Order-4 24-cell honeycomb honeycomb explained

bgcolor=#e7dcc3 colspan=2	Order-4 24-cell honeycomb honeycomb
bgcolor=#ffffff align=center colspan=2	(No image)
Type	Hyperbolic regular honeycomb
Schläfli symbol
Coxeter diagram	↔
5-faces
4-faces
Cells
Faces
Cell figure
Face figure
Edge figure
Vertex figure
Dual	Tesseractic honeycomb honeycomb
Coxeter group	5, [3,4,3,3,4]
Properties	Regular

In the geometry of hyperbolic 5-space, the order-4 24-cell honeycomb honeycomb is one of five 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, it has four 24-cell honeycombs around each cell. It is dual to the tesseractic honeycomb honeycomb.

Related honeycombs

It is related to the regular Euclidean 4-space 24-cell honeycomb,, as well as the hyperbolic 5-space order-3 24-cell honeycomb honeycomb, .

See also

• List of regular polytopes

References

• Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. . (Tables I and II: Regular polytopes and honeycombs, pp. 294–296)
• Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999 (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II, III, IV, V, p212-213)