24-cell honeycomb honeycomb(No image)TypeHyperbolic regular honeycombSchläfli symbol{3,4,3,3,3}Coxeter diagram = 5-faces {3,4,3,3}4-faces {3,4,3}Cells {3,4}Faces {3}Cell figure {3}Face figure {3,3}Edge figure {3,3,3}Vertex figure {4,3,3,3}Dual5-orthoplex honeycombCoxeter group5, [3,3,3,4,3]PropertiesRegular In the geometry of hyperbolic 5-space, the 24-cell honeycomb honeycomb is one of five paracompact regular space-filling tessellations (or honeycombs). It is called paracompact because it has infinite facets, whose vertices exist on 4-horospheres and converge to a single ideal point at infinity. With Schläfli symbol {3,4,3,3,3}, it has three 24-cell honeycombs around each cell. It is dual to the 5-orthoplex honeycomb.
Related honeycombs It is related to the regular Euclidean 4-space 24-cell honeycomb, {3,4,3,3}, and the hyperbolic 5-space order-4 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, pp. 212–213)