Hexicated 8-simplexOrthogonal projection on A8 Coxeter planeTypeuniform 8-polytopeSchläfli symbol t0,6{3,3,3,3,3,3,3}Coxeter-Dynkin diagrams7-faces6-faces5-faces4-facesCellsFacesEdges2268 Vertices252 Vertex figureCoxeter groupsA8, , order 362880Propertiesconvex In eight-dimensional geometry, a hexicated 8-simplex is a uniform 8-polytope, being a hexication (6th order truncation) of the regular 8-simplex. Acronym: supane (Jonathan Bowers)Klitzing, (x3o3o3o3o3o3x3o - supane)
Coordinates The Cartesian coordinates of the vertices of the hexicated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,1,1,1,1,1,2). This construction is based on facets of the hexicated 9-orthoplex.
Images
Related polytopes This polytope is one of 135 uniform 8-polytopes with A8 symmetry.
Notes
References H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivić Weiss, Wiley-Interscience Publication, 1995, wiley.com, (Paper 22) H.S.M. Coxeter, Regular and Semi-Regular Polytopes I, [Math. Zeit. 46 (1940) 380–407, MR 2,10] (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559–591] (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3–45] Norman Johnson Uniform Polytopes, Manuscript (1991) N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, PhD x3o3o3o3o3o3x3o - supane
External links Polytopes of Various Dimensions Multi-dimensional Glossary