120-cell honeycomb(No image)TypeHyperbolic regular honeycombSchläfli symbol{5,3,3,3}Coxeter diagram4-faces {5,3,3}Cells {5,3}Faces {5}Face figure {3}Edge figure {3,3}Vertex figure {3,3,3}DualOrder-5 5-cell honeycombCoxeter group4, [5,3,3,3]PropertiesRegular In the geometry of hyperbolic 4-space, the 120-cell honeycomb is one of five compact regular space-filling tessellations (or honeycombs). With Schläfli symbol {5,3,3,3}, it has three 120-cells around each face. Acronym: hitte
Its dual is the order-5 5-cell honeycomb, {3,3,3,5}.
Related honeycombs It is related to the order-4 120-cell honeycomb, {5,3,3,4}, and order-5 120-cell honeycomb, {5,3,3,5}.
It is topologically similar to the finite 5-cube, {4,3,3,3}, and 5-simplex, {3,3,3,3}.
It is analogous to the 120-cell, {5,3,3}, and dodecahedron, {5,3}.
See also List of regular polytopes Great 120-cell honeycomb
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) o3o3o3o5x - hitte