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