Cubic honeycomb honeycomb
From Wikipedia, the free encyclopedia
In the geometry of hyperbolic 4-space, the cubic honeycomb honeycomb is one of two paracompact regular space-filling tessellations (or honeycombs). It is called paracompact because it has infinite facets, whose vertices exist on 3-horospheres and converge to a single ideal point at infinity. With Schläfli symbol {4,3,4,3}, it has three cubic honeycombs around each face, and with a {3,4,3} vertex figure. It is dual to the order-4 24-cell honeycomb.
Cubic honeycomb honeycomb | |
---|---|
(No image) | |
Type | Hyperbolic regular honeycomb |
Schläfli symbol | {4,3,4,3} {4,31,1,1} |
Coxeter diagram | ↔ ↔ |
4-faces | {4,3,4} |
Cells | {4,3} |
Faces | {4} |
Face figure | {3} |
Edge figure | {4,3} |
Vertex figure | {3,4,3} |
Dual | Order-4 24-cell honeycomb |
Coxeter group | R4, [4,3,4,3] |
Properties | Regular |