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10-cube
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In geometry, a 10-cube is a ten-dimensional hypercube. It can be named by its Schläfli symbol, being composed of 3 9-cubes around each 8-face and it is a part of an infinite family of polytopes, called hypercubes. The dual of a dekeract can be called a 10-orthoplex or decacross, cartesian coordinates for the vertices of a dekeract centered at the origin and edge length 2 are while the interior of the same consists of all points with −1 < xi <1. Applying an alternation operation, deleting alternating vertices of the dekeract, creates another uniform polytope, called a 10-demicube, which has 20 demienneractic and 512 enneazettonic facets. Coxeter, Coxeter, Regular Polytopes, Dover edition, ISBN 0-486-61480-8, p.296, Table I, Regular Polytopes, three regular polytopes in n-dimensions H. S. M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York,1973, p.296, Table I, Regular Polytopes, Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication,1995, ISBN 978-0-471-01003-6 H. S. M, Coxeter, Regular and Semi Regular Polytopes I, H. S. M. Coxeter, Regular and Semi-Regular Polytopes II, H. S. M, Coxeter, Regular and Semi-Regular Polytopes III, Norman Johnson Uniform Polytopes, Manuscript N. W. Johnson, The Theory of Uniform Polytopes and Honeycombs, Ph. D, 10D uniform polytopes o3o3o3o3o3o3o3o3o4x - deker. Archived from the original on 4 February 2007, multi-dimensional Glossary, hypercube Garrett Jones Sloanes A135289, Hypercubes, 10-cube. The On-Line Encyclopedia of Integer Sequences