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Hexateric-dishexateric honeycomb (No image) Type Uniform honeycomb Family Simplectic hypercubic honeycomb Schläfli symbol {3[6]} Coxeter–Dynkin diagrams 5-face types {3,3,3,3} t1{3,3,3,3} t2{3,3,3,3} 4-face types {3,3,3}, t1{3,3,3} Cell types {3,3}, t1{3,3} Face types triangle {3} Vertex figure Stericated 5-simplex Coxeter groups , [3[6]] Properties vertex-transitive, edge-transitive, face-transitive, cell-transitive, facet-transitive In five-dimensional Euclidean geometry, the hexateric-dishexateric honeycomb is a space-filling tessellation (or honeycomb or pentacomb). Each vertex contains 12 hexaterons, 30 rectified hexaterons, and 20 birectified hexaterons. This vertex arrangement is called the A5 lattice and the 30 vertices of the stericated 5-simplex vertex figure represent the 30 roots of the Coxeter group.[1] Contents 1 Related polytopes and honeycombs 2 See also 3 Notes 4 References Related polytopes and honeycombs This honeycomb is one of 12 unique uniform honycombs constructed by the Coxeter group. The other 11 have Coxeter–Dynkin diagrams as: , , , , , , , , , , . See also Regular honeycombs in 5-space: Penteractic honeycomb Demipenteractic honeycomb Notes ^ http://www2.research.att.com/~njas/lattices/A5.html 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, ISBN 978-0-471-01003-6 [1] (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] This geometry-related article is a stub. You can help Wikipedia by expanding it.v · d · e