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Order-5 tesseractic honeycomb

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Order-5 tesseractic honeycomb
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Type Hyperbolic regular honeycomb
Schläfli symbol {4,3,3,5}
Coxeter diagram
4-faces {4,3,3}
Cells {4,3}
Faces {4}
Face figure {5}
Edge figure {3,5}
Vertex figure {3,3,5}
Dual Order-4 120-cell honeycomb
Coxeter group BH4, [5,3,3,4]
Properties Regular

In the geometry of hyperbolic 4-space, the order-5 tesseractic honeycomb is one of five compact regular space-filling tessellations (or honeycombs). With Schläfli symbol {4,3,3,5}, it has five 8-cells (also known as tesseracts) around each face. Its dual is the order-4 120-cell honeycomb, {5,3,3,4}.

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It is related to the Euclidean 4-space (order-4) tesseractic honeycomb, {4,3,3,4}, and the 5-cube, {4,3,3,3} in Euclidean 5-space. The 5-cube can also be seen as an order-3 tesseractic honeycomb on the surface of a 4-sphere.

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, p212-213)