Related Honeycombs
It is in a dimensional series of uniform polytopes and honeycombs, expressed by Coxeter as 3k1 series. A degenerate 4-dimensional case exists as 3-sphere tiling, a tetrahedral hosohedron.
| n | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|
| Coxeter group |
A3×A1 | A5 | D6 | E7 | =E7+ | E7++ |
| Coxeter diagram |
||||||
| Symmetry (order) |
(48) |
(720) |
] (46,080) |
(2,903,040) |
(∞) |
(∞) |
| Graph | ∞ | ∞ | ||||
| Name | 31,-1 | 310 | 311 | 321 | 331 | 341 |
Read more about this topic: 3 31 Honeycomb
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—Ralph Waldo Emerson (1803–1882)