Research Article

The maximum numbers of faces of a convex polytope

P. McMullena1

a1 Western Washington State College, Bellingham, Washington and University College, London


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).

(Received August 10 1970)