The number of polyhedral ($3$connected planar) graphs
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 by A. J. W. Duijvestijn and P. J. Federico PDF
 Math. Comp. 37 (1981), 523532 Request permission
Abstract:
Data is presented on the number of 3connected 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 10hedra to be presented for the first time, as well as estimates of the number of 11hedra and dodecahedra.References

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Additional Information
 © Copyright 1981 American Mathematical Society
 Journal: Math. Comp. 37 (1981), 523532
 MSC: Primary 05C30; Secondary 05C10, 52A25
 DOI: https://doi.org/10.1090/S00255718198106287133
 MathSciNet review: 628713