5-orthoplex honeycomb(No image)TypeHyperbolic regular honeycombSchläfli symbol{3,3,3,4,3}Coxeter diagram = 5-faces {3,3,3,4}4-faces {3,3,3}Cells {3,3}Faces {3}Cell figure {3}Face figure {4,3}Edge figure {3,4,3}Vertex figure {3,3,4,3}Dual24-cell honeycomb honeycombCoxeter group5, [3,3,3,4,3]PropertiesRegular In the geometry of hyperbolic 5-space, the 5-orthoplex honeycomb is one of five paracompact regular space-filling tessellations (or honeycombs). It is paracompact because it has infinite vertex figures, with all vertices as ideal points at infinity. With Schläfli symbol {3,3,3,4,3}, it has three 5-orthoplexes around each cell. It is dual to the 24-cell honeycomb honeycomb.
Related honeycombs Its vertex figure is the 16-cell honeycomb, {3,3,4,3}.
See also List of regular polytopes
References 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)