5-orthoplex honeycomb | |
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(No image) | |
Type | Hyperbolic regular honeycomb |
Schläfli symbol | {3,3,3,4,3} |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5-faces | ![]() |
4-faces | ![]() |
Cells | ![]() |
Faces | ![]() |
Cell figure | ![]() |
Face figure | ![]() |
Edge figure | ![]() |
Vertex figure | ![]() |
Dual | 24-cell honeycomb honeycomb |
Coxeter group | U5, [3,3,3,4,3] |
Properties | Regular |
In the geometry of hyperbolic 5-space, the 5-orthoplex honeycomb is one of five paracompact regular space-filling tessellations (or honeycombs). It is paracompact because the fundamental domain of its symmetry group has finite volume. With Schläfli symbol {3,3,3,4,3}, it has three 5-orthoplexes around each cell. It is dual to the 24-cell honeycomb honeycomb.
Related honeycombs
editIts vertex figure is the 16-cell honeycomb, {3,3,4,3}.
See also
editReferences
edit- Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999 ISBN 0-486-40919-8 (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II, III, IV, V, p. 212-213)