Tesseractic honeycomb honeycomb(No image)TypeHyperbolic regular honeycombSchläfli symbol{4,3,3,4,3}{4,3,31,1,1}Coxeter diagram ↔ 5-faces {4,3,3,4}4-faces {4,3,3}Cells {4,3}Faces {4}Cell figure {3}Face figure {4,3}Edge figure {3,4,3}Vertex figure {3,3,4,3}DualOrder-4 24-cell honeycomb honeycombCoxeter group5, [3,4,3,3,4]PropertiesRegular In the geometry of hyperbolic 5-space, the tesseractic 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 {4,3,3,4,3}, it has three tesseractic honeycombs around each cell. It is dual to the order-4 24-cell honeycomb honeycomb.
Related honeycombs It is related to the regular Euclidean 4-space tesseractic honeycomb, {4,3,3,4}.
It is analogous to the paracompact cubic honeycomb honeycomb, {4,3,4,3}, in 4-dimensional hyperbolic space, square tiling honeycomb, {4,4,3}, in 3-dimensional hyperbolic space, and the order-3 apeirogonal tiling, {∞,3} of 2-dimensional hyperbolic space, each with hypercube honeycomb facets.
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)