Difference between revisions of "Template:Honeycombs"
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| − | !colspan="7" style="background: | + | !colspan="7" style="background:lightsteelblue;"|{{navbar-collapsible|Fundamental convex [[regular honeycomb|regular]] and [[uniform honeycomb]]s in dimensions 2-9|Honeycombs}} |
|- style="text-align:center;" | |- style="text-align:center;" | ||
| − | !class="navbox-group" style="background: | + | !class="navbox-group" style="background:gainsboro;"|Space |
| − | !class="navbox-group" style="background: | + | !class="navbox-group" style="background:gainsboro;"|[[Coxeter_group#Finite_Coxeter_groups|Family]] |
| − | |style="background: | + | |style="background:gainsboro;"|<math>{\tilde{A}}_{n-1}</math> |
| − | |style="background: | + | |style="background:gainsboro;"|<math>{\tilde{C}}_{n-1}</math> |
| − | |style="background: | + | |style="background:gainsboro;"|<math>{\tilde{B}}_{n-1}</math> |
| − | |style="background: | + | |style="background:gainsboro;"|<math>{\tilde{D}}_{n-1}</math> |
| − | |style="background: | + | |style="background:gainsboro;"|<math>{\tilde{G}}_2</math> / <math>{\tilde{F}}_4</math> / <math>{\tilde{E}}_{n-1}</math> |
|- style="text-align:center;" | |- style="text-align:center;" | ||
| − | !class="navbox-group" style="background: | + | !class="navbox-group" style="background:gainsboro;"|E<sup>2</sup> |
| − | !class="navbox-group" style="background: | + | !class="navbox-group" style="background:gainsboro;"|[[Uniform tiling]] |
| − | |style="background: | + | |style="background:whitesmoke;"|[[Triangular tiling|{3<sup>[3]</sup>}]] |
| − | |style="background: | + | |style="background:whitesmoke;"|[[Square tiling|<big>δ<sub>3</sub></big>]] |
| − | |style="background: | + | |style="background:whitesmoke;"|[[Square tiling|<big>hδ<sub>3</sub></big>]] |
| − | |style="background: | + | |style="background:whitesmoke;"|[[Square tiling|<big>qδ<sub>3</sub></big>]] |
| − | |style="background:# | + | |style="background:#e0e0f0;"| [[Hexagonal tiling|Hexagonal]] |
|- style="text-align:center;" | |- style="text-align:center;" | ||
| − | !class="navbox-group" style="background: | + | !class="navbox-group" style="background:gainsboro;"|E<sup>3</sup> |
| − | !class="navbox-group" style="background: | + | !class="navbox-group" style="background:gainsboro;" |[[Uniform convex honeycomb]] |
|[[Tetrahedral-octahedral honeycomb|{3<sup>[4]</sup>}]] | |[[Tetrahedral-octahedral honeycomb|{3<sup>[4]</sup>}]] | ||
|[[Cubic honeycomb|<big>δ<sub>4</sub></big>]] | |[[Cubic honeycomb|<big>δ<sub>4</sub></big>]] | ||
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|- style="text-align:center;" | |- style="text-align:center;" | ||
| − | !class="navbox-group" style="background: | + | !class="navbox-group" style="background:gainsboro;"|E<sup>4</sup> |
| − | !class="navbox-group" style="background: | + | !class="navbox-group" style="background:gainsboro;"|[[Uniform 4-honeycomb]] |
| − | |style="background: | + | |style="background:whitesmoke;"|[[5-cell honeycomb|{3<sup>[5]</sup>}]] |
| − | |style="background: | + | |style="background:whitesmoke;"|[[Tesseractic honeycomb|<big>δ<sub>5</sub></big>]] |
| − | |style="background: | + | |style="background:whitesmoke;"|[[16-cell honeycomb|<big>hδ<sub>5</sub></big>]] |
| − | |style="background: | + | |style="background:whitesmoke;"|[[Rectified tesseractic honeycomb|<big>qδ<sub>5</sub></big>]] |
| − | |style="background:# | + | |style="background:#e0f0e0;"| [[24-cell honeycomb]] |
|- style="text-align:center;" | |- style="text-align:center;" | ||
| − | !class="navbox-group" style="background: | + | !class="navbox-group" style="background:gainsboro;"|E<sup>5</sup> |
| − | !class="navbox-group" style="background: | + | !class="navbox-group" style="background:gainsboro;"|[[Uniform 5-honeycomb]] |
|[[5-simplex honeycomb|{3<sup>[6]</sup>}]] | |[[5-simplex honeycomb|{3<sup>[6]</sup>}]] | ||
|[[5-cubic honeycomb|<big>δ<sub>6</sub></big>]] | |[[5-cubic honeycomb|<big>δ<sub>6</sub></big>]] | ||
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|- style="text-align:center;" | |- style="text-align:center;" | ||
| − | !class="navbox-group" style="background: | + | !class="navbox-group" style="background:gainsboro;"|E<sup>6</sup> |
| − | !class="navbox-group" style="background: | + | !class="navbox-group" style="background:gainsboro;"|[[Uniform 6-honeycomb]] |
| − | |style="background: | + | |style="background:whitesmoke;"|[[6-simplex honeycomb|{3<sup>[7]</sup>}]] |
| − | |style="background: | + | |style="background:whitesmoke;"|[[6-cubic honeycomb|<big>δ<sub>7</sub></big>]] |
| − | |style="background: | + | |style="background:whitesmoke;"|[[6-demicubic honeycomb|<big>hδ<sub>7</sub></big>]] |
| − | |style="background: | + | |style="background:whitesmoke;"|[[quarter 6-cubic honeycomb|<big>qδ<sub>7</sub></big>]] |
| − | |style="background:# | + | |style="background:#f0e0e0;"| [[2_22 honeycomb|2<sub>22</sub>]] |
|- style="text-align:center;" | |- style="text-align:center;" | ||
| − | !class="navbox-group" style="background: | + | !class="navbox-group" style="background:gainsboro;"|E<sup>7</sup> |
| − | !class="navbox-group" style="background: | + | !class="navbox-group" style="background:gainsboro;"|[[Uniform 7-honeycomb]] |
|[[7-simplex honeycomb|{3<sup>[8]</sup>}]] | |[[7-simplex honeycomb|{3<sup>[8]</sup>}]] | ||
|[[7-cubic honeycomb|<big>δ<sub>8</sub></big>]] | |[[7-cubic honeycomb|<big>δ<sub>8</sub></big>]] | ||
|[[7-demicubic honeycomb|<big>hδ<sub>8</sub></big>]] | |[[7-demicubic honeycomb|<big>hδ<sub>8</sub></big>]] | ||
|[[quarter 7-cubic honeycomb|<big>qδ<sub>8</sub></big>]] | |[[quarter 7-cubic honeycomb|<big>qδ<sub>8</sub></big>]] | ||
| − | |style="background:# | + | |style="background:#f0e0e0;"| [[1_33 honeycomb|1<sub>33</sub>]] • [[3_31 honeycomb|3<sub>31</sub>]] |
|- style="text-align:center;" | |- style="text-align:center;" | ||
| − | !class="navbox-group" style="background: | + | !class="navbox-group" style="background:gainsboro;"|E<sup>8</sup> |
| − | !class="navbox-group" style="background: | + | !class="navbox-group" style="background:gainsboro;"|[[Uniform 8-honeycomb]] |
| − | |style="background: | + | |style="background:whitesmoke;"|[[8-simplex honeycomb|{3<sup>[9]</sup>}]] |
| − | |style="background: | + | |style="background:whitesmoke;"|[[8-cubic honeycomb|<big>δ<sub>9</sub></big>]] |
| − | |style="background: | + | |style="background:whitesmoke;"|[[8-demicubic honeycomb|<big>hδ<sub>9</sub></big>]] |
| − | |style="background: | + | |style="background:whitesmoke;"|<big>qδ<sub>9</sub></big> |
| − | |style="background:# | + | |style="background:#f0e0e0;"| [[1_52 honeycomb|1<sub>52</sub>]] • [[2_51 honeycomb|2<sub>51</sub>]] • [[5_21 honeycomb|5<sub>21</sub>]] |
|- style="text-align:center;" | |- style="text-align:center;" | ||
| − | !class="navbox-group" style="background: | + | !class="navbox-group" style="background:gainsboro;"|E<sup>9</sup> |
| − | !class="navbox-group" style="background: | + | !class="navbox-group" style="background:gainsboro;"|[[Uniform 9-honeycomb]] |
|{3<sup>[10]</sup>} | |{3<sup>[10]</sup>} | ||
|<big>δ<sub>10</sub></big> | |<big>δ<sub>10</sub></big> | ||
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|- style="text-align:center;" | |- style="text-align:center;" | ||
| − | !class="navbox-group" style="background: | + | !class="navbox-group" style="background:gainsboro;"|E<sup>''n''-1</sup> |
| − | !class="navbox-group" style="background: | + | !class="navbox-group" style="background:gainsboro;"|Uniform (''n''-1)-[[Honeycomb (geometry)|honeycomb]] |
| − | |style="background: | + | |style="background:whitesmoke;"|[[simplectic honeycomb|{3<sup>[n]</sup>}]] |
| − | |style="background: | + | |style="background:whitesmoke;"|[[hypercubic honeycomb|<big>δ<sub>n</sub></big>]] |
| − | |style="background: | + | |style="background:whitesmoke;"|[[Alternated hypercubic honeycomb|<big>hδ<sub>n</sub></big>]] |
| − | |style="background: | + | |style="background:whitesmoke;"|[[quarter hypercubic honeycomb|<big>qδ<sub>n</sub></big>]] |
| − | |style="background:# | + | |style="background:#f0e0e0;"|[[Uniform 1 k2 polytope|1<sub>k2</sub>]] • [[Uniform 2 k1 polytope|2<sub>k1</sub>]] • [[Uniform k 21 polytope|k<sub>21</sub>]] |
|}<noinclude> | |}<noinclude> | ||
{{documentation|content= | {{documentation|content= | ||
Latest revision as of 07:20, 12 April 2018
Fundamental convex regular and uniform honeycombs in dimensions 2-9
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|---|---|---|---|---|---|---|
| Space | Family | <math>{\tilde{A}}_{n-1}</math> | <math>{\tilde{C}}_{n-1}</math> | <math>{\tilde{B}}_{n-1}</math> | <math>{\tilde{D}}_{n-1}</math> | <math>{\tilde{G}}_2</math> / <math>{\tilde{F}}_4</math> / <math>{\tilde{E}}_{n-1}</math> |
| E2 | Uniform tiling | {3[3]} | δ3 | hδ3 | qδ3 | Hexagonal |
| E3 | Uniform convex honeycomb | {3[4]} | δ4 | hδ4 | qδ4 | |
| E4 | Uniform 4-honeycomb | {3[5]} | δ5 | hδ5 | qδ5 | 24-cell honeycomb |
| E5 | Uniform 5-honeycomb | {3[6]} | δ6 | hδ6 | qδ6 | |
| E6 | Uniform 6-honeycomb | {3[7]} | δ7 | hδ7 | qδ7 | 222 |
| E7 | Uniform 7-honeycomb | {3[8]} | δ8 | hδ8 | qδ8 | 133 • 331 |
| E8 | Uniform 8-honeycomb | {3[9]} | δ9 | hδ9 | qδ9 | 152 • 251 • 521 |
| E9 | Uniform 9-honeycomb | {3[10]} | δ10 | hδ10 | qδ10 | |
| En-1 | Uniform (n-1)-honeycomb | {3[n]} | δn | hδn | qδn | 1k2 • 2k1 • k21 |
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