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
Famous quotes containing the word related:
“Becoming responsible adults is no longer a matter of whether children hang up their pajamas or put dirty towels in the hamper, but whether they care about themselves and others—and whether they see everyday chores as related to how we treat this planet.”
—Eda Le Shan (20th century)