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5-orthoplex honeycomb

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5-orthoplex honeycomb
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Type Hyperbolic regular honeycomb
Schläfli symbol {3,3,3,4,3}
Coxeter diagram
=
5-faces {3,3,3,4}
4-faces {3,3,3}
Cells {3,3}
Faces {3}
Cell figure {3}
Face figure {4,3}
Edge figure {3,4,3}
Vertex figure {3,3,4,3}
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.

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Its vertex figure is the 16-cell honeycomb, {3,3,4,3}.

See also

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References

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  • 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)