Rectified 6-cubes
In six-dimensional geometry, a rectified 6-cube is a convex uniform 6-polytope, being a rectification of the regular 6-cube. There are unique 6 degrees of rectifications, the zeroth being the 6-cube, and the 6th and last being the 6-orthoplex. Vertices of the rectified 6-cube are located at the edge-centers of the 6-cube. Vertices of the birectified 6-cube are located in the square face centers of the 6-cube. Rectified 6-cube Alternate names Rectified hexeract (acronym: rax) (Jonathan Bowers) Construction The rectified 6-cube may be constructed from the 6-cube by truncating its vertices at the midpoints of its edges. Coordinates The Cartesian coordinates of the vertices of the rectified 6-cube with edge length are all permutations of: Images Birectified 6-cube Alternate names Birectified hexeract (acronym: brox) (Jonathan Bowers) Rectified 6-demicube Construction The birectified 6-cube may be constructed from the 6-cube by truncating its vertices at the midpoints of its edges. Coordinates The Cartesian coordinates of the vertices of the rectified 6-cube with edge length are all permutations of: Images Related polytopes These polytopes are part of a set of 63 uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-cube or 6-orthoplex. 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. o3x3o3o3o4o - rax, o3o3x3o3o4o - brox, External links Polytopes of Various Dimensions Multi-dimensional Glossary 6-polytopes