Order-4 24-cell honeycomb

Order-4 24-cell honeycomb(No image)TypeHyperbolic regular honeycombSchläfli symbol{3,4,3,4}{3,4,31,1}Coxeter diagram ↔ 4-faces {3,4,3}Cells {3,4}Faces {3}Face figure {4}Edge figure {3,4}Vertex figure {4,3,4}DualCubic honeycomb honeycombCoxeter group4, [4,3,4,3]PropertiesRegular 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. Acronym: n/a

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

Notes

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) x3o4o3o4o