16-cell honeycomb honeycomb

16-cell honeycomb honeycomb(No image)TypeHyperbolic regular honeycombSchläfli symbol{3,3,4,3,3}Coxeter diagramnode_1 3 node 3 node 4 node 3 node 3 node5-faces50px {3,3,4,3}4-faces50px {3,3,4}Cells50px {3,3}Faces50px {3}Cell figure50px {3}Face figure50px {3,3}Edge figure50px {4,3,3}Vertex figure50px {3,4,3,3}Dualself-dualCoxeter groupX5, [3,3,4,3,3]PropertiesRegular In the geometry of hyperbolic 5-space, the 16-cell 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 {3,3,4,3,3}, it has three 16-cell honeycombs around each cell. It is self-dual. Related honeycombs It is related to the regular Euclidean 4-space 16-cell honeycomb, {3,3,4,3}. See also List of regular polytopes References Coxeter, Regular Polytopes, 3rd ed., Dover Publications, 1973. 0-486-61480-8. (Tables I and II: Regular polytopes and honeycombs, pp. 294–296) Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999, 0-486-40919-8, (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II, III, IV, V, pp. 212–213) Category:Honeycombs (geometry)