Cantic 8-cubeD8 Coxeter plane projectionTypeuniform 8-polytopeSchläfli symbol t0,1{3,35,1}h2{4,3,3,3,3,3,3}Coxeter-Dynkin diagram7-faces16 truncated 7-demicubes128 truncated 7-simplexes128 rectified 7-simplexes6-faces112 truncated 6-demicubes1024 truncated 6-simplexes1024 rectified 6-simplexes1024 6-simplexes5-faces448 truncated 5-demicubes3584 rectified 5-simplexes7168 5-simplexes4-faces1120 truncated 16-cells7168 truncated 5-cells7168 rectified 5-cells21504 5-cellsCells1792 truncated tetrahedra8960 truncated tetrahedra8960 octahedra35840 tetrahedraFaces7168 hexagons7168 triangles35840 trianglesEdges1792 segments21504 segmentsVertices3584Vertex figure( )v{ }x{3,3,3,3}Coxeter groupsD8, [35,1,1]Propertiesconvex In eight-dimensional geometry, a cantic 8-cube or truncated 8-demicube is a uniform 8-polytope, being a truncation of the 8-demicube.
Alternate names Truncated demiocteract Truncated hemiocteract; Acronym: thocto (Jonathan Bowers)
Cartesian coordinates The Cartesian coordinates for the vertices of a truncated 8-demicube centered at the origin and edge length 6√2 are coordinate permutations: (±1,±1,±3,±3,±3,±3,±3,±3) with an odd number of plus signs.
Images
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, Ph.D. x3x3o *b3o3o3o3o3o - thocto
External links
Polytopes of Various Dimensions Multi-dimensional Glossary