List of uniform polychora (Meta, 11)
From Hi.gher. Space
This page tabulates simple data for each of the uniform polychora.
Families
Pyromorphs
| Dx | CD | Variant | Verf cell counts | Element counts | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
| CC (5×) | CF (10×) | CE (10×) | CV (5×) | |C| | |F| | |E| | |V| | |||
| 1 | xooo | parent (1-tome) | (33)4 | -- | -- | -- | 5 | 10 | 10 | 5 |
| 3 | xxoo | truncate (2-tome) | (3·62)3 | -- | -- | (33)1 | 10 | 30 | 40 | 20 |
| 2 | oxoo | hemicate (3-tome) | (34)3 | -- | -- | (33)2 | 10 | 30 | 30 | 10 |
| 6 | oxxo | mesotruncate (4-tome) | (3·62)2 | -- | -- | (3·62)2 | 10 | 40 | 60 | 30 |
| 5 | xoxo | cantellate | ({3·4}2)2 | -- | (3·42)2 | (34)1 | 20 | 80 | 90 | 30 |
| 7 | xxxo | cantitruncate | (4·62)2 | -- | (3·42)1 | (3·62)1 | 20 | 80 | 120 | 60 |
| 9 | xoox | runcinate | (33)1 | (3·42)3 | (3·42)3 | (33)1 | 30 | 70 | 60 | 20 |
| 11 | xxox | runcitruncate | (3·62)1 | (6·42)2 | (3·42)1 | ({3·4}2)1 | 30 | 120 | 150 | 60 |
| 15 | xxxx | omnitruncate (pantome) | (4·62)1 | (6·42)1 | (6·42)1 | (4·62)1 | 30 | 150 | 240 | 120 |
Stauromorphs
| Dx | CD | Variant | Verf cell counts | Element counts | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
| CC (8×) | CF (24×) | CE (32×) | CV (16×) | |C| | |F| | |E| | |V| | |||
| 1 | xooo | parent (1-tome) | (43)4 | -- | -- | -- | 8 | 24 | 32 | 16 |
| 3 | xxoo | truncate (2-tome) | (3·82)3 | -- | -- | (33)1 | 24 | 88 | 128 | 64 |
| 2 | oxoo | hemicate (3-tome) | ({3·4}2)3 | -- | -- | (33)2 | 24 | 88 | 96 | 32 |
| 6 | oxxo | mesotruncate (4-tome) | (4·62)2 | -- | -- | (3·62)2 | 24 | 120 | 192 | 96 |
| 4 | ooxo | dual hemicate (5-tome) | (34)2 | -- | -- | (34)4 | 24 | 96 | 96 | 24 |
| 12 | ooxx | dual truncate (6-tome) | (34)1 | -- | -- | (3·62)4 | 24 | 96 | 120 | 48 |
| 8 | ooox | dual (7-tome) | -- | -- | -- | (33)8 | 16 | 32 | 24 | 8 |
| 5 | xoxo | cantellate | (3·43)2 | -- | (3·42)2 | (34)1 | 56 | 248 | 288 | 96 |
| 10 | oxox | dual cantellate | ({3·4}2)1 | (4·42)2 | -- | ({3·4}2)2 | 48 | 240 | 288 | 96 |
| 7 | xxxo | cantitruncate | (4·6·8)2 | -- | (3·42)1 | (3·62)1 | 56 | 248 | 384 | 192 |
| 14 | oxxx | dual cantitruncate | (4·62)1 | (4·42)1 | -- | (4·62)2 | 48 | 240 | 384 | 192 |
| 9 | xoox | runcinate | (43)1 | (4·42)3 | (3·42)3 | (33)1 | 80 | 208 | 192 | 64 |
| 11 | xxox | runcitruncate | (3·82)1 | (8·42)2 | (3·42)1 | ({3·4}2)1 | 80 | 368 | 480 | 192 |
| 13 | xoxx | dual runcitruncate | (3·43)1 | (4·42)1 | (6·42)2 | (3·62)1 | 80 | 368 | 480 | 192 |
| 15 | xxxx | omnitruncate (pantome) | (4·6·8)1 | (8·42)1 | (6·42)1 | (4·62)1 | 80 | 464 | 768 | 384 |
Xylomorphs
| Dx | CD | Variant | Verf cell counts | Element counts | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
| CC (24×) | CF (96×) | CE (96×) | CV (24×) | |C| | |F| | |E| | |V| | |||
| 1 | xooo | parent (1-tome) | (34)6 | -- | -- | -- | 24 | 96 | 96 | 24 |
| 3 | xxoo | truncate (2-tome) | (4·62)3 | -- | -- | (43)1 | 48 | 240 | 384 | 192 |
| 2 | oxoo | hemicate (3-tome) | ({3·4}2)3 | -- | -- | (43)2 | 48 | 240 | 288 | 96 |
| 6 | oxxo | mesotruncate (4-tome) | (3·82)2 | -- | -- | (3·82)2 | 48 | 366 | 576 | 288 |
| 5 | xoxo | cantellate | (3·43)2 | -- | (3·42)2 | ({3·4}2)1 | 144 | 720 | 864 | 288 |
| 7 | xxxo | cantitruncate | (4·6·8)2 | -- | (3·42)1 | (3·82)1 | 144 | 720 | 1152 | 576 |
| 9 | xoox | runcinate | (34)1 | (3·42)3 | (3·42)3 | (34)1 | 240 | 672 | 576 | 144 |
| 11 | xxox | runcitruncate | (4·62)1 | (6·42)2 | (3·42)1 | (3·43)1 | 240 | 1104 | 1440 | 576 |
| 15 | xxxx | omnitruncate (pantome) | (4·6·8)1 | (6·42)1 | (6·42)1 | (4·6·8)1 | 240 | 1392 | 2304 | 1152 |
Rhodomorphs
| Dx | CD | Variant | Verf cell counts | Element counts | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
| CC (120×) | CF (720×) | CE (1200×) | CV (600×) | |C| | |F| | |E| | |V| | |||
| 1 | xooo | parent (1-tome) | (53)4 | -- | -- | -- | 120 | 720 | 1200 | 600 |
| 3 | xxoo | truncate (2-tome) | (3·102)3 | -- | -- | (33)1 | 720 | 3120 | 4800 | 2400 |
| 2 | oxoo | hemicate (3-tome) | ({3·5}2)3 | -- | -- | (33)2 | 720 | 3120 | 3600 | 1200 |
| 6 | oxxo | mesotruncate (4-tome) | (5·62)2 | -- | -- | (3·62)2 | 720 | 4320 | 7200 | 3600 |
| 4 | ooxo | dual hemicate (5-tome) | (35)2 | -- | -- | (34)5 | 720 | 3600 | 3600 | 720 |
| 12 | ooxx | dual truncate (6-tome) | (35)1 | -- | -- | (3·62)5 | 720 | 3600 | 4320 | 1440 |
| 8 | ooox | dual (7-tome) | -- | -- | -- | (33)20 | 600 | 1200 | 720 | 120 |
| 5 | xoxo | cantellate | (3·4·5·4)2 | -- | (3·42)2 | (34)1 | 1920 | 9120 | 10800 | 3600 |
| 10 | oxox | dual cantellate | ({3·5}2)1 | (5·42)2 | -- | ({3·4}2)2 | 1440 | 8640 | 10800 | 3600 |
| 7 | xxxo | cantitruncate | (4·6·10)2 | -- | (3·42)1 | (3·62)1 | 1920 | 9120 | 14400 | 7200 |
| 14 | oxxx | dual cantitruncate | (5·62)1 | (5·42)1 | -- | (4·62)2 | 1440 | 8640 | 14400 | 7200 |
| 9 | xoox | runcinate | (53)1 | (5·42)3 | (3·42)3 | (33)1 | 2640 | 7440 | 7200 | 2400 |
| 11 | xxox | runcitruncate | (3·102)1 | (10·42)2 | (3·42)1 | ({3·4}2)1 | 2640 | 13440 | 18000 | 7200 |
| 13 | xoxx | dual runcitruncate | (3·4·5·4)1 | (5·42)1 | (6·42)2 | (3·62)1 | 2640 | 13440 | 18000 | 7200 |
| 15 | xxxx | omnitruncate (pantome) | (4·6·10)1 | (10·42)1 | (6·42)1 | (4·62)1 | 2640 | 17040 | 28800 | 14400 |
Uniform polyhedra usage statistics
| # | Polyhedron | Unique uses | ||||
|---|---|---|---|---|---|---|
| Pyromorphs | Stauromorphs | Xylomorphs | Rhodomorphs | Total | ||
| Tetrahedral | ||||||
| 1 | Tetrahedron | 5 | 4 | 4 | 13 | |
| 6 | Tetrahedral truncate | 5 | 4 | 4 | 13 | |
| 111 | Triangular prism | 5 | 4 | 5 | 4 | 18 |
| 112 | Hexagonal prism | 3 | 2 | 3 | 2 | 10 |
| Octahedral | ||||||
| 2 | Cube | 6 | 2 | 8 | ||
| 3 | Octahedron | 2 | 4 | 3 | 2 | 11 |
| 7 | Cuboctahedron | 2 | 4 | 2 | 2 | 10 |
| 8 | Cubic truncate | 2 | 3 | 5 | ||
| 9 | Octahedral truncate | 3 | 4 | 2 | 2 | 11 |
| 10 | Cuboctahedral rectate | 2 | 2 | 4 | ||
| 11 | Cuboctahedral truncate | 2 | 3 | 5 | ||
| 113 | Octagonal prism | 2 | 2 | |||
| Icosahedral | ||||||
| 4 | Dodecahedron | 2 | 2 | |||
| 5 | Icosahedron | 2 | 2 | |||
| 13 | Icosidodecahedron | 2 | 2 | |||
| 14 | Dodecahedral truncate | 2 | 2 | |||
| 15 | Icosahedral truncate | 2 | 2 | |||
| 16 | Icosidodecahedral rectate | 2 | 2 | |||
| 17 | Icosidodecahedral truncate | 2 | 2 | |||
| 115 | Pentagonal prism | 4 | 4 | |||
| 116 | Decagonal prism | 2 | 2 | |||
| Totals | 25 | 40 | 25 | 40 | 130 | |
