The number of polyhedral (3-connected planar) graphs

Abstract

Data is presented on the number of 3-connected planar graphs, isomorphic to the graphs of convex polyhedra, with up to 22 edges. The numbers of such graphs having the same number of edges, and the same number of vertices and faces, are tabulated. Conjectured asymptotic formulas by W. T. Tutte and by R. C. Mullin and P. J. Schellenberg are discussed. Additional data beyond 22 edges are given enabling the number of 10-hedra to be presented for the first time, as well as estimates of the number of 11-hedra and dodecahedra.