24-cell honeycomb honeycomb
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In the geometry of hyperbolic 5-space, the 24-cell honeycomb honeycomb is one of five paracompact regular space-filling tessellations (or honeycombs). It is called paracompact because it has infinite facets, whose vertices exist on 4-horospheres and converge to a single ideal point at infinity. With Schläfli symbol {3,4,3,3,3}, it has three 24-cell honeycombs around each cell. It is dual to the 5-orthoplex honeycomb.
24-cell honeycomb honeycomb | |
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Type | Hyperbolic regular honeycomb |
Schläfli symbol | {3,4,3,3,3} |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5-faces | ![]() |
4-faces | ![]() |
Cells | ![]() |
Faces | ![]() |
Cell figure | ![]() |
Face figure | ![]() |
Edge figure | ![]() |
Vertex figure | ![]() |
Dual | 5-orthoplex honeycomb |
Coxeter group | U5, [3,3,3,4,3] |
Properties | Regular |