Order-5 5-cell honeycomb

Order-5 5-cell honeycomb(No image)TypeHyperbolic regular honeycombSchläfli symbol{3,3,3,5}Coxeter diagram4-faces {3,3,3}Cells {3,3}Faces {3}Face figure {5}Edge figure {3,5}Vertex figure {3,3,5}Dual120-cell honeycombCoxeter group4, [5,3,3,3]PropertiesRegular In the geometry of hyperbolic 4-space, the order-5 5-cell honeycomb is one of five compact regular space-filling tessellations (or honeycombs). With Schläfli symbol {3,3,3,5}, it has five 5-cells around each face. Acronym: pente

Its dual is the 120-cell honeycomb, {5,3,3,3}.

Related honeycombs It is related to the order-5 tesseractic honeycomb, {4,3,3,5}, and order-5 120-cell honeycomb, {5,3,3,5}.

It is topologically similar to the finite 5-orthoplex, {3,3,3,4}, and 5-simplex, {3,3,3,3}.

It is analogous to the 600-cell, {3,3,5}, and icosahedron, {3,5}.

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) x3o3o3o5o - pente