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The maximum numbers of faces of a convex polytope

Published online by Cambridge University Press:  26 February 2010

P. McMullen
Western Washington State College, Bellingham, WashingtonandUniversity College, London


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In this paper we give a proof of the long-standing Upper-bound Conjecture for convex polytopes, which states that, for 1 ≤ j < d < v, the maximum possible number of j-faces of a d-polytope with v vertices is achieved by a cyclic polytope C(v, d).

Research Article
Copyright © University College London 1970


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