Data table for Uniform polychoron
Index | JB Name | Name | Cell type count | C1 | C2 | C3 | C4 | # C1/v | # C2/v | # C3/v | # C4/v | # C/v | # C1 | # C2 | # C3 | # C4 | Vertex figure | Euler | C | F | E | V | {3} | {4} | {5} | {6} | {8} | {10} | |
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Pentachoric (5-cell) Symmetry: 1-9 | |||||||||||||||||||||||||||||
0 | 1 | PEN | 5-cell {3,3,3} | 1 | {3,3} | 4 | 4 | 5 | {3,3} | 0 | 5 | 10 | 10 | 5 | 10 | 0 | 0 | 0 | 0 | 0 | |||||||||
1 | 3 | TIP | Truncated 5-cell | 2 | {3,3} | 3.6.6 | 1 | 3 | 4 | 5 | 5 | {3,3} | 0 | 10 | 30 | 40 | 20 | 20 | 0 | 0 | 10 | 0 | 0 | ||||||
2 | 2 | RAP | Rectified 5-cell | 2 | {3,3} | {3,4} | 2 | 3 | 5 | 5 | 5 | 3.4.4 | 0 | 10 | 30 | 30 | 10 | 30 | 0 | 0 | 0 | 0 | 0 | ||||||
3 | 4 | SRIP | Cantellated 5-cell | 3 | 3.4.4 | {3,4} | 3.4.3.4 | 2 | 1 | 2 | 5 | 10 | 5 | 5 | 3.4.4 | 0 | 20 | 80 | 90 | 30 | 50 | 30 | 0 | 0 | 0 | 0 | |||
4 | 7 | GRIP | Cantitruncated 5-cell | 3 | 3.4.4 | 3.6.6 | 4.6.6 | 1 | 1 | 2 | 4 | 10 | 5 | 5 | {3,3} | 0 | 20 | 80 | 120 | 60 | 20 | 30 | 0 | 30 | 0 | 0 | |||
5 | 8 | PRIP | Runcitruncated 5-cell | 4 | 3.4.4 | 3.6.6 | 4.4.6 | 3.4.4.4 | 1 | 1 | 2 | 1 | 5 | 10 | 5 | 10 | 5 | 4-pyr | 0 | 30 | 120 | 150 | 60 | 40 | 60 | 0 | 20 | 0 | 0 |
6 | 6 | DECA | Bitruncated 5-cell | 1 | 3.6.6 | 4 | 4 | 10 | {3,3} | 0 | 10 | 40 | 60 | 30 | 20 | 0 | 0 | 20 | 0 | 0 | |||||||||
7 | 5 | SPID | Runcinated 5-cell | 2 | {3,3} | 3.4.4 | 2 | 6 | 8 | 10 | 20 | {3,4} | 0 | 30 | 70 | 60 | 20 | 40 | 30 | 0 | 0 | 0 | 0 | ||||||
8 | 9 | GIPPID | Omnitruncated 5-cell | 2 | 4.4.6 | 4.6.6 | 2 | 2 | 4 | 20 | 10 | {3,3} | 0 | 30 | 150 | 240 | 120 | 0 | 90 | 0 | 60 | 0 | 0 | ||||||
Hexadecachoric (16 cell) Symmetry: 10-21 | |||||||||||||||||||||||||||||
0 | 10 | TES | Tesseract {4,3,3} | 1 | {4,3} | 4 | 4 | 8 | {3,3} | 0 | 8 | 24 | 32 | 16 | 0 | 24 | 0 | 0 | 0 | 0 | |||||||||
0.5 | 12 | HEX | 16-cell {3,3,4} | 1 | {3,3} | 8 | 8 | 16 | {3,4} | 0 | 16 | 32 | 24 | 8 | 32 | 0 | 0 | 0 | 0 | 0 | |||||||||
1 | 13 | TAT | Truncated tesseract | 2 | {3,3} | 3.8.8 | 1 | 3 | 4 | 16 | 8 | {3,3} | 0 | 24 | 88 | 128 | 64 | 64 | 0 | 0 | 0 | 24 | 0 | ||||||
1.5 | 17 | THEX | Truncated 16-cell | 2 | 3.6.6 | {3,4} | 4 | 1 | 5 | 16 | 8 | 4-pyr | 0 | 24 | 96 | 120 | 48 | 64 | 0 | 0 | 32 | 0 | 0 | ||||||
2 | 11 | RIT | Rectified tesseract | 2 | {3,3} | 3.4.3.4 | 3 | 2 | 5 | 16 | 8 | 3.4.4 | 0 | 24 | 88 | 96 | 32 | 64 | 24 | 0 | 0 | 0 | 0 | ||||||
2.5 | -- | -- | Rectified 16-cell (24-cell) | 24 | 96 | 96 | 24 | 96 | 0 | 0 | 0 | 0 | 0 | ||||||||||||||||
3 | 14 | SRIT | Cantellated tesseract | 3 | 3.4.4 | {3,4} | 3.4.4.4 | 2 | 1 | 2 | 5 | 32 | 16 | 8 | 3.4.4 | 0 | 56 | 248 | 288 | 96 | 128 | 120 | 0 | 0 | 0 | 0 | |||
3.5 | -- | -- | Cantellated 16-cell (Rect. 24-cell) |
48 | 240 | 288 | 96 | 96 | 144 | 0 | 0 | 0 | 0 | ||||||||||||||||
4 | 18 | GRIT | Cantitruncated tesseract | 3 | 3.4.4 | 3.6.6 | 4.6.8 | 1 | 1 | 2 | 4 | 32 | 16 | 8 | {3,3} | 0 | 56 | 248 | 384 | 192 | 64 | 96 | 0 | 64 | 24 | 0 | |||
4.5 | -- | -- | Cantitruncated 16-cell (Trunc. 24-cell) |
48 | 240 | 384 | 192 | 0 | 144 | 0 | 96 | 0 | 0 | ||||||||||||||||
5 | 19 | PROH | Runcitruncated tesseract | 4 | 3.4.4 | 3.8.8 | 4.4.8 | 3.4.3.4 | 1 | 1 | 2 | 1 | 5 | 32 | 8 | 24 | 16 | 4-pyr | 0 | 80 | 368 | 480 | 192 | 128 | 192 | 0 | 0 | 48 | 0 |
5.5 | 20 | PRIT | Runcitruncated 16-cell | 4 | 3.6.6 | {4,3} | 4.4.6 | 3.4.4.4 | 1 | 1 | 2 | 1 | 5 | 16 | 24 | 32 | 8 | 4-pyr | 0 | 80 | 368 | 480 | 192 | 64 | 240 | 0 | 64 | 0 | 0 |
6 | 16 | TAH | Bitruncated tesseract | 2 | 3.6.6 | 4.6.6 | 2 | 2 | 4 | 16 | 8 | {3,3} | 0 | 24 | 120 | 192 | 96 | 32 | 24 | 0 | 64 | 0 | 0 | ||||||
7 | 15 | SIDPITH | Runcinated tesseract | 3 | {3,3} | 3.4.4 | {4,3} | 1 | 3 | 4 | 8 | 16 | 32 | 32 | {3,4} | 0 | 80 | 208 | 192 | 64 | 64 | 144 | 0 | 0 | 0 | 0 | |||
8 | 21 | GIDPITH | Omnitruncated tesseract | 4 | 4.4.6 | 4.4.8 | 4.6.6 | 4.6.8 | 1 | 1 | 1 | 1 | 4 | 32 | 24 | 16 | 8 | {3,3} | 0 | 80 | 464 | 768 | 384 | 0 | 288 | 0 | 128 | 48 | 0 |
Icositetrachoric (24-cell) Symmetry: 22-31 | |||||||||||||||||||||||||||||
0 | 22 | ICO | 24-cell {3,4,3} | 1 | {3,4} | 6 | 6 | 24 | {4,3} | 0 | 24 | 96 | 96 | 24 | 96 | 0 | 0 | 0 | 0 | 0 | |||||||||
1 | 24 | TICO | Truncated 24-cell | 2 | {4,3} | 4.6.6 | 1 | 3 | 4 | 24 | 24 | {3,3} | 0 | 48 | 240 | 384 | 192 | 0 | 144 | 0 | 96 | 0 | 0 | ||||||
2 | 23 | RICO | Rectified 24-cell | 2 | {4,3} | 3.4.3.4 | 2 | 3 | 5 | 24 | 24 | 3.4.4 | 0 | 48 | 240 | 288 | 96 | 96 | 144 | 0 | 0 | 0 | 0 | ||||||
3 | 25 | SRICO | Cantellated 24-cell | 3 | 3.4.4 | 3.4.3.4 | 3.4.4.4 | 2 | 2 | 1 | 5 | 96 | 24 | 24 | 3.4.4 | 0 | 144 | 720 | 864 | 288 | 288 | 432 | 0 | 0 | 0 | 0 | |||
4 | 28 | GRICO | Cantitruncated 24-cell | 3 | 3.4.4 | 3.8.8 | 4.6.8 | 1 | 1 | 2 | 4 | 96 | 24 | 24 | {3,3} | 0 | 144 | 720 | 1152 | 576 | 192 | 288 | 0 | 96 | 144 | 0 | |||
5 | 29 | PRICO | Runcitruncated 24-cell | 4 | 3.4.4 | 4.4.6 | 4.6.6 | 3.4.4.4 | 1 | 2 | 1 | 1 | 5 | 96 | 96 | 24 | 24 | 4-pyr | 0 | 240 | 1104 | 1440 | 576 | 192 | 720 | 0 | 192 | 0 | 0 |
6 | 27 | CONT | Bitruncated 24-cell | 1 | 3.8.8 | 4 | 4 | 48 | {3,3} | 0 | 48 | 336 | 576 | 288 | 192 | 0 | 0 | 0 | 144 | 0 | |||||||||
7 | 26 | SPIC | Runcinated 24-cell | 2 | 3.4.4 | {3,4} | 8 | 2 | 10 | 192 | 48 | 3.3.3.4 | 0 | 240 | 672 | 576 | 144 | 384 | 288 | 0 | 0 | 0 | 0 | ||||||
8 | 30 | GIPPIC | Omnitruncated 24-cell | 2 | 4.4.6 | 4.6.8 | 2 | 2 | 4 | 192 | 48 | {3,3} | 0 | 240 | 1392 | 2304 | 1152 | 0 | 864 | 0 | 384 | 144 | 0 | ||||||
9 | 31 | SADI | Snub 24-cell | 2 | {3,3} | {3,5} | 5 | 3 | 8 | 120 | 24 | tridim | 0 | 144 | 480 | 432 | 96 | 480 | 0 | 0 | 0 | 0 | 0 | ||||||
Hexacosichoric (600-cell) Symmetry: 32-46 | |||||||||||||||||||||||||||||
0 | 32 | HI | 120-cell {5,3,3} | 1 | {5,3} | 4 | 4 | 120 | {3,3} | 0 | 120 | 720 | 1200 | 600 | 0 | 0 | 720 | 0 | 0 | 0 | |||||||||
0.5 | 35 | EX | 600-cell {3,3,5} | 1 | {3,3} | 20 | 20 | 600 | {3,5} | 0 | 600 | 1200 | 720 | 120 | 1200 | 0 | 0 | 0 | 0 | 0 | |||||||||
1 | 36 | THI | Truncated 120-cell | 2 | {3,3} | 3.10.10 | 1 | 3 | 4 | 600 | 120 | {3,3} | 0 | 720 | 3120 | 4800 | 2400 | 2400 | 0 | 0 | 0 | 0 | 720 | ||||||
1.5 | 41 | TEX | Truncated 600-cell | 2 | 3.6.6 | 3.3.3.3.4 | 5 | 1 | 6 | 600 | 120 | 5-pyr | 0 | 720 | 3600 | 4320 | 1440 | 2400 | 0 | 0 | 1200 | 0 | 0 | ||||||
2 | 33 | RAHI | Rectified 120-cell | 2 | {3,3} | 3.5.3.5 | 2 | 3 | 5 | 600 | 120 | 3.4.4 | 0 | 720 | 3120 | 3600 | 1200 | 2400 | 0 | 720 | 0 | 0 | 0 | ||||||
2.5 | 34 | ROX | Rectified 600-cell | 2 | {3,4} | {3,5} | 5 | 2 | 7 | 600 | 120 | 4.4.5 | 0 | 720 | 3600 | 3600 | 720 | 3600 | 0 | 0 | 0 | 0 | 0 | ||||||
3 | 37 | SRAHI | Cantellated 120-cell | 3 | 3.4.4 | {3,4} | 3.4.5.4 | 2 | 1 | 2 | 5 | 1200 | 600 | 120 | 3.4.4 | 0 | 1920 | 9120 | 10800 | 3600 | 4800 | 3600 | 720 | 0 | 0 | 0 | |||
3.5 | 40 | SRIX | Cantellated 600-cell | 3 | 4.4.5 | 3.4.3.4 | 3.5.3.5 | 2 | 2 | 1 | 5 | 720 | 600 | 120 | 3.4.4 | 0 | 1440 | 8640 | 10800 | 3600 | 3600 | 3600 | 1440 | 0 | 0 | 0 | |||
4 | 42 | GRAHI | Cantitruncated 120-cell | 3 | 3.4.4 | 3.6.6 | 4.6.10 | 1 | 1 | 2 | 4 | 1200 | 600 | 120 | {3,3} | 0 | 1920 | 9120 | 14400 | 7200 | 2400 | 3600 | 0 | 2400 | 0 | 720 | |||
4.5 | 45 | GRIX | Cantitruncated 600-cell | 3 | 4.4.5 | 4.6.6 | 5.6.6 | 1 | 2 | 1 | 4 | 720 | 600 | 120 | {3,3} | 0 | 1440 | 8640 | 14400 | 7200 | 0 | 3600 | 1440 | 3600 | 0 | 0 | |||
5 | 43 | PRIX | Runcitruncated 120-cell | 4 | 3.4.4 | 3.10.10 | 4.4.10 | 3.4.3.4 | 1 | 1 | 2 | 1 | 5 | 1200 | 120 | 720 | 600 | 4-pyr | 0 | 2640 | 13440 | 18000 | 7200 | 4800 | 7200 | 0 | 0 | 0 | 1440 |
5.5 | 44 | PRAHI | Runcitruncated 600-cell | 4 | 3.6.6 | 4.4.5 | 4.4.6 | 3.4.5.4 | 1 | 1 | 2 | 1 | 5 | 600 | 720 | 1200 | 120 | 4-pyr | 0 | 2640 | 13440 | 18000 | 7200 | 2400 | 7200 | 1440 | 2400 | 0 | 0 |
6 | 39 | XHI | Bitruncated 120-cell | 2 | 3.6.6 | 5.6.6 | 2 | 2 | 4 | 600 | 120 | {3,3} | 0 | 720 | 4320 | 7200 | 3600 | 1200 | 0 | 720 | 2400 | 0 | 0 | ||||||
7 | 38 | SIDPIXHI | Runcinated 120-cell | 4 | {3,3} | 3.6.6 | 4.4.5 | {5,3} | 1 | 3 | 3 | 1 | 8 | 600 | 1200 | 720 | 120 | {3,4} | 0 | 2640 | 7440 | 7200 | 2400 | 2400 | 3600 | 1440 | 0 | 0 | 0 |
8 | 46 | GIDPIXHI | Omnitruncated 120-cell | 4 | 4.4.6 | 4.4.10 | 4.6.6 | 4.6.10 | 1 | 1 | 1 | 1 | 4 | 1200 | 720 | 600 | 120 | {3,3} | 0 | 2640 | 17040 | 28800 | 14400 | 0 | 10800 | 0 | 4800 | 0 | 1440 |
Grand-Antiprism: 47 | |||||||||||||||||||||||||||||
47 | GAP | Grand antiprism | 2 | {3,3} | 3.3.3.5 | 10 | 2 | 12 | 300 | 20 | {3,5}/2 | 0 | 320 | 720 | 500 | 100 | 700 | 0 | 20 | 0 | 0 | 0 | |||||||
Archimedean-Prisms: 48-64 | |||||||||||||||||||||||||||||
48 | TEPE | Tetrahedral hyperprism | 2 | {3,3} | 3.4.4 | 1 | 3 | 4 | 2 | 4 | {3,3} | 0 | 6 | 14 | 16 | 8 | 8 | 6 | 0 | 0 | 0 | 0 | |||||||
49 | TUTTIP | Truncated-tetrahedral hyperprism | 3 | 3.4.4 | 3.6.6 | 4.4.6 | 1 | 1 | 2 | 4 | 4 | 2 | 4 | {3,3} | 0 | 10 | 34 | 48 | 24 | 8 | 18 | 0 | 8 | 0 | 0 | ||||
50 | COPE | Cuboctahedral hyperprism | 3 | 3.4.4 | {4,3} | 3.4.3.4 | 2 | 2 | 1 | 5 | 8 | 6 | 2 | 4-pyr | 0 | 16 | 52 | 60 | 24 | 16 | 36 | 0 | 0 | 0 | 0 | ||||
51 | OPE | Octahedral hyperprism | 2 | 3.4.4 | {4,3} | 4 | 1 | 5 | 8 | 2 | 4-pyr | 0 | 10 | 28 | 30 | 12 | 16 | 12 | 0 | 0 | 0 | 0 | |||||||
52 | TICCUP | Truncated-cubic hyperprism | 3 | 3.4.4 | 3.8.8 | 4.4.6 | 1 | 1 | 2 | 4 | 8 | 2 | 6 | {3,3} | 0 | 16 | 64 | 96 | 48 | 16 | 36 | 0 | 0 | 12 | 0 | ||||
53 | SIRCOPE | Rhombicuboctahedral hyperprism | 3 | 3.4.4 | {4,3} | 3.4.4.4 | 1 | 3 | 1 | 5 | 8 | 18 | 2 | 4-pyr | 0 | 28 | 100 | 120 | 48 | 16 | 84 | 0 | 0 | 0 | 0 | ||||
54 | TOPE | Truncated-octahedral hyperprism | 3 | {4,3} | 4.4.6 | 4.6.6 | 1 | 2 | 1 | 4 | 6 | 8 | 2 | {3,3} | 0 | 16 | 64 | 96 | 48 | 0 | 48 | 0 | 16 | 0 | 0 | ||||
55 | GIRCOPE | Truncated cuboctahedral hyperprism | 4 | {4,3} | 4.4.6 | 4.4.8 | 4.6.8 | 1 | 1 | 1 | 1 | 4 | 12 | 8 | 6 | 2 | {3,3} | 0 | 28 | 124 | 192 | 96 | 0 | 96 | 0 | 16 | 12 | 0 | |
56 | SNICCUP | Snub-cubic hyperprism | 3 | 3.4.4 | {4,3} | 3.3.3.3.4 | 4 | 1 | 1 | 6 | 32 | 6 | 2 | 5-pyr | 0 | 40 | 136 | 144 | 48 | 64 | 72 | 0 | 0 | 0 | 0 | ||||
57 | DOPE | Dodecahedral hyperprism | 2 | 4.4.5 | {5,3} | 3 | 1 | 4 | 12 | 2 | {3,3} | 0 | 14 | 54 | 80 | 40 | 0 | 30 | 24 | 0 | 0 | 0 | |||||||
58 | IDDIP | Icosidodecahdral hyperprism | 3 | 3.4.4 | 4.4.5 | 3.5.3.5 | 2 | 2 | 1 | 5 | 20 | 12 | 2 | 4-pyr | 0 | 34 | 124 | 150 | 60 | 40 | 60 | 24 | 0 | 0 | 0 | ||||
59 | IPE | Icosahedral hyperprism | 2 | 3.4.4 | {3,5} | 5 | 1 | 6 | 20 | 2 | 5-pyr | 0 | 22 | 70 | 72 | 24 | 40 | 30 | 0 | 0 | 0 | 0 | |||||||
60 | TIDDIP | Truncated-dodecahedral hyperprism | 3 | 3.4.4 | 3.10.10 | 4.4.10 | 1 | 1 | 2 | 4 | 20 | 2 | 12 | {3,3} | 0 | 34 | 154 | 240 | 120 | 40 | 90 | 0 | 0 | 0 | 24 | ||||
61 | SRIDDIP | Rhombicosidodecahedral hyperprism | 4 | 3.4.4 | {4,3} | 4.4.5 | 3.4.5.4 | 1 | 2 | 1 | 1 | 5 | 20 | 30 | 12 | 2 | 4-pyr | 0 | 64 | 244 | 300 | 120 | 40 | 180 | 24 | 0 | 0 | 0 | |
62 | TIPE | Truncated-icosahedral hyperprism | 3 | 4.4.5 | 4.4.6 | 5.6.6 | 1 | 2 | 1 | 4 | 12 | 20 | 2 | {3,3} | 0 | 34 | 154 | 240 | 120 | 0 | 90 | 24 | 40 | 0 | 0 | ||||
63 | GRIDDIP | Truncated icosidodecahedral hyperprism | 4 | {4,3} | 4.4.6 | 4.4.10 | 4.6.10 | 1 | 1 | 1 | 1 | 4 | 30 | 20 | 12 | 2 | {3,3} | 0 | 64 | 304 | 480 | 240 | 0 | 240 | 0 | 40 | 0 | 24 | |
64 | SNIDDIP | Snub-dodecahedral hyperprism | 3 | 3.4.4 | 4.4.5 | 3.3.3.3.5 | 4 | 1 | 1 | 6 | 80 | 12 | 2 | 5-pyr | 0 | 94 | 334 | 360 | 120 | 160 | 150 | 24 | 0 | 0 | 0 |