List of convex regular-faced polyhedra (Meta, 13)
From Hi.gher. Space
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</tr><tr class='row2'> | </tr><tr class='row2'> | ||
<td class='key'>24 = J<sub>6</sub></td> | <td class='key'>24 = J<sub>6</sub></td> | ||
| - | <td>[[Pentagonal rotunda]]</td><td><tt>----</tt></td><td> | + | <td>[[Pentagonal rotunda]]</td><td><tt>----</tt></td><td>xox5ofx</td> |
<td>17</td><td>35</td><td>20</td> | <td>17</td><td>35</td><td>20</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row1'> | </tr><tr class='row1'> | ||
<td class='key'>25 = J<sub>7</sub></td> | <td class='key'>25 = J<sub>7</sub></td> | ||
| - | <td>[[Elongated triangular pyramid]]<br />(elongated tetrahedron)</td><td><tt>----</tt></td><td> | + | <td>[[Elongated triangular pyramid]]<br />(elongated tetrahedron)</td><td><tt>----</tt></td><td>oxx3ooo</td> |
<td>7</td><td>12</td><td>7</td> | <td>7</td><td>12</td><td>7</td> | ||
<td colspan='3'>''Self-dual''</td> | <td colspan='3'>''Self-dual''</td> | ||
</tr><tr class='row2'> | </tr><tr class='row2'> | ||
<td class='key'>26 = J<sub>8</sub></td> | <td class='key'>26 = J<sub>8</sub></td> | ||
| - | <td>[[Elongated square pyramid]]<br />(augmented cube)</td><td><tt>----</tt></td><td> | + | <td>[[Elongated square pyramid]]<br />(augmented cube)</td><td><tt>----</tt></td><td>oxx4ooo</td> |
<td>9</td><td>16</td><td>9</td> | <td>9</td><td>16</td><td>9</td> | ||
<td colspan='3'>''Self-dual''</td> | <td colspan='3'>''Self-dual''</td> | ||
</tr><tr class='row1'> | </tr><tr class='row1'> | ||
<td class='key'>27 = J<sub>9</sub></td> | <td class='key'>27 = J<sub>9</sub></td> | ||
| - | <td>[[Elongated pentagonal pyramid]]</td><td><tt>----</tt></td><td> | + | <td>[[Elongated pentagonal pyramid]]</td><td><tt>----</tt></td><td>oxx5ooo</td> |
<td>11</td><td>20</td><td>11</td> | <td>11</td><td>20</td><td>11</td> | ||
<td colspan='3'>''Self-dual''</td> | <td colspan='3'>''Self-dual''</td> | ||
</tr><tr class='row2'> | </tr><tr class='row2'> | ||
<td class='key'>28 = J<sub>10</sub></td> | <td class='key'>28 = J<sub>10</sub></td> | ||
| - | <td>[[Gyroelongated square pyramid]]</td><td><tt>----</tt></td><td> | + | <td>[[Gyroelongated square pyramid]]</td><td><tt>----</tt></td><td>oxo4oox</td> |
<td>13</td><td>20</td><td>9</td> | <td>13</td><td>20</td><td>9</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row1'> | </tr><tr class='row1'> | ||
<td class='key'>29 = J<sub>11</sub></td> | <td class='key'>29 = J<sub>11</sub></td> | ||
| - | <td>[[Gyroelongated pentagonal pyramid]]<br />(diminished icosahedron)</td><td><tt>----</tt></td><td> | + | <td>[[Gyroelongated pentagonal pyramid]]<br />(diminished icosahedron)</td><td><tt>----</tt></td><td>oxo5oox</td> |
<td>16</td><td>25</td><td>11</td> | <td>16</td><td>25</td><td>11</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row2'> | </tr><tr class='row2'> | ||
<td class='key'>30 = J<sub>12</sub></td> | <td class='key'>30 = J<sub>12</sub></td> | ||
| - | <td>[[Triangular bipyramid]]</td><td><tt>----</tt></td><td> | + | <td>[[Triangular bipyramid]]</td><td><tt>----</tt></td><td>oxo3ooo</td> |
<td>6</td><td>9</td><td>5</td> | <td>6</td><td>9</td><td>5</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row1'> | </tr><tr class='row1'> | ||
<td class='key'>31 = J<sub>13</sub></td> | <td class='key'>31 = J<sub>13</sub></td> | ||
| - | <td>[[Pentagonal bipyramid]]</td><td><tt>----</tt></td><td> | + | <td>[[Pentagonal bipyramid]]</td><td><tt>----</tt></td><td>oxo5ooo</td> |
<td>10</td><td>15</td><td>7</td> | <td>10</td><td>15</td><td>7</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row2'> | </tr><tr class='row2'> | ||
<td class='key'>32 = J<sub>14</sub></td> | <td class='key'>32 = J<sub>14</sub></td> | ||
| - | <td>[[Elongated triangular bipyramid]]</td><td><tt>----</tt></td><td> | + | <td>[[Elongated triangular bipyramid]]</td><td><tt>----</tt></td><td>oxxo3oooo</td> |
<td>9</td><td>15</td><td>8</td> | <td>9</td><td>15</td><td>8</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row1'> | </tr><tr class='row1'> | ||
<td class='key'>33 = J<sub>15</sub></td> | <td class='key'>33 = J<sub>15</sub></td> | ||
| - | <td>[[Elongated square bipyramid]]<br />(biaugmented cube)</td><td><tt>B---</tt></td><td> | + | <td>[[Elongated square bipyramid]]<br />(biaugmented cube)</td><td><tt>B---</tt></td><td>oxxo4oooo</td> |
<td>12</td><td>20</td><td>10</td> | <td>12</td><td>20</td><td>10</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row2'> | </tr><tr class='row2'> | ||
<td class='key'>34 = J<sub>16</sub></td> | <td class='key'>34 = J<sub>16</sub></td> | ||
| - | <td>[[Elongated pentagonal bipyramid]]</td><td><tt>----</tt></td><td> | + | <td>[[Elongated pentagonal bipyramid]]</td><td><tt>----</tt></td><td>oxxo5oooo</td> |
<td>15</td><td>25</td><td>12</td> | <td>15</td><td>25</td><td>12</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row1'> | </tr><tr class='row1'> | ||
<td class='key'>35 = J<sub>17</sub></td> | <td class='key'>35 = J<sub>17</sub></td> | ||
| - | <td>[[Gyroelongated square bipyramid]]</td><td><tt>----</tt></td><td> | + | <td>[[Gyroelongated square bipyramid]]</td><td><tt>----</tt></td><td>oxoo4oooo</td> |
<td>16</td><td>24</td><td>10</td> | <td>16</td><td>24</td><td>10</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row2'> | </tr><tr class='row2'> | ||
<td class='key'>36 = J<sub>18</sub></td> | <td class='key'>36 = J<sub>18</sub></td> | ||
| - | <td>[[Elongated triangular cupola]]</td><td><tt>----</tt></td><td> | + | <td>[[Elongated triangular cupola]]</td><td><tt>----</tt></td><td>oxx3xxx</td> |
<td>14</td><td>27</td><td>15</td> | <td>14</td><td>27</td><td>15</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row1'> | </tr><tr class='row1'> | ||
<td class='key'>37 = J<sub>19</sub></td> | <td class='key'>37 = J<sub>19</sub></td> | ||
| - | <td>[[Elongated square cupola]]<br />(diminished rhombicuboctahedron)</td><td><tt>----</tt></td><td> | + | <td>[[Elongated square cupola]]<br />(diminished rhombicuboctahedron)</td><td><tt>----</tt></td><td>oxx4xxx</td> |
<td>18</td><td>36</td><td>20</td> | <td>18</td><td>36</td><td>20</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row2'> | </tr><tr class='row2'> | ||
<td class='key'>38 = J<sub>20</sub></td> | <td class='key'>38 = J<sub>20</sub></td> | ||
| - | <td>[[Elongated pentagonal cupola]]</td><td><tt>----</tt></td><td> | + | <td>[[Elongated pentagonal cupola]]</td><td><tt>----</tt></td><td>oxx5xxx</td> |
<td>22</td><td>45</td><td>25</td> | <td>22</td><td>45</td><td>25</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row1'> | </tr><tr class='row1'> | ||
<td class='key'>39 = J<sub>21</sub></td> | <td class='key'>39 = J<sub>21</sub></td> | ||
| - | <td>[[Elongated pentagonal rotunda]]</td><td><tt>----</tt></td><td> | + | <td>[[Elongated pentagonal rotunda]]</td><td><tt>----</tt></td><td>xoxx5ofxx</td> |
<td>27</td><td>55</td><td>30</td> | <td>27</td><td>55</td><td>30</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
| Line 252: | Line 252: | ||
</tr><tr class='row1'> | </tr><tr class='row1'> | ||
<td class='key'>45 = J<sub>27</sub></td> | <td class='key'>45 = J<sub>27</sub></td> | ||
| - | <td>[[Triangular orthobicupola]]<br />(gyrate cuboctahedron)</td><td><tt>----</tt></td><td> | + | <td>[[Triangular orthobicupola]]<br />(gyrate cuboctahedron)</td><td><tt>----</tt></td><td>oxo3xox</td> |
<td>14</td><td>24</td><td>12</td> | <td>14</td><td>24</td><td>12</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row2'> | </tr><tr class='row2'> | ||
<td class='key'>46 = J<sub>28</sub></td> | <td class='key'>46 = J<sub>28</sub></td> | ||
| - | <td>[[Square orthobicupola]]</td><td><tt>B---</tt></td><td> | + | <td>[[Square orthobicupola]]</td><td><tt>B---</tt></td><td>oxo4xxx</td> |
<td>18</td><td>32</td><td>16</td> | <td>18</td><td>32</td><td>16</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row1'> | </tr><tr class='row1'> | ||
<td class='key'>47 = J<sub>29</sub></td> | <td class='key'>47 = J<sub>29</sub></td> | ||
| - | <td>[[Square gyrobicupola]]</td><td><tt>----</tt></td><td> | + | <td>[[Square gyrobicupola]]</td><td><tt>----</tt></td><td>xxo4oxx</td> |
<td>18</td><td>32</td><td>16</td> | <td>18</td><td>32</td><td>16</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row2'> | </tr><tr class='row2'> | ||
<td class='key'>48 = J<sub>30</sub></td> | <td class='key'>48 = J<sub>30</sub></td> | ||
| - | <td>[[Pentagonal orthobicupola]]</td><td><tt>----</tt></td><td> | + | <td>[[Pentagonal orthobicupola]]</td><td><tt>----</tt></td><td>oxo5xxx</td> |
<td>22</td><td>40</td><td>20</td> | <td>22</td><td>40</td><td>20</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row1'> | </tr><tr class='row1'> | ||
<td class='key'>49 = J<sub>31</sub></td> | <td class='key'>49 = J<sub>31</sub></td> | ||
| - | <td>[[Pentagonal gyrobicupola]]</td><td><tt>----</tt></td><td> | + | <td>[[Pentagonal gyrobicupola]]</td><td><tt>----</tt></td><td>oxx5xxo</td> |
<td>22</td><td>40</td><td>20</td> | <td>22</td><td>40</td><td>20</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row2'> | </tr><tr class='row2'> | ||
<td class='key'>50 = J<sub>32</sub></td> | <td class='key'>50 = J<sub>32</sub></td> | ||
| - | <td>[[Pentagonal orthocupolarotunda]]</td><td><tt>----</tt></td><td> | + | <td>[[Pentagonal orthocupolarotunda]]</td><td><tt>----</tt></td><td>oxfo5xxox</td> |
<td>27</td><td>50</td><td>25</td> | <td>27</td><td>50</td><td>25</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row1'> | </tr><tr class='row1'> | ||
<td class='key'>51 = J<sub>33</sub></td> | <td class='key'>51 = J<sub>33</sub></td> | ||
| - | <td>[[Pentagonal gyrocupolarotunda]]</td><td><tt>----</tt></td><td> | + | <td>[[Pentagonal gyrocupolarotunda]]</td><td><tt>----</tt></td><td>xxfo5oxox</td> |
<td>27</td><td>50</td><td>25</td> | <td>27</td><td>50</td><td>25</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row2'> | </tr><tr class='row2'> | ||
<td class='key'>52 = J<sub>34</sub></td> | <td class='key'>52 = J<sub>34</sub></td> | ||
| - | <td>[[Pentagonal orthobirotunda]]<br />(gyrate icosidodecahedron)</td><td><tt>----</tt></td><td> | + | <td>[[Pentagonal orthobirotunda]]<br />(gyrate icosidodecahedron)</td><td><tt>----</tt></td><td>xoxox5ofofo</td> |
<td>32</td><td>60</td><td>30</td> | <td>32</td><td>60</td><td>30</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row1'> | </tr><tr class='row1'> | ||
<td class='key'>53 = J<sub>35</sub></td> | <td class='key'>53 = J<sub>35</sub></td> | ||
| - | <td>[[Elongated triangular orthobicupola]]</td><td><tt>----</tt></td><td> | + | <td>[[Elongated triangular orthobicupola]]</td><td><tt>----</tt></td><td>xxxxx3oxxxo</td> |
<td>20</td><td>36</td><td>18</td> | <td>20</td><td>36</td><td>18</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row2'> | </tr><tr class='row2'> | ||
<td class='key'>54 = J<sub>36</sub></td> | <td class='key'>54 = J<sub>36</sub></td> | ||
| - | <td>[[Elongated triangular gyrobicupola]]</td><td><tt>----</tt></td><td> | + | <td>[[Elongated triangular gyrobicupola]]</td><td><tt>----</tt></td><td>oxxxx3xxxxo</td> |
<td>20</td><td>36</td><td>18</td> | <td>20</td><td>36</td><td>18</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row1'> | </tr><tr class='row1'> | ||
<td class='key'>55 = J<sub>37</sub></td> | <td class='key'>55 = J<sub>37</sub></td> | ||
| - | <td>[[Elongated square gyrobicupola]]<br />(gyrate rhombicuboctahedron)</td><td><tt>----</tt></td><td> | + | <td>[[Elongated square gyrobicupola]]<br />(gyrate rhombicuboctahedron)</td><td><tt>----</tt></td><td>oxxx4xxxo</td> |
<td>26</td><td>48</td><td>24</td> | <td>26</td><td>48</td><td>24</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row2'> | </tr><tr class='row2'> | ||
<td class='key'>56 = J<sub>38</sub></td> | <td class='key'>56 = J<sub>38</sub></td> | ||
| - | <td>[[Elongated pentagonal orthobicupola]]</td><td><tt>----</tt></td><td> | + | <td>[[Elongated pentagonal orthobicupola]]</td><td><tt>----</tt></td><td>xxxx5oxxo</td> |
<td>32</td><td>60</td><td>30</td> | <td>32</td><td>60</td><td>30</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row1'> | </tr><tr class='row1'> | ||
<td class='key'>57 = J<sub>39</sub></td> | <td class='key'>57 = J<sub>39</sub></td> | ||
| - | <td>[[Elongated pentagonal gyrobicupola]]</td><td><tt>----</tt></td><td> | + | <td>[[Elongated pentagonal gyrobicupola]]</td><td><tt>----</tt></td><td>oxxxx5xxxxo</td> |
<td>32</td><td>60</td><td>30</td> | <td>32</td><td>60</td><td>30</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row2'> | </tr><tr class='row2'> | ||
<td class='key'>58 = J<sub>40</sub></td> | <td class='key'>58 = J<sub>40</sub></td> | ||
| - | <td>[[Elongated pentagonal orthocupolarotunda]]</td><td><tt>----</tt></td><td> | + | <td>[[Elongated pentagonal orthocupolarotunda]]</td><td><tt>----</tt></td><td>xxox5oxfo</td> |
<td>37</td><td>70</td><td>35</td> | <td>37</td><td>70</td><td>35</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row1'> | </tr><tr class='row1'> | ||
<td class='key'>59 = J<sub>41</sub></td> | <td class='key'>59 = J<sub>41</sub></td> | ||
| - | <td>[[Elongated pentagonal gyrocupolarotunda]]</td><td><tt>----</tt></td><td> | + | <td>[[Elongated pentagonal gyrocupolarotunda]]</td><td><tt>----</tt></td><td>oxox5xxfo</td> |
<td>37</td><td>70</td><td>35</td> | <td>37</td><td>70</td><td>35</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row2'> | </tr><tr class='row2'> | ||
<td class='key'>60 = J<sub>42</sub></td> | <td class='key'>60 = J<sub>42</sub></td> | ||
| - | <td>[[Elongated pentagonal orthobirotunda]]</td><td><tt>----</tt></td><td> | + | <td>[[Elongated pentagonal orthobirotunda]]</td><td><tt>----</tt></td><td>xoxxox5ofxxfo</td> |
<td>42</td><td>80</td><td>40</td> | <td>42</td><td>80</td><td>40</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row1'> | </tr><tr class='row1'> | ||
<td class='key'>61 = J<sub>43</sub></td> | <td class='key'>61 = J<sub>43</sub></td> | ||
| - | <td>[[Elongated pentagonal gyrobirotunda]]</td><td><tt>----</tt></td><td> | + | <td>[[Elongated pentagonal gyrobirotunda]]</td><td><tt>----</tt></td><td>xoxxfo5ofxxox</td> |
<td>42</td><td>80</td><td>40</td> | <td>42</td><td>80</td><td>40</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
| Line 362: | Line 362: | ||
</tr><tr class='row1'> | </tr><tr class='row1'> | ||
<td class='key'>67 = J<sub>49</sub></td> | <td class='key'>67 = J<sub>49</sub></td> | ||
| - | <td>[[Augmented triangular prism]]</td><td><tt>----</tt></td><td> | + | <td>[[Augmented triangular prism]]</td><td><tt>----</tt></td><td>oxo2oxx</td> |
<td>8</td><td>13</td><td>7</td> | <td>8</td><td>13</td><td>7</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
| Line 377: | Line 377: | ||
</tr><tr class='row2'> | </tr><tr class='row2'> | ||
<td class='key'>70 = J<sub>52</sub></td> | <td class='key'>70 = J<sub>52</sub></td> | ||
| - | <td>[[Augmented pentagonal prism]]</td><td><tt>----</tt></td><td> | + | <td>[[Augmented pentagonal prism]]</td><td><tt>----</tt></td><td>oxfo2oxxx</td> |
<td>10</td><td>19</td><td>11</td> | <td>10</td><td>19</td><td>11</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
| Line 387: | Line 387: | ||
</tr><tr class='row2'> | </tr><tr class='row2'> | ||
<td class='key'>72 = J<sub>54</sub></td> | <td class='key'>72 = J<sub>54</sub></td> | ||
| - | <td>[[Augmented hexagonal prism]]</td><td><tt>----</tt></td><td> | + | <td>[[Augmented hexagonal prism]]</td><td><tt>----</tt></td><td>oxhx2oxxx</td> |
<td>11</td><td>22</td><td>13</td> | <td>11</td><td>22</td><td>13</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row1'> | </tr><tr class='row1'> | ||
<td class='key'>73 = J<sub>55</sub></td> | <td class='key'>73 = J<sub>55</sub></td> | ||
| - | <td>[[Parabiaugmented hexagonal prism]]</td><td><tt>B---</tt></td><td> | + | <td>[[Parabiaugmented hexagonal prism]]</td><td><tt>B---</tt></td><td>oxhxo2oxxxo</td> |
<td>14</td><td>26</td><td>14</td> | <td>14</td><td>26</td><td>14</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
| Line 407: | Line 407: | ||
</tr><tr class='row2'> | </tr><tr class='row2'> | ||
<td class='key'>76 = J<sub>58</sub></td> | <td class='key'>76 = J<sub>58</sub></td> | ||
| - | <td>[[Augmented dodecahedron]]</td><td><tt>----</tt></td><td> | + | <td>[[Augmented dodecahedron]]</td><td><tt>----</tt></td><td>oxfoo5oofx</td> |
<td>16</td><td>35</td><td>21</td> | <td>16</td><td>35</td><td>21</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row1'> | </tr><tr class='row1'> | ||
<td class='key'>77 = J<sub>59</sub></td> | <td class='key'>77 = J<sub>59</sub></td> | ||
| - | <td>[[Parabiaugmented dodecahedron]]</td><td><tt>----</tt></td><td> | + | <td>[[Parabiaugmented dodecahedron]]</td><td><tt>----</tt></td><td>oxfooo5ooofxo</td> |
<td>20</td><td>40</td><td>22</td> | <td>20</td><td>40</td><td>22</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
| Line 432: | Line 432: | ||
</tr><tr class='row1'> | </tr><tr class='row1'> | ||
<td class='key'>81 = J<sub>63</sub></td> | <td class='key'>81 = J<sub>63</sub></td> | ||
| - | <td>[[Tridiminished icosahedron]]</td><td><tt>----</tt></td><td> | + | <td>[[Tridiminished icosahedron]]</td><td><tt>----</tt></td><td>xfo3oox</td> |
<td>8</td><td>15</td><td>9</td> | <td>8</td><td>15</td><td>9</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
</tr><tr class='row2'> | </tr><tr class='row2'> | ||
<td class='key'>82 = J<sub>64</sub></td> | <td class='key'>82 = J<sub>64</sub></td> | ||
| - | <td>[[Augmented tridiminished icosahedron]]</td><td><tt>----</tt></td><td> | + | <td>[[Augmented tridiminished icosahedron]]</td><td><tt>----</tt></td><td>oxfo3ooox</td> |
<td>10</td><td>18</td><td>10</td> | <td>10</td><td>18</td><td>10</td> | ||
<td colspan='3'>''Unknown''</td> | <td colspan='3'>''Unknown''</td> | ||
Revision as of 13:11, 26 February 2014
See also: CRF polychora discovery project
Key to classes used in the table below:
- B = Brick: point (x, y, z) implies point (±x, ±y, ±z)
- C = Chiral: there is no 3D rotation which can map the polyhedron onto its reflection in x = 0
- S = Simple: exactly three faces meet at each vertex
- Z = Zonotope: each face has point symmetry
| Index | Parent | Elements | Dual | ||||||
|---|---|---|---|---|---|---|---|---|---|
| Name | Classes | Symbol | Faces | Edges | Vertices | Name | Classes | Symbol | |
| Platonic solids (total 5) | |||||||||
| 1 | Tetrahedron | --S- | x3o3o | 4 | 6 | 4 | Self-dual | ||
| 2 | Cube | B-SZ | x4o3o | 6 | 12 | 8 | 3. Octahedron (below) | ||
| 3 | Octahedron | B--- | x3o4o | 8 | 12 | 6 | 2. Cube (above) | ||
| 4 | Dodecahedron | B-S- | x5o3o | 12 | 30 | 20 | 5. Icosahedron (below) | ||
| 5 | Icosahedron | B--- | x3o5o | 20 | 30 | 12 | 4. Dodecahedron (above) | ||
| Archimedean solids (total 13) | |||||||||
| 6 | Tetrahedral truncate | --S- | x3x3o | 8 | 18 | 12 | Triakis tetrahedron | ---- | m3m3o |
| 7 | Stauromesohedron | B--- | o4x3o | 14 | 24 | 12 | Rhombic dodecahedron | B--Z | o4m3o |
| 8 | Cubic truncate | B-S- | x4x3o | 14 | 36 | 24 | Triakis octahedron | B--- | m4m3o |
| 9 | Octahedral truncate | B-S- | x3x4o | 14 | 36 | 24 | Tetrakis hexahedron | B--- | m3m4o |
| 10 | Stauroperihedron | B--- | x4o3x | 26 | 48 | 24 | Deltoidal icositetrahedron | B--- | m4o3m |
| 11 | Stauropantohedron | B-SZ | x4x3x | 26 | 72 | 48 | Disdyakis dodecahedron | B--- | m4m3m |
| 12 | Snub staurohedron | -C-- | s4s3s | 38 | 60 | 24 | Pentagonal icositetrahedron | -C-- | g4g3g |
| 13 | Rhodomesohedron | B--- | o5x3o | 32 | 60 | 30 | Rhombic triacontahedron | B--Z | o5m3o |
| 14 | Dodecahedral truncate | B-S- | x5x3o | 32 | 90 | 60 | Triakis icosahedron | B--- | m5m3o |
| 15 | Icosahedral truncate | B-S- | x3x5o | 32 | 90 | 30 | Pentakis dodecahedron | B--- | m3m5o |
| 16 | Rhodoperihedron | B--- | x5o3x | 62 | 120 | 60 | Deltoidal hexecontahedron | B--- | m5o3m |
| 17 | Rhodopantohedron | B-SZ | x5x3x | 62 | 180 | 120 | Disdyakis triacontahedron | B--- | m3m5m |
| 18 | Snub rhodohedron | -C-- | s5s3s | 92 | 150 | 60 | Pentagonal hexecontahedron | -C-- | g5g3g |
| Johnson solids (total 92) | |||||||||
| 19 = J1 | Square pyramid | ---- | xo4oo | 5 | 8 | 5 | Self-dual | ||
| 20 = J2 | Pentagonal pyramid | ---- | xo5oo | 6 | 10 | 6 | Self-dual | ||
| 21 = J3 | Triangular cupola | ---- | xx3xo | 8 | 15 | 9 | Unknown | ||
| 22 = J4 | Square cupola | ---- | xx4xo | 10 | 20 | 12 | Unknown | ||
| 23 = J5 | Pentagonal cupola | ---- | xx5xo | 12 | 25 | 15 | Unknown | ||
| 24 = J6 | Pentagonal rotunda | ---- | xox5ofx | 17 | 35 | 20 | Unknown | ||
| 25 = J7 | Elongated triangular pyramid (elongated tetrahedron) | ---- | oxx3ooo | 7 | 12 | 7 | Self-dual | ||
| 26 = J8 | Elongated square pyramid (augmented cube) | ---- | oxx4ooo | 9 | 16 | 9 | Self-dual | ||
| 27 = J9 | Elongated pentagonal pyramid | ---- | oxx5ooo | 11 | 20 | 11 | Self-dual | ||
| 28 = J10 | Gyroelongated square pyramid | ---- | oxo4oox | 13 | 20 | 9 | Unknown | ||
| 29 = J11 | Gyroelongated pentagonal pyramid (diminished icosahedron) | ---- | oxo5oox | 16 | 25 | 11 | Unknown | ||
| 30 = J12 | Triangular bipyramid | ---- | oxo3ooo | 6 | 9 | 5 | Unknown | ||
| 31 = J13 | Pentagonal bipyramid | ---- | oxo5ooo | 10 | 15 | 7 | Unknown | ||
| 32 = J14 | Elongated triangular bipyramid | ---- | oxxo3oooo | 9 | 15 | 8 | Unknown | ||
| 33 = J15 | Elongated square bipyramid (biaugmented cube) | B--- | oxxo4oooo | 12 | 20 | 10 | Unknown | ||
| 34 = J16 | Elongated pentagonal bipyramid | ---- | oxxo5oooo | 15 | 25 | 12 | Unknown | ||
| 35 = J17 | Gyroelongated square bipyramid | ---- | oxoo4oooo | 16 | 24 | 10 | Unknown | ||
| 36 = J18 | Elongated triangular cupola | ---- | oxx3xxx | 14 | 27 | 15 | Unknown | ||
| 37 = J19 | Elongated square cupola (diminished rhombicuboctahedron) | ---- | oxx4xxx | 18 | 36 | 20 | Unknown | ||
| 38 = J20 | Elongated pentagonal cupola | ---- | oxx5xxx | 22 | 45 | 25 | Unknown | ||
| 39 = J21 | Elongated pentagonal rotunda | ---- | xoxx5ofxx | 27 | 55 | 30 | Unknown | ||
| 40 = J22 | Gyroelongated triangular cupola | ---- | Unknown | 20 | 33 | 15 | Unknown | ||
| 41 = J23 | Gyroelongated square cupola | ---- | Unknown | 26 | 44 | 20 | Unknown | ||
| 42 = J24 | Gyroelongated pentagonal cupola | ---- | Unknown | 32 | 55 | 25 | Unknown | ||
| 43 = J25 | Gyroelongated pentagonal rotunda | ---- | Unknown | 37 | 65 | 30 | Unknown | ||
| 44 = J26 | Gyrobifastigium | ---- | Unknown | 8 | 14 | 8 | Unknown | ||
| 45 = J27 | Triangular orthobicupola (gyrate cuboctahedron) | ---- | oxo3xox | 14 | 24 | 12 | Unknown | ||
| 46 = J28 | Square orthobicupola | B--- | oxo4xxx | 18 | 32 | 16 | Unknown | ||
| 47 = J29 | Square gyrobicupola | ---- | xxo4oxx | 18 | 32 | 16 | Unknown | ||
| 48 = J30 | Pentagonal orthobicupola | ---- | oxo5xxx | 22 | 40 | 20 | Unknown | ||
| 49 = J31 | Pentagonal gyrobicupola | ---- | oxx5xxo | 22 | 40 | 20 | Unknown | ||
| 50 = J32 | Pentagonal orthocupolarotunda | ---- | oxfo5xxox | 27 | 50 | 25 | Unknown | ||
| 51 = J33 | Pentagonal gyrocupolarotunda | ---- | xxfo5oxox | 27 | 50 | 25 | Unknown | ||
| 52 = J34 | Pentagonal orthobirotunda (gyrate icosidodecahedron) | ---- | xoxox5ofofo | 32 | 60 | 30 | Unknown | ||
| 53 = J35 | Elongated triangular orthobicupola | ---- | xxxxx3oxxxo | 20 | 36 | 18 | Unknown | ||
| 54 = J36 | Elongated triangular gyrobicupola | ---- | oxxxx3xxxxo | 20 | 36 | 18 | Unknown | ||
| 55 = J37 | Elongated square gyrobicupola (gyrate rhombicuboctahedron) | ---- | oxxx4xxxo | 26 | 48 | 24 | Unknown | ||
| 56 = J38 | Elongated pentagonal orthobicupola | ---- | xxxx5oxxo | 32 | 60 | 30 | Unknown | ||
| 57 = J39 | Elongated pentagonal gyrobicupola | ---- | oxxxx5xxxxo | 32 | 60 | 30 | Unknown | ||
| 58 = J40 | Elongated pentagonal orthocupolarotunda | ---- | xxox5oxfo | 37 | 70 | 35 | Unknown | ||
| 59 = J41 | Elongated pentagonal gyrocupolarotunda | ---- | oxox5xxfo | 37 | 70 | 35 | Unknown | ||
| 60 = J42 | Elongated pentagonal orthobirotunda | ---- | xoxxox5ofxxfo | 42 | 80 | 40 | Unknown | ||
| 61 = J43 | Elongated pentagonal gyrobirotunda | ---- | xoxxfo5ofxxox | 42 | 80 | 40 | Unknown | ||
| 62 = J44 | Gyroelongated triangular bicupola | -C-- | Unknown | 26 | 42 | 18 | Unknown | ||
| 63 = J45 | Gyroelongated square bicupola | -C-- | Unknown | 34 | 56 | 24 | Unknown | ||
| 64 = J46 | Gyroelongated pentagonal bicupola | -C-- | Unknown | 42 | 70 | 30 | Unknown | ||
| 65 = J47 | Gyroelongated pentagonal cupolarotunda | -C-- | Unknown | 47 | 80 | 35 | Unknown | ||
| 66 = J48 | Gyroelongated pentagonal birotunda | -C-- | Unknown | 52 | 90 | 40 | Unknown | ||
| 67 = J49 | Augmented triangular prism | ---- | oxo2oxx | 8 | 13 | 7 | Unknown | ||
| 68 = J50 | Biaugmented triangular prism | ---- | Unknown | 11 | 17 | 8 | Unknown | ||
| 69 = J51 | Triaugmented triangular prism | ---- | Unknown | 14 | 21 | 9 | Unknown | ||
| 70 = J52 | Augmented pentagonal prism | ---- | oxfo2oxxx | 10 | 19 | 11 | Unknown | ||
| 71 = J53 | Biaugmented pentagonal prism | ---- | Unknown | 13 | 23 | 12 | Unknown | ||
| 72 = J54 | Augmented hexagonal prism | ---- | oxhx2oxxx | 11 | 22 | 13 | Unknown | ||
| 73 = J55 | Parabiaugmented hexagonal prism | B--- | oxhxo2oxxxo | 14 | 26 | 14 | Unknown | ||
| 74 = J56 | Metabiaugmented hexagonal prism | ---- | Unknown | 14 | 26 | 14 | Unknown | ||
| 75 = J57 | Triaugmented hexagonal prism | ---- | Unknown | 17 | 30 | 15 | Unknown | ||
| 76 = J58 | Augmented dodecahedron | ---- | oxfoo5oofx | 16 | 35 | 21 | Unknown | ||
| 77 = J59 | Parabiaugmented dodecahedron | ---- | oxfooo5ooofxo | 20 | 40 | 22 | Unknown | ||
| 78 = J60 | Metabiaugmented dodecahedron | ---- | Unknown | 20 | 40 | 22 | Unknown | ||
| 79 = J61 | Triaugmented dodecahedron | ---- | Unknown | 24 | 45 | 23 | Unknown | ||
| 80 = J62 | Metabidiminished icosahedron | ---- | Unknown | 12 | 20 | 10 | Unknown | ||
| 81 = J63 | Tridiminished icosahedron | ---- | xfo3oox | 8 | 15 | 9 | Unknown | ||
| 82 = J64 | Augmented tridiminished icosahedron | ---- | oxfo3ooox | 10 | 18 | 10 | Unknown | ||
| 83 = J65 | Augmented truncated tetrahedron | ---- | Unknown | 14 | 27 | 15 | Unknown | ||
| 84 = J66 | Augmented truncated cube | ---- | Unknown | 22 | 48 | 28 | Unknown | ||
| 85 = J67 | Biaugmented truncated cube | B--- | Unknown | 30 | 60 | 32 | Unknown | ||
| 86 = J68 | Augmented truncated dodecahedron | ---- | Unknown | 42 | 105 | 65 | Unknown | ||
| 87 = J69 | Parabiaugmented truncated dodecahedron | ---- | Unknown | 52 | 120 | 70 | Unknown | ||
| 88 = J70 | Metabiaugmented truncated dodecahedron | ---- | Unknown | 52 | 120 | 70 | Unknown | ||
| 89 = J71 | Triaugmented truncated dodecahedron | ---- | Unknown | 62 | 135 | 75 | Unknown | ||
| 90 = J72 | Gyrate rhodoperihedron | ---- | Unknown | 62 | 120 | 60 | Unknown | ||
| 91 = J73 | Parabigyrate rhodoperihedron | ---- | Unknown | 62 | 120 | 60 | Unknown | ||
| 92 = J74 | Metabigyrate rhodoperihedron | ---- | Unknown | 62 | 120 | 60 | Unknown | ||
| 93 = J75 | Trigyrate rhodoperihedron | ---- | Unknown | 62 | 120 | 60 | Unknown | ||
| 94 = J76 | Diminished rhodoperihedron | ---- | Unknown | 52 | 105 | 55 | Unknown | ||
| 95 = J77 | Paragyrate diminished rhodoperihedron | ---- | Unknown | 52 | 105 | 55 | Unknown | ||
| 96 = J78 | Metagyrate diminished rhodoperihedron | ---- | Unknown | 52 | 105 | 55 | Unknown | ||
| 97 = J79 | Bigyrate diminished rhodoperihedron | ---- | Unknown | 52 | 105 | 55 | Unknown | ||
| 98 = J80 | Parabidiminished rhodoperihedron | ---- | Unknown | 42 | 90 | 50 | Unknown | ||
| 99 = J81 | Metabidiminished rhodoperihedron | ---- | Unknown | 42 | 90 | 50 | Unknown | ||
| 100 = J82 | Gyrate bidiminished rhodoperihedron | ---- | Unknown | 42 | 90 | 50 | Unknown | ||
| 101 = J83 | Tridiminished rhodoperihedron | ---- | Unknown | 32 | 75 | 45 | Unknown | ||
| 102 = J84 | Snub disphenoid (Siamese dodecahedron) | ---- | Unknown | 12 | 18 | 8 | Unknown | ||
| 103 = J85 | Snub square antiprism | ---- | Unknown | 26 | 40 | 16 | Unknown | ||
| 104 = J86 | Sphenocorona | ---- | Unknown | 14 | 22 | 10 | Unknown | ||
| 105 = J87 | Augmented sphenocorona | ---- | Unknown | 17 | 26 | 11 | Unknown | ||
| 106 = J88 | Sphenomegacorona | ---- | Unknown | 18 | 28 | 12 | Unknown | ||
| 107 = J89 | Hebesphenomegacorona | ---- | Unknown | 21 | 33 | 14 | Unknown | ||
| 108 = J90 | Disphenocingulum | ---- | Unknown | 24 | 38 | 16 | Unknown | ||
| 109 = J91 | Bilunabirotunda | B--- | Unknown | 14 | 26 | 14 | Unknown | ||
| 110 = J92 | Triangular hebesphenorotunda | ---- | Unknown | 20 | 36 | 18 | Unknown | ||
| Utility prisms (total 7) | |||||||||
| 111 | Triangular prism | --S- | x3o2x | 5 | 9 | 6 | 30. Triangular bipyramid (above) | ||
| 112 | Hexagonal prism | B-SZ | x3x2x | 8 | 18 | 12 | Hexagonal bipyramid | B--- | oxo3oxo |
| 113 | Octagonal prism | B-SZ | x4x2x | 10 | 24 | 16 | Octagonal bipyramid | B--- | oxo4oxo |
| 114 | Square antiprism | ---- | xo4ox | 10 | 16 | 8 | Tetragonal trapezohedron | ---- | Unknown |
| 115 | Pentagonal prism | --S- | x5o2x | 7 | 15 | 10 | 31. Pentagonal bipyramid (above) | ||
| 116 | Decagonal prism | B-SZ | x5x2x | 12 | 30 | 20 | Decagonal bipyramid | B--- | oxo5oxo |
| 117 | Pentagonal antiprism | ---- | xo5ox | 12 | 20 | 10 | Pentagonal trapezohedron | ---- | Unknown |
The utility prisms are so named because they are the only prisms which appear as cells in higher-dimensional uniform polytopes. The antiprisms of the same symmetry groups are included for completeness.
