Hyperbolic Forms
There are 9 Coxeter group families of compact uniform honeycombs in hyperbolic 3-space, generated as Wythoff constructions, and represented by ring permutations of the Coxeter-Dynkin diagrams for each family.
From these 9 families, there are a total of 76 unique honeycombs generated:
- : - 9 forms
- : - 15 forms
- : - 9 forms
- : - 11 forms (7 overlap with family, 4 are unique)
- : - 9 forms
- : - 6 forms
- : - 9 forms
- : - 9 forms
- : - 6 forms
The full list of hyperbolic uniform honeycombs has not been proven and an unknown number of non-Wythoffian forms exist. One known example is in the {3,5,3} family.
There are also 23 noncompact Coxeter groups of rank 4. These families can produce uniform honeycombs with unbounded facets or vertex figure, including ideal vertices at infinity:
| 7 | , |
|---|---|
| 7 | , ,, |
| 6 | , |
| 3 | , |
Read more about this topic: Convex Uniform Honeycomb
Famous quotes containing the word forms:
“It is not however, adulthood itself, but parenthood that forms the glass shroud of memory. For there is an interesting quirk in the memory of women. At 30, women see their adolescence quite clearly. At 30 a woman’s adolescence remains a facet fitting into her current self.... At 40, however, memories of adolescence are blurred. Women of this age look much more to their earlier childhood for memories of themselves and of their mothers. This links up to her typical parenting phase.”
—Terri Apter (20th century)