Cyclotruncated 5-simplex honeycomb(No image)TypeUniform honeycombFamilyCyclotruncated simplectic honeycombSchläfli symbolt0,1{3}Coxeter diagram or 5-face types{3,3,3,3} t{3,3,3,3} 2t{3,3,3,3} 4-face types{3,3,3} t{3,3,3} Cell types{3,3} t{3,3} Face types{3} t{3} Vertex figureElongated 5-cell antiprismCoxeter groups×22, Propertiesvertex-transitive In five-dimensional Euclidean geometry, the cyclotruncated 5-simplex honeycomb or cyclotruncated hexateric honeycomb is a space-filling tessellation (or honeycomb). It is composed of 5-simplex, truncated 5-simplex, and bitruncated 5-simplex facets in a ratio of 1:1:1. Structure Its vertex figure is an elongated 5-cell antiprism, two parallel 5-cells in dual configurations, connected by 10 tetrahedral pyramids (elongated 5-cells) from the cell of one side to a point on the other. The vertex figure has 8 vertices and 12 5-cells.
It can be constructed as six sets of parallel hyperplanes that divide space. The hyperplane intersections generate cyclotruncated 5-cell honeycomb divisions on each hyperplane.
Related polytopes and honeycombs
See also Regular and uniform honeycombs in 5-space: 5-cubic honeycomb 5-demicubic honeycomb 5-simplex honeycomb Omnitruncated 5-simplex honeycomb
Notes
References Norman Johnson Uniform Polytopes, Manuscript (1991) Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10] (1.9 Uniform space-fillings) (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]