List of uniform polychora (Meta, 11)
From Hi.gher. Space
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<td>[[Octahedral truncate|(4·6<sup>2</sup>)]]<sup>2</sup></td><td>--</td><td>--</td><td>[[Tetrahedral truncate|(3·6<sup>2</sup>)]]<sup>2</sup></td> | <td>[[Octahedral truncate|(4·6<sup>2</sup>)]]<sup>2</sup></td><td>--</td><td>--</td><td>[[Tetrahedral truncate|(3·6<sup>2</sup>)]]<sup>2</sup></td> | ||
<td>24</td><td>120</td><td>192</td><td>96</td> | <td>24</td><td>120</td><td>192</td><td>96</td> | ||
| + | </tr><tr class='row1'> | ||
| + | <td>4</td><td>[[Xylochoron|dual hemicate (5-tome)]]</td> | ||
| + | <td>[[Octahedron|(3<sup>4</sup>)]]<sup>2</sup></td><td>--</td><td>--</td><td>[[Octahedron|(3<sup>4</sup>)]]<sup>4</sup></td> | ||
| + | <td>24</td><td>96</td><td>96</td><td>24</td> | ||
| + | </tr><tr class='row2'> | ||
| + | <td>12</td><td>[[2-aerotomochoron|dual truncate (6-tome)]]</td> | ||
| + | <td>[[Octahedron|(3<sup>4</sup>)]]<sup>1</sup></td><td>--</td><td>--</td><td>[[Tetrahedral truncate|(3·6<sup>2</sup>)]]<sup>4</sup></td> | ||
| + | <td>24</td><td>96</td><td>120</td><td>48</td> | ||
| + | </tr><tr class='row1'> | ||
| + | <td>8</td><td>[[Aerochoron|dual (7-tome)]]</td> | ||
| + | <td>--</td><td>--</td><td>--</td><td>[[Tetrahedron|(3<sup>3</sup>)]]<sup>8</sup></td> | ||
| + | <td>16</td><td>32</td><td>24</td><td>8</td> | ||
| + | </tr><tr> | ||
| + | <td class='cat' colspan='10'></td> | ||
</tr><tr class='row1'> | </tr><tr class='row1'> | ||
<td>5</td><td>[[cantellated 8-cell|cantellate (xoxo)]]</td> | <td>5</td><td>[[cantellated 8-cell|cantellate (xoxo)]]</td> | ||
| Line 95: | Line 109: | ||
<td>56</td><td>248</td><td>288</td><td>96</td> | <td>56</td><td>248</td><td>288</td><td>96</td> | ||
</tr><tr class='row2'> | </tr><tr class='row2'> | ||
| + | <td>10</td><td>[[3-xylotomochoron|dual cantellate (oxox)]]</td> | ||
| + | <td>[[Cuboctahedron|({3·4}<sup>2</sup>)]]<sup>1</sup></td><td>[[Square prism|(4·4<sup>2</sup>)]]<sup>2</sup></td><td>--</td><td>[[Cuboctahedron|({3·4}<sup>2</sup>)]]<sup>2</sup></td> | ||
| + | <td>48</td><td>240</td><td>288</td><td>96</td> | ||
| + | </tr><tr class='row1'> | ||
<td>7</td><td>[[cantitruncated 8-cell|cantitruncate (xxxo)]]</td> | <td>7</td><td>[[cantitruncated 8-cell|cantitruncate (xxxo)]]</td> | ||
| - | <td>[[Cuboctahedral truncate|(4·6·8)<sup>2</sup> | + | <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>[[Tetrahedral truncate|(3·6<sup>2</sup>)]]<sup>1</sup></td> |
<td>56</td><td>248</td><td>384</td><td>192</td> | <td>56</td><td>248</td><td>384</td><td>192</td> | ||
| + | </tr><tr class='row2'> | ||
| + | <td>14</td><td>[[2-xylotomochoron|dual cantitruncate (oxxx)]]</td> | ||
| + | <td>[[Octahedral truncate|(4·6<sup>2</sup>)]]<sup>1</sup></td><td>[[Square prism|(4·4<sup>2</sup>)]]<sup>1</sup></td><td>--</td><td>[[Octahedral truncate|(4·6<sup>2</sup>)]]<sup>2</sup></td> | ||
| + | <td>48</td><td>240</td><td>384</td><td>192</td> | ||
</tr><tr class='row1'> | </tr><tr class='row1'> | ||
<td>9</td><td>[[runcinated 8-cell|runcinate (xoox)]]</td> | <td>9</td><td>[[runcinated 8-cell|runcinate (xoox)]]</td> | ||
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<td>80</td><td>368</td><td>480</td><td>192</td> | <td>80</td><td>368</td><td>480</td><td>192</td> | ||
</tr><tr class='row1'> | </tr><tr class='row1'> | ||
| + | <td>13</td><td>[[runcitruncated 16-cell|dual runcitruncate (xoxx)]]</td> | ||
| + | <td>[[Cuboctahedral rectate|(3·4<sup>3</sup>)]]<sup>1</sup></td><td>[[Square prism|(4·4<sup>2</sup>)]]<sup>1</sup></td><td>[[Hexagonal prism|(6·4<sup>2</sup>)]]<sup>2</sup></td><td>[[Tetrahedral truncate|(3·6<sup>2</sup>)]]<sup>1</sup></td> | ||
| + | <td>80</td><td>368</td><td>480</td><td>192</td> | ||
| + | </tr><tr class='row2'> | ||
<td>15</td><td>[[stauropantomochoron|omnitruncate (pantome)]]</td> | <td>15</td><td>[[stauropantomochoron|omnitruncate (pantome)]]</td> | ||
<td>[[Cuboctahedral truncate|(4·6·8)]]<sup>1</sup></td><td>[[Octagonal prism|(8·4<sup>2</sup>)]]<sup>1</sup></td><td>[[Hexagonal prism|(6·4<sup>2</sup>)]]<sup>1</sup></td><td>[[Octahedral truncate|(4·6<sup>2</sup>)]]<sup>1</sup></td> | <td>[[Cuboctahedral truncate|(4·6·8)]]<sup>1</sup></td><td>[[Octagonal prism|(8·4<sup>2</sup>)]]<sup>1</sup></td><td>[[Hexagonal prism|(6·4<sup>2</sup>)]]<sup>1</sup></td><td>[[Octahedral truncate|(4·6<sup>2</sup>)]]<sup>1</sup></td> | ||
Revision as of 14:09, 18 December 2010
This page tabulates simple data for each of the uniform polychora.
Families
Pyromorphs
| Dx | Variant | Verf cell counts | Element counts | ||||||
|---|---|---|---|---|---|---|---|---|---|
| CC (5×) | CF (10×) | CE (10×) | CV (5×) | |C| | |F| | |E| | |V| | ||
| 1 | parent (1-tome) | (33)4 | -- | -- | -- | 5 | 10 | 10 | 5 |
| 3 | truncate (2-tome) | (3·62)3 | -- | -- | (33)1 | 10 | 30 | 40 | 20 |
| 2 | hemicate (3-tome) | (34)3 | -- | -- | (33)2 | 10 | 30 | 30 | 10 |
| 6 | mesotruncate (4-tome) | (3·62)2 | -- | -- | (3·62)2 | 30 | 70 | 60 | 20 |
| 5 | cantellate (xoxo) | ({3·4}2)2 | -- | (3·42)2 | (34)1 | 20 | 80 | 90 | 30 |
| 7 | cantitruncate (xxxo) | (4·62)2 | -- | (3·42)1 | (3·62)1 | 20 | 80 | 120 | 60 |
| 9 | runcinate (xoox) | (33)1 | (3·42)3 | (3·42)3 | (33)1 | 30 | 70 | 60 | 20 |
| 11 | runcitruncate (xxox) | (3·62)1 | (6·42)2 | (3·42)1 | ({3·4}2)1 | 30 | 120 | 150 | 60 |
| 15 | omnitruncate (pantome) | (4·62)1 | (6·42)1 | (6·42)1 | (4·62)1 | 30 | 150 | 240 | 120 |
Stauromorphs
| Dx | Variant | Verf cell counts | Element counts | ||||||
|---|---|---|---|---|---|---|---|---|---|
| CC (8×) | CF (24×) | CE (32×) | CV (16×) | |C| | |F| | |E| | |V| | ||
| 1 | parent (1-tome) | (43)4 | -- | -- | -- | 8 | 24 | 32 | 16 |
| 3 | truncate (2-tome) | (3·82)3 | -- | -- | (33)1 | 24 | 88 | 128 | 64 |
| 2 | hemicate (3-tome) | ({3·4}2)3 | -- | -- | (33)2 | 24 | 88 | 96 | 32 |
| 6 | mesotruncate (4-tome) | (4·62)2 | -- | -- | (3·62)2 | 24 | 120 | 192 | 96 |
| 4 | dual hemicate (5-tome) | (34)2 | -- | -- | (34)4 | 24 | 96 | 96 | 24 |
| 12 | dual truncate (6-tome) | (34)1 | -- | -- | (3·62)4 | 24 | 96 | 120 | 48 |
| 8 | dual (7-tome) | -- | -- | -- | (33)8 | 16 | 32 | 24 | 8 |
| 5 | cantellate (xoxo) | (3·43)2 | -- | (3·42)2 | (34)1 | 56 | 248 | 288 | 96 |
| 10 | dual cantellate (oxox) | ({3·4}2)1 | (4·42)2 | -- | ({3·4}2)2 | 48 | 240 | 288 | 96 |
| 7 | cantitruncate (xxxo) | (4·6·8)2 | -- | (3·42)1 | (3·62)1 | 56 | 248 | 384 | 192 |
| 14 | dual cantitruncate (oxxx) | (4·62)1 | (4·42)1 | -- | (4·62)2 | 48 | 240 | 384 | 192 |
| 9 | runcinate (xoox) | (43)1 | (4·42)3 | (3·42)3 | (33)1 | 80 | 208 | 192 | 64 |
| 11 | runcitruncate (xxox) | (4·62)1 | (8·42)2 | (3·42)1 | ({3·4}2)1 | 80 | 368 | 480 | 192 |
| 13 | dual runcitruncate (xoxx) | (3·43)1 | (4·42)1 | (6·42)2 | (3·62)1 | 80 | 368 | 480 | 192 |
| 15 | omnitruncate (pantome) | (4·6·8)1 | (8·42)1 | (6·42)1 | (4·62)1 | 80 | 464 | 768 | 384 |
Xylomorphs
| Dx | Variant | Verf cell counts | Element counts | ||||||
|---|---|---|---|---|---|---|---|---|---|
| CC (24×) | CF (96×) | CE (96×) | CV (24×) | |C| | |F| | |E| | |V| | ||
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 | ||||
| 6 | Tetrahedral truncate | 5 | ||||
| 111 | Triangular prism | 5 | ||||
| 112 | Hexagonal prism | 3 | ||||
| Octahedral | ||||||
| 2 | Cube | |||||
| 3 | Octahedron | 2 | ||||
| 7 | Cuboctahedron | 2 | ||||
| 8 | Cubic truncate | |||||
| 9 | Octahedral truncate | 3 | ||||
| 10 | Cuboctahedral rectate | |||||
| 11 | Cuboctahedral truncate | |||||
| 2 | Square prism | |||||
| 113 | Octagonal prism | |||||
| 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 | |||||
