Rectified 10-cubes
In ten-dimensional geometry, a rectified 10-cube is a convex uniform 10-polytope, being a rectification of the regular 10-cube. There are 10 rectifications of the 10-cube, with the zeroth being the 10-cube itself. Vertices of the rectified 10-cube are located at the edge-centers of the 10-cube. Vertices of the birectified 10-cube are located in the square face centers of the 10-cube. Vertices of the trirectified 10-cube are located in the cubic cell centers of the 10-cube. The others are more simply constructed relative to the 10-cube dual polytope, the 10-orthoplex. These polytopes are part of a family 1023 uniform 10-polytopes with BC10 symmetry. Rectified 10-cube Alternate names Rectified dekeract (Acronym rade) (Jonathan Bowers) Cartesian coordinates Cartesian coordinates for the vertices of a rectified 10-cube, centered at the origin, edge length are all permutations of: (±1,±1,±1,±1,±1,±1,±1,±1,±1,0) Images Birectified 10-cube Alternate names Birectified dekeract (Acronym brade) (Jonathan Bowers) Cartesian coordinates Cartesian coordinates for the vertices of a birectified 10-cube, centered at the origin, edge length are all permutations of: (±1,±1,±1,±1,±1,±1,±1,±1,0,0) Images Trirectified 10-cube Alternate names Tririrectified dekeract (Acronym trade) (Jonathan Bowers) Cartesian coordinates Cartesian coordinates for the vertices of a triirectified 10-cube, centered at the origin, edge length are all permutations of: (±1,±1,±1,±1,±1,±1,±1,0,0,0) Images Quadrirectified 10-cube Alternate names Quadrirectified dekeract Quadrirectified decacross (Acronym terade) (Jonathan Bowers) Cartesian coordinates Cartesian coordinates for the vertices of a quadrirectified 10-cube, centered at the origin, edge length are all permutations of: (±1,±1,±1,±1,±1,±1,0,0,0,0) 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 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] (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. (1966) x3o3o3o3o3o3o3o3o4o - ka, o3x3o3o3o3o3o3o3o4o - rake, o3o3x3o3o3o3o3o3o4o - brake, o3o3o3x3o3o3o3o3o4o - trake, o3o3o3o3x3o3o3o3o4o - terake, o3o3o3o3o3x3o3o3o4o - terade, o3o3o3o3o3o3x3o3o4o - trade, o3o3o3o3o3o3o3x3o4o - brade, o3o3o3o3o3o3o3o3x4o - rade, o3o3o3o3o3o3o3o3o4x - deker External links Polytopes of Various Dimensions Multi-dimensional Glossary 10-polytopes