List of uniform polychora (Meta, 11)

From Hi.gher. Space

(Difference between revisions)
m (→Uniform polyhedra usage statistics)
(→Rhodomorphs: add rhodomorphs)
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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:35%;' class='key' rowspan='2'>Variant</th>
+
<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 216: Line 217:
<th style='width:5%;'>|V|</th>
<th style='width:5%;'>|V|</th>
</tr><tr>
</tr><tr>
-
<td class='cat' colspan='10'></td>
+
<td class='cat' colspan='11'></td>
 +
</tr><tr class='row1'>
 +
<td>1</td><td>xooo</td><td>[[Cosmochoron|parent (1-tome)]]</td>
 +
<td>[[Dodecahedron|(5<sup>3</sup>)]]<sup>4</sup></td><td>--</td><td>--</td><td>--</td>
 +
<td>120</td><td>720</td><td>1200</td><td>600</td>
 +
</tr><tr class='row2'>
 +
<td>3</td><td>xxoo</td><td>[[2-cosmotomochoron|truncate (2-tome)]]</td>
 +
<td>[[Dodecahedral truncate|(3·10<sup>2</sup>)]]<sup>3</sup></td><td>--</td><td>--</td><td>[[Tetrahedron|(3<sup>3</sup>)]]<sup>1</sup></td>
 +
<td>720</td><td>3120</td><td>4800</td><td>2400</td>
 +
</tr><tr class='row1'>
 +
<td>2</td><td>oxoo</td><td>[[3-cosmotomochoron|hemicate (3-tome)]]</td>
 +
<td>[[Icosidodecahedron|({3·5}<sup>2</sup>)]]<sup>3</sup></td><td>--</td><td>--</td><td>[[Tetrahedron|(3<sup>3</sup>)]]<sup>2</sup></td>
 +
<td>720</td><td>3120</td><td>3600</td><td>1200</td>
 +
</tr><tr class='row2'>
 +
<td>6</td><td>oxxo</td><td>[[stauromesochoron|mesotruncate (4-tome)]]</td>
 +
<td>[[Icosahedral truncate|(5·6<sup>2</sup>)]]<sup>2</sup></td><td>--</td><td>--</td><td>[[Tetrahedral truncate|(3·6<sup>2</sup>)]]<sup>2</sup></td>
 +
<td>720</td><td>4320</td><td>7200</td><td>3600</td>
 +
</tr><tr class='row1'>
 +
<td>4</td><td>ooxo</td><td>[[3-hydrotomochoron|dual hemicate (5-tome)]]</td>
 +
<td>[[Icosahedron|(3<sup>5</sup>)]]<sup>2</sup></td><td>--</td><td>--</td><td>[[Octahedron|(3<sup>4</sup>)]]<sup>5</sup></td>
 +
<td>720</td><td>3600</td><td>3600</td><td>720</td>
 +
</tr><tr class='row2'>
 +
<td>12</td><td>ooxx</td><td>[[2-hydrotomochoron|dual truncate (6-tome)]]</td>
 +
<td>[[Icosahedron|(3<sup>5</sup>)]]<sup>1</sup></td><td>--</td><td>--</td><td>[[Tetrahedral truncate|(3·6<sup>2</sup>)]]<sup>5</sup></td>
 +
<td>720</td><td>3600</td><td>4320</td><td>1440</td>
 +
</tr><tr class='row1'>
 +
<td>8</td><td>ooox</td><td>[[Hydrochoron|dual (7-tome)]]</td>
 +
<td>--</td><td>--</td><td>--</td><td>[[Tetrahedron|(3<sup>3</sup>)]]<sup>20</sup></td>
 +
<td>600</td><td>1200</td><td>720</td><td>120</td>
 +
</tr><tr>
 +
<td class='cat' colspan='11'></td>
 +
</tr><tr class='row1'>
 +
<td>5</td><td>xoxo</td><td>[[cantellated 120-cell|cantellate]]</td>
 +
<td>[[Icosidodecahedral rectate|(3·4·5·4)]]<sup>2</sup></td><td>--</td><td>[[Triangular prism|(3·4<sup>2</sup>)]]<sup>2</sup></td><td>[[Octahedron|(3<sup>4</sup>)]]<sup>1</sup></td>
 +
<td>1920</td><td>9120</td><td>10800</td><td>3600</td>
 +
</tr><tr class='row2'>
 +
<td>10</td><td>oxox</td><td>[[cantellated 600-cell|dual cantellate]]</td>
 +
<td>[[Icosidodecahedron|({3·5}<sup>2</sup>)]]<sup>1</sup></td><td>[[Pentagonal prism|(4·4<sup>2</sup>)]]<sup>2</sup></td><td>--</td><td>[[Cuboctahedron|({3·4}<sup>2</sup>)]]<sup>2</sup></td>
 +
<td>1440</td><td>8640</td><td>10800</td><td>3600</td>
 +
</tr><tr class='row1'>
 +
<td>7</td><td>xxxo</td><td>[[cantitruncated 120-cell|cantitruncate]]</td>
 +
<td>[[Icosidodecahedral truncate|(4·6·10)]]<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>1920</td><td>9120</td><td>14400</td><td>7200</td>
 +
</tr><tr class='row2'>
 +
<td>14</td><td>oxxx</td><td>[[cantitruncated 600-cell|dual cantitruncate]]</td>
 +
<td>[[Icosahedral truncate|(5·6<sup>2</sup>)]]<sup>1</sup></td><td>[[Pentagonal prism|(5·4<sup>2</sup>)]]<sup>1</sup></td><td>--</td><td>[[Octahedral truncate|(4·6<sup>2</sup>)]]<sup>2</sup></td>
 +
<td>1440</td><td>8640</td><td>14400</td><td>7200</td>
 +
</tr><tr class='row1'>
 +
<td>9</td><td>xoox</td><td>[[runcinated 120-cell|runcinate]]</td>
 +
<td>[[Dodecahedron|(5<sup>3</sup>)]]<sup>1</sup></td><td>[[Pentagonal prism|(5·4<sup>2</sup>)]]<sup>3</sup></td><td>[[Triangular prism|(3·4<sup>2</sup>)]]<sup>3</sup></td><td>[[Tetrahedron|(3<sup>3</sup>)]]<sup>1</sup></td>
 +
<td>2640</td><td>7440</td><td>7200</td><td>2400</td>
 +
</tr><tr class='row2'>
 +
<td>11</td><td>xxox</td><td>[[runcitruncated 120-cell|runcitruncate]]</td>
 +
<td>[[Dodecahedral truncate|(4·6<sup>2</sup>)]]<sup>1</sup></td><td>[[Decagonal prism|(10·4<sup>2</sup>)]]<sup>2</sup></td><td>[[Triangular prism|(3·4<sup>2</sup>)]]<sup>1</sup></td><td>[[Cuboctahedron|({3·4}<sup>2</sup>)]]<sup>1</sup></td>
 +
<td>2640</td><td>13440</td><td>18000</td><td>7200</td>
 +
</tr><tr class='row1'>
 +
<td>13</td><td>xoxx</td><td>[[runcitruncated 600-cell|dual runcitruncate]]</td>
 +
<td>[[Icosidodecahedral rectate|(3·4·5·4)]]<sup>1</sup></td><td>[[Pentagonal prism|(5·4<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>2640</td><td>13440</td><td>18000</td><td>7200</td>
 +
</tr><tr class='row2'>
 +
<td>15</td><td>xxxx</td><td>[[stauropantomochoron|omnitruncate (pantome)]]</td>
 +
<td>[[Icosidodecahedral truncate|(4·6·10)]]<sup>1</sup></td><td>[[Decagonal prism|(10·4<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>2640</td><td>17040</td><td>28800</td><td>14400</td>
</tr></table>
</tr></table>

Revision as of 23:27, 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|
1xoooparent (1-tome) (33)4------ 510105
3xxootruncate (2-tome) (3·62)3----(33)1 10304020
2oxoohemicate (3-tome) (34)3----(33)2 10303010
6oxxomesotruncate (4-tome) (3·62)2----(3·62)2 10406030
5xoxocantellate ({3·4}2)2--(3·42)2(34)1 20809030
7xxxocantitruncate (4·62)2--(3·42)1(3·62)1 208012060
9xooxruncinate (33)1(3·42)3(3·42)3(33)1 30706020
11xxoxruncitruncate (3·62)1(6·42)2(3·42)1({3·4}2)1 3012015060
15xxxxomnitruncate (pantome) (4·62)1(6·42)1(6·42)1(4·62)1 30150240120

Stauromorphs

Dx CD Variant Verf cell counts Element counts
CC (8×) CF (24×) CE (32×) CV (16×) |C| |F| |E| |V|
1xoooparent (1-tome) (43)4------ 8243216
3xxootruncate (2-tome) (3·82)3----(33)1 248812864
2oxoohemicate (3-tome) ({3·4}2)3----(33)2 24889632
6oxxomesotruncate (4-tome) (4·62)2----(3·62)2 2412019296
4ooxodual hemicate (5-tome) (34)2----(34)4 24969624
12ooxxdual truncate (6-tome) (34)1----(3·62)4 249612048
8oooxdual (7-tome) ------(33)8 1632248
5xoxocantellate (3·43)2--(3·42)2(34)1 5624828896
10oxoxdual cantellate ({3·4}2)1(4·42)2--({3·4}2)2 4824028896
7xxxocantitruncate (4·6·8)2--(3·42)1(3·62)1 56248384192
14oxxxdual cantitruncate (4·62)1(4·42)1--(4·62)2 48240384192
9xooxruncinate (43)1(4·42)3(3·42)3(33)1 8020819264
11xxoxruncitruncate (3·82)1(8·42)2(3·42)1({3·4}2)1 80368480192
13xoxxdual runcitruncate (3·43)1(4·42)1(6·42)2(3·62)1 80368480192
15xxxxomnitruncate (pantome) (4·6·8)1(8·42)1(6·42)1(4·62)1 80464768384

Xylomorphs

Dx CD Variant Verf cell counts Element counts
CC (24×) CF (96×) CE (96×) CV (24×) |C| |F| |E| |V|
1xoooparent (1-tome) (34)6------ 24969624
3xxootruncate (2-tome) (4·62)3----(43)1 48240384192
2oxoohemicate (3-tome) ({3·4}2)3----(43)2 4824028896
6oxxomesotruncate (4-tome) (3·82)2----(3·82)2 48366576288
5xoxocantellate (3·43)2--(3·42)2({3·4}2)1 144720864288
7xxxocantitruncate (4·6·8)2--(3·42)1(3·82)1 1447201152576
9xooxruncinate (34)1(3·42)3(3·42)3(34)1 240672576144
11xxoxruncitruncate (4·62)1(6·42)2(3·42)1(3·43)1 24011041440576
15xxxxomnitruncate (pantome) (4·6·8)1(6·42)1(6·42)1(4·6·8)1 240139223041152

Rhodomorphs

Dx CD Variant Verf cell counts Element counts
CC (120×) CF (720×) CE (1200×) CV (600×) |C| |F| |E| |V|
1xoooparent (1-tome) (53)4------ 1207201200600
3xxootruncate (2-tome) (3·102)3----(33)1 720312048002400
2oxoohemicate (3-tome) ({3·5}2)3----(33)2 720312036001200
6oxxomesotruncate (4-tome) (5·62)2----(3·62)2 720432072003600
4ooxodual hemicate (5-tome) (35)2----(34)5 72036003600720
12ooxxdual truncate (6-tome) (35)1----(3·62)5 720360043201440
8oooxdual (7-tome) ------(33)20 6001200720120
5xoxocantellate (3·4·5·4)2--(3·42)2(34)1 19209120108003600
10oxoxdual cantellate ({3·5}2)1(4·42)2--({3·4}2)2 14408640108003600
7xxxocantitruncate (4·6·10)2--(3·42)1(3·62)1 19209120144007200
14oxxxdual cantitruncate (5·62)1(5·42)1--(4·62)2 14408640144007200
9xooxruncinate (53)1(5·42)3(3·42)3(33)1 2640744072002400
11xxoxruncitruncate (4·62)1(10·42)2(3·42)1({3·4}2)1 264013440180007200
13xoxxdual runcitruncate (3·4·5·4)1(5·42)1(6·42)2(3·62)1 264013440180007200
15xxxxomnitruncate (pantome) (4·6·10)1(10·42)1(6·42)1(4·62)1 2640170402880014400

Uniform polyhedra usage statistics

#PolyhedronUnique uses
PyromorphsStauromorphsXylomorphsRhodomorphsTotal
Tetrahedral
1 Tetrahedron 54
6 Tetrahedral truncate 54
111 Triangular prism 545
112 Hexagonal prism 323
Octahedral
2 Cube 22
3 Octahedron 243
7 Cuboctahedron 242
8 Cubic truncate 23
9 Octahedral truncate 342
10 Cuboctahedral rectate 22
11 Cuboctahedral truncate 23
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 254025
Retrieved from "http://hi.gher.space/wiki/List_of_uniform_polychora"