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1. The maximum numbers of faces of a convex polytope

Author

Peter McMullen

Subjects
medicine.medical_specialty, Mathematics::Combinatorics, Birkhoff polytope, General Mathematics, Polyhedral combinatorics, Uniform k 21 polytope, Cyclic polytope, Simplicial polytope, Combinatorics, Cross-polytope, Convex polytope, medicine, Mathematics::Metric Geometry, Vertex enumeration problem, Mathematics
Abstract

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).

Published
1970