sidpixhi Siddapady H4
467 Great spinoprismatohecatonicosihecatonicosachoron Gnaphihy 120 doe
720 pip
120 ri
Sidpixhi Siddapady H4
468 Small dishexacosidishecatonicosachoron Sadixady Triangular antipodium 120 gissid
600 tet
120 tiggy
600 tut
Semiuniform

Sidpixhi

Sadixady
7200 edges
H4
469 Small hexacosifaceted hexacosidishecatonicosachoron Six fixady Triangular hemiantipodium 120 gissid
600 tut
120 siid
Semiuniform

Sidpixhi

Sadixady H4
470 Small hecatonicosafaceted hexacosidishecatonicosachoron Shi fixady Triangular hemiantipodium 600 tet
120 tiggy
120 siid
Semiuniform

Sidpixhi

Sadixady H4
471 Small ditrigonal hecatonicosihexacosihecatonicosachoron Sidthixhi Crossed triangular frustrum 120 gissid
600 tet
120 sidditdid
Semiuniform

Sidpixhi

Sadixady H4
472 Hecatonicosihecatonicosihexacosichoron Hihix Inverted triangular antipodium 120 tiggy
600 tut
120 sidditdid
Semiuniform

Sidpixhi

Sadixady H4
473 Small spinotrishecatonicosachoron Snathi 120 gissid
120 tiggy
120 siddy
Semiuniform

Sidpixhi

Sadixady H4
474 Small spinohecatonicosidishexacosichoron Sanhiddix 600 tet
600 tut
120 siddy
Semiuniform

Sidpixhi

Sadixady H4
475 Great hexacosihecatonicosidishecatonicosachoron Gixhidy Triangular antipodium 120 doe
600 tet
120 quit gissid
120 quit sissid
Semiuniform

Sidpixhi

Gixhidy
7200 edges
H4
476 Great hecatonicosafaceted hecatonicosihexacosihecatonicosachoron Gohi fohixhi Triangular hemiantipodium 600 tet
120 quit sissid
120 gidditdid
Semiuniform

Sidpixhi

Gixhidy H4
477 Great hexacosifaceted trishecatonicosachoron Gaxifthi Triangular hemiantipodium 120 doe
120 quit gissid
120 gidditdid
Semiuniform

Sidpixhi

Gixhidy H4
478 Great hecatonicosihecatonicosihexacosichoron Gohihix Crossed triangular frustrum 120 doe
600 tet
120 giid
Semiuniform

Sidpixhi

Gixhidy H4
479 Hecatonicosidishecatonicosachoron Hidy Inverted triangular antipodium 120 quit gissid
120 quit sissid
120 giid
Semiuniform

Sidpixhi

Gixhidy H4
480 Great spinohexacosidishecatonicosachoron Ganxady 600 tet
120 quit gissid
120 giddy
Semiuniform

Sidpixhi

Gixhidy H4
481 Great spinohecatonicosidishecatonicosachoron Gun hidy 120 doe
120 quit sissid
120 giddy
Semiuniform

Sidpixhi

Gixhidy H4

Category 12: Podiumverts (#482-511)[edit | edit source]

These are the uniform polychora with triangular podium vertex figures and their facetings. There are 4 regiments with 7 members each as well as 2 additional members of a previous regiment. The quasiruncinations are included in this category.

Index Name OBSA Picture Coxeter diagram Vertex figure Cells Army Regiment Company Symmetry
482 Small trisoctachoron Sto 8 tet
8 oho
8 tut
Rit
32 vertices
Rit
96 edges
D4
483 Great trisoctachoron Gotto 8 tet
8 cho
8 tut
Rit Rit D4
484 Great tesseractitesseractihexadecachoron Gittith Triangular podium 8 gocco
8 cube
16 tet
Tat
64 vertices
Gittith
192 edges
B4
485 Quasidisprismatotesseractihexadecachoron Quidpith Triangular retroantipodium 8+24 cube
16 tet
32 trip
Tat Gittith B4
486 Prismatocubintercepted tesseract Picnut Inverted triangular podium 8 gocco
32 trip
24 cube
Tat Gittith B4
487 Great tesseractifaceted cubitesseractihexadecachoron Gittifcoth Triangular hemipodium 8 querco
16 tet
24 cube
Tat Gittith B4
488 Great hexadecafaceted prismatotesseractioctachoron Gahfipto Triangular hemipodium 8 querco
8 cube
32 trip
Tat Gittith B4
489 Great spinoprismatotesseractihexadecachoron Gnappoth 8 groh
16 tet
32 trip
Tat Gittith B4
490 Great spinoprismatotesseractioctachoron Gnipto 8 groh
8 cube
24 cube
Tat Gittith B4
491 Great ditrigonal hecatonicosihexacosihecatonicosachoron Gidthixhi Triangular podium 120 gidditdid
120 doe
600 tet
Thi Gidthixhi H4
492 Great dishexacosidishecatonicosachoron Gadixady Triangular retroantipodium 120 doe
600 tet
120 ti
600 tut
Thi
2400 vertices
Gidthixhi
7200 edges
H4
493 Hexacosihecatonicosintercepted hecatonicosachoron Xhinhi Inverted triangular podium 120 gidditdid
120 ti
600 tut
Thi Gidthixhi H4
494 Great hexacosifaceted hexacosidishecatonicosachoron Gix fixady Triangular hemipodium 120 giid
120 doe
600 tut
Thi Gidthixhi H4
495 Great hecatonicosafaceted hexacosidishecatonicosachoron Gohi fixady Triangular hemipodium 120 giid
600 tet
120 ti
Thi Gidthixhi H4
496 Great spinotrishecatonicosachoro