Order-4 24-cell honeycomb

Order-4 24-cell honeycomb
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Type	Hyperbolic regular honeycomb
Schläfli symbol	{3,4,3,4} {3,4,3^1,1}
Coxeter diagram	↔
4-faces	{3,4,3}
Cells	{3,4}
Faces	{3}
Face figure	{4}
Edge figure	{3,4}
Vertex figure	{4,3,4}
Dual	Cubic honeycomb honeycomb
Coxeter group	R4, [4,3,4,3]
Properties	Regular

In the geometry of hyperbolic 4-space, the order-4 24-cell honeycomb is one of two paracompact regular space-filling tessellations (or honeycombs). It is called paracompact because it has infinite vertex figures, with all vertices as ideal points at infinity. With Schläfli symbol {3,4,3,4}, it has four 24-cells around each face. It is dual to the cubic honeycomb honeycomb.

Related honeycombs

It is related to the regular Euclidean 4-space 24-cell honeycomb, {3,4,3,3}, with 24-cell facets.

See also

• List of regular polytopes

References

• Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. ISBN 0-486-61480-8. (Tables I and II: Regular polytopes and honeycombs, pp. 294–296)
• 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)