Source: http://www.ams.org/journals/mcom/1981-37-156/S0025-5718-1981-0628713-3/home.html
Timestamp: 2019-04-26 04:37:33+00:00

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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.
 L. Euler, "Elementa doctrinae solidorum," Novi Comm. Acad. Petrop. 1752-3, v. 4, 1758, pp. 109-140; Opera (I), v. 26, pp. 71-93. Read November 25, 1750.
 J. Steiner, "Problème de situation," Ann. de Math., v. 19, 1828, p. 36; Gesammelte Werke, vol. 1, p. 227. Descriptions: 4, 5 and 6 faces.
 T. P. Kirkman, "Application of the theory of the polyhedra to the enumeration and registration of resulte," Proc. Roy. Soc. London, v. 12, 1862-3, pp. 341-380. Numbers: all classes with up to 8 faces or 8 vertices and class with 9 faces and 9 vertices.
 O. Hermes, "Die Formen der Vielflache," J. Reine Angew. Math., [I], v. 120, 1899, pp. 27-59; [II], v. 120, 1899, pp. 305-353, plate 1; [III], v. 122, 1900, pp. 124-154, plates 1, 2; [IV], v. 123, 1901, pp. 312-342, plate 1. Descriptions: all with up to 8 faces, Part II; all trilinear (cubic) with up to 10 faces, Part I. Contains erroneous tables for 9 faces and 9 vertices and erroneous numbers for trilinear (cubic) with 11 and 12 faces .
 M. Brückner, Vielecke und Vielflache, Teubner, Leipzig, 1900. Drawings: all trilinear (cubic) with up to 10 faces, folding plates 2-5. Figure 6 on plate 2 belongs with the 10-faced ones on plates 3-5.
 C. J. Bouwkamp, A. J. W. Duijvestijn & P. Medema, Table of c-Nets of Orders 8 to 19, Inclusive, Philips Research Laboratories, Eindhoven, Netherlands, 2 vols., 1960. Unpublished available in UMT file. Descriptions: all with 8 to 19 edges except that only one of a dual pair is listed. See  for description. The 3-connected planar graphs were called c-nete in the papers on squared rectangles, see , .
 D. W. Grace, Computer Search for Non-Isomorphic Convex Polyhedra, Report CS15, Computer Sci. Dept., Stanford Univ., 1965 (copy obtainable from National Technical Information Service, Dept. of Commerce, Springfield, Va. 22151 as Document AD611, 366). Descriptions: trilinear (cubic) with up to 11 faces.
 W. T. Tutte, "Counting planar maps," J. Recreational Math., v. 1, 1968, pp. 19-27.
 C. J. Bouwkamp, Review of , Math. Comp., v. 24, 1970, pp. 995-997.
 Doyle Britton & J. D. Dunitz, "A complete catalogue of polyhedra with eight or fewer vertices," Acta Cryst. Sect. A, v. A29, 1973, pp. 362-371. Drawings: all classes with up to 8 vertices.
 P. J. Federico, "The number of polyhedra," Philips Res. Rep., v. 30, 1975, pp. 220 -231 .
 A. J. W. Duijvestijn, Algorithmic Calculation of the Order of the Automorphism Group of a Graph, Memorandum No. 221, Twente Univ. of Technology, Enschede, Netherlands, 1978.
 A. J. W. Duijvestijn, List of 3-Connected Planar Graphs with 6 to 22 Edges, Twente Univ. of Technology, Enschede, Netherlands, 1979. (Computer tape.) Descriptions: These are arranged in files, each file containing graphs of the same number of edges ordered by identification number. Only one of a dual pair is listed the one with fewer vertices than faces; if the number of these is the same for a dual pair, the one with the larger identification number is listed. The graphs are coded by lettering the vertices A, B, C, D, ... and giving the circuit of vertices for each face, with a separation mark. Each entry gives first the code of the graph and then follows in order, an indication whether the graph is self-dual or not, the order of the automorphism group, and the identification number. Arrangements for obtaining a copy of the tape can be made by communicating with the author.

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