Order-5 tesseractic honeycomb

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}.

Related polytopes and honeycombs

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

• List of regular polytopes

References

• 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)

This page was last edited on 28 January 2024, at 00:14