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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“The near explains the far. The drop is a small ocean. A man is related to all nature. This perception of the worth of the vulgar is fruitful in discoveries. Goethe, in this very thing the most modern of the moderns, has shown us, as none ever did, the genius of the ancients.”
—Ralph Waldo Emerson (1803–1882)