List of uniform polychora (Meta, 11)
From Hi.gher. Space
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<table class='shapelist dx'><tr> | <table class='shapelist dx'><tr> | ||
<th style='width:5%;' class='key' rowspan='2'>Dx</th> | <th style='width:5%;' class='key' rowspan='2'>Dx</th> | ||
| - | <th style='width: | + | <th style='width:7%;' class='key' rowspan='2'>CD</th> |
| + | <th style='width:28%;' class='key' rowspan='2'>Variant</th> | ||
<th colspan='4'>Verf cell counts</th> | <th colspan='4'>Verf cell counts</th> | ||
<th colspan='4'>Element counts</th> | <th colspan='4'>Element counts</th> | ||
| Line 158: | Line 159: | ||
<th style='width:5%;'>|V|</th> | <th style='width:5%;'>|V|</th> | ||
</tr><tr> | </tr><tr> | ||
| - | <td class='cat' colspan=' | + | <td class='cat' colspan='11'></td> |
| + | </tr><tr class='row1'> | ||
| + | <td>1</td><td>xooo</td><td>[[Xylochoron|parent (1-tome)]]</td> | ||
| + | <td>[[Octahedron|(3<sup>4</sup>)]]<sup>6</sup></td><td>--</td><td>--</td><td>--</td> | ||
| + | <td>24</td><td>96</td><td>96</td><td>24</td> | ||
| + | </tr><tr class='row2'> | ||
| + | <td>3</td><td>xxoo</td><td>[[2-xylotomochoron|truncate (2-tome)]]</td> | ||
| + | <td>[[Octahedral truncate|(4·6<sup>2</sup>)]]<sup>3</sup></td><td>--</td><td>--</td><td>[[Cube|(4<sup>3</sup>)]]<sup>1</sup></td> | ||
| + | <td>48</td><td>240</td><td>384</td><td>192</td> | ||
| + | </tr><tr class='row1'> | ||
| + | <td>2</td><td>oxoo</td><td>[[3-xylotomochoron|hemicate (3-tome)]]</td> | ||
| + | <td>[[Cuboctahedron|({3·4}<sup>2</sup>)]]<sup>3</sup></td><td>--</td><td>--</td><td>[[Cube|(4<sup>3</sup>)]]<sup>2</sup></td> | ||
| + | <td>48</td><td>240</td><td>288</td><td>96</td> | ||
| + | </tr><tr class='row2'> | ||
| + | <td>6</td><td>oxxo</td><td>[[Xylomesochoron|mesotruncate (4-tome)]]</td> | ||
| + | <td>[[Cubic truncate|(3·8<sup>2</sup>)]]<sup>2</sup></td><td>--</td><td>--</td><td>[[Cubic truncate|(3·8<sup>2</sup>)]]<sup>2</sup></td> | ||
| + | <td>48</td><td>366</td><td>576</td><td>288</td> | ||
| + | </tr><tr> | ||
| + | <td class='cat' colspan='11'></td> | ||
| + | </tr><tr class='row1'> | ||
| + | <td>5</td><td>xoxo</td><td>[[cantellated 24-cell|cantellate]]</td> | ||
| + | <td>[[Cuboctahedral rectate|(3·4<sup>3</sup>)]]<sup>2</sup></td><td>--</td><td>[[Triangular prism|(3·4<sup>2</sup>)]]<sup>2</sup></td><td>[[Cuboctahedron|({3·4}<sup>2</sup>)]]<sup>1</sup></td> | ||
| + | <td>144</td><td>720</td><td>864</td><td>288</td> | ||
| + | </tr><tr class='row2'> | ||
| + | <td>7</td><td>xxxo</td><td>[[cantitruncated 24-cell|cantitruncate]]</td> | ||
| + | <td>[[Cuboctahedral truncate|(4·6·8)]]<sup>2</sup></td><td>--</td><td>[[Triangular prism|(3·4<sup>2</sup>)]]<sup>1</sup></td><td>[[Cubic truncate|(3·8<sup>2</sup>)]]<sup>1</sup></td> | ||
| + | <td>144</td><td>720</td><td>1152</td><td>576</td> | ||
| + | </tr><tr class='row1'> | ||
| + | <td>9</td><td>xoox</td><td>[[runcinated 24-cell|runcinate]]</td> | ||
| + | <td>[[Octahedron|(3<sup>4</sup>)]]<sup>1</sup></td><td>[[Triangular prism|(3·4<sup>2</sup>)]]<sup>3</sup></td><td>[[Triangular prism|(3·4<sup>2</sup>)]]<sup>3</sup></td><td>[[Octahedron|(3<sup>4</sup>)]]<sup>1</sup></td> | ||
| + | <td>240</td><td>672</td><td>576</td><td>144</td> | ||
| + | </tr><tr class='row2'> | ||
| + | <td>11</td><td>xxox</td><td>[[runcitruncated 24-cell|runcitruncate]]</td> | ||
| + | <td>[[Octahedral truncate|(4·6<sup>2</sup>)]]<sup>1</sup></td><td>[[Hexagonal prism|(6·4<sup>2</sup>)]]<sup>2</sup></td><td>[[Triangular prism|(3·4<sup>2</sup>)]]<sup>1</sup></td><td>[[Cuboctahedral rectate|(3·4<sup>3</sup>)]]<sup>1</sup></td> | ||
| + | <td>240</td><td>1104</td><td>1440</td><td>576</td> | ||
| + | </tr><tr class='row1'> | ||
| + | <td>15</td><td>xxxx</td><td>[[xylopantomochoron|omnitruncate (pantome)]]</td> | ||
| + | <td>[[Cuboctahedral truncate|(4·6·8)]]<sup>1</sup></td><td>[[Hexagonal prism|(6·4<sup>2</sup>)]]<sup>1</sup></td><td>[[Hexagonal prism|(6·4<sup>2</sup>)]]<sup>1</sup></td><td>[[Cuboctahedral truncate|(4·6·8)]]<sup>1</sup></td> | ||
| + | <td>240</td><td>1392</td><td>2304</td><td>1152</td> | ||
</tr></table> | </tr></table> | ||
Revision as of 20:01, 18 December 2010
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 | (4·62)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 | Variant | Verf cell counts | Element counts | ||||||
|---|---|---|---|---|---|---|---|---|---|
| CC (120×) | CF (720×) | CE (1200×) | CV (600×) | |C| | |F| | |E| | |V| | ||
Uniform polyhedra usage statistics
| # | Polyhedron | Unique uses | ||||
|---|---|---|---|---|---|---|
| Pyromorphs | Stauromorphs | Xylomorphs | Rhodomorphs | Total | ||
| Tetrahedral | ||||||
| 1 | Tetrahedron | 5 | 4 | |||
| 6 | Tetrahedral truncate | 5 | 4 | |||
| 111 | Triangular prism | 5 | 4 | |||
| 112 | Hexagonal prism | 3 | 2 | |||
| Octahedral | ||||||
| 2 | Cube | 2 | ||||
| 3 | Octahedron | 2 | 4 | |||
| 7 | Cuboctahedron | 2 | 4 | |||
| 8 | Cubic truncate | 1 | ||||
| 9 | Octahedral truncate | 3 | 5 | |||
| 10 | Cuboctahedral rectate | 2 | ||||
| 11 | Cuboctahedral truncate | 2 | ||||
| 2 | Square prism | 4 | ||||
| 113 | Octagonal prism | 2 | ||||
| Icosahedral | ||||||
| 4 | Dodecahedron | |||||
| 5 | Icosahedron | |||||
| 13 | Icosidodecahedron | |||||
| 14 | Dodecahedral truncate | |||||
| 15 | Icosahedral truncate | |||||
| 16 | Icosidodecahedral rectate | |||||
| 17 | Icosidodecahedral truncate | |||||
| 115 | Pentagonal prism | |||||
| 116 | Decagonal prism | |||||
| Totals | 25 | 40 | ||||
