On face vectors and vertex vectors of convex polyhedra (Q685585)

Let \(S\) be a convex polyhedron and let \(p_ i(S)\) or \(v_ i(S)\) denote the number of its \(i\)-gonal faces or \(i\)-valent vertices, respectively. The purpose of this paper is to make some contributions towards the solution of the problem of determining which pair of sequences of nonnegative integers \((p_ i/ i\geq 3)\) and \((v_ i/ i\geq 3)\) associated in a natural way with the polyhedron \(S\) can appear.