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. 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
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)
Honeycombs (geometry)