List of convex regular-faced polyhedra (Meta, 13)
From Hi.gher. Space
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</tr><tr class='row1'> | </tr><tr class='row1'> | ||
<td class='key'>1</td> | <td class='key'>1</td> | ||
| - | <td>[[Tetrahedron]]</td><td>S</td><td>Kt1</td> | + | <td>[[Tetrahedron]]</td><td><tt>-S-</tt></td><td>Kt1</td> |
<td>4</td><td>6</td><td>4</td> | <td>4</td><td>6</td><td>4</td> | ||
<td colspan='3'>''Self-dual''</td> | <td colspan='3'>''Self-dual''</td> | ||
| - | </tr><tr class=' | + | </tr><tr class='row2'> |
<td class='key'>2</td> | <td class='key'>2</td> | ||
| - | <td>[[Cube]]</td><td>BSZ</td><td>Ko1</td> | + | <td>[[Cube]]</td><td><tt>BSZ</tt></td><td>Ko1</td> |
<td>6</td><td>12</td><td>8</td> | <td>6</td><td>12</td><td>8</td> | ||
<td colspan='3'>3. Octahedron ''(below)''</td> | <td colspan='3'>3. Octahedron ''(below)''</td> | ||
</tr><tr class='row1'> | </tr><tr class='row1'> | ||
<td class='key'>3</td> | <td class='key'>3</td> | ||
| - | <td>[[Octahedron]]</td><td>B</td><td>Ko4</td> | + | <td>[[Octahedron]]</td><td><tt>B--</tt></td><td>Ko4</td> |
<td>8</td><td>12</td><td>6</td> | <td>8</td><td>12</td><td>6</td> | ||
<td colspan='3'>2. Cube ''(above)''</td> | <td colspan='3'>2. Cube ''(above)''</td> | ||
| - | </tr><tr class=' | + | </tr><tr class='row2'> |
<td class='key'>4</td> | <td class='key'>4</td> | ||
| - | <td>[[Dodecahedron]]</td><td>BS</td><td>Ki1</td> | + | <td>[[Dodecahedron]]</td><td><tt>BS-</tt></td><td>Ki1</td> |
<td>12</td><td>30</td><td>20</td> | <td>12</td><td>30</td><td>20</td> | ||
<td colspan='3'>5. Icosahedron ''(below)''</td> | <td colspan='3'>5. Icosahedron ''(below)''</td> | ||
</tr><tr class='row1'> | </tr><tr class='row1'> | ||
<td class='key'>5</td> | <td class='key'>5</td> | ||
| - | <td>[[Icosahedron]]</td><td>-</td><td>Ki4</td> | + | <td>[[Icosahedron]]</td><td><tt>B--</tt></td><td>Ki4</td> |
<td>20</td><td>30</td><td>12</td> | <td>20</td><td>30</td><td>12</td> | ||
<td colspan='3'>4. Dodecahedron ''(above)''</td> | <td colspan='3'>4. Dodecahedron ''(above)''</td> | ||
</tr><tr> | </tr><tr> | ||
<td class='cat' colspan='10'>Archimedean solids (total 13)</td> | <td class='cat' colspan='10'>Archimedean solids (total 13)</td> | ||
| + | </tr><tr class='row1'> | ||
| + | <td class='key'>6</td> | ||
| + | <td>[[Tetrahedral truncate]]</td><td><tt>-S-</tt></td><td>Kt3</td> | ||
| + | <td>8</td><td>18</td><td>12</td> | ||
| + | <td>[[Triakis tetrahedron]]</td><td><tt>---</tt></td><td>''Unknown''</td> | ||
| + | </tr><tr class='row2'> | ||
| + | <td class='key'>7</td> | ||
| + | <td>[[Cuboctahedron]]</td><td><tt>B--</tt></td><td>Ko2</td> | ||
| + | <td>14</td><td>24</td><td>12</td> | ||
| + | <td>[[Rhombic dodecahedron]]</td><td><tt>B-Z</tt></td><td>''Unknown''</td> | ||
| + | </tr><tr class='row1'> | ||
| + | <td class='key'>8</td> | ||
| + | <td>[[Cubic truncate]]</td><td><tt>BS-</tt></td><td>Ko3</td> | ||
| + | <td>14</td><td>36</td><td>24</td> | ||
| + | <td>[[Triakis octahedron]]</td><td><tt>B--</tt></td><td>''Unknown''</td> | ||
</tr><tr> | </tr><tr> | ||
<td class='cat' colspan='10'>Utility prisms (total 9)</td> | <td class='cat' colspan='10'>Utility prisms (total 9)</td> | ||
Revision as of 11:54, 5 December 2010
Three classes used in the table below:
- B = Brick: point (x, y, z) implies point (±x, ±y, ±z)
- S = Simple: exactly three faces meet at each vertex
- Z = Zonotope: each face has point symmetry
| Index | Parent | Elements | Dual | ||||||
|---|---|---|---|---|---|---|---|---|---|
| Name | Classes | SSC2 | Faces | Edges | Vertices | Name | Classes | SSC2 | |
| Platonic solids (total 5) | |||||||||
| 1 | Tetrahedron | -S- | Kt1 | 4 | 6 | 4 | Self-dual | ||
| 2 | Cube | BSZ | Ko1 | 6 | 12 | 8 | 3. Octahedron (below) | ||
| 3 | Octahedron | B-- | Ko4 | 8 | 12 | 6 | 2. Cube (above) | ||
| 4 | Dodecahedron | BS- | Ki1 | 12 | 30 | 20 | 5. Icosahedron (below) | ||
| 5 | Icosahedron | B-- | Ki4 | 20 | 30 | 12 | 4. Dodecahedron (above) | ||
| Archimedean solids (total 13) | |||||||||
| 6 | Tetrahedral truncate | -S- | Kt3 | 8 | 18 | 12 | Triakis tetrahedron | --- | Unknown |
| 7 | Cuboctahedron | B-- | Ko2 | 14 | 24 | 12 | Rhombic dodecahedron | B-Z | Unknown |
| 8 | Cubic truncate | BS- | Ko3 | 14 | 36 | 24 | Triakis octahedron | B-- | Unknown |
| Utility prisms (total 9) | |||||||||
| Johnson solids (total 92) | |||||||||
