A000944 Number of polyhedra (or 3-connected simple planar graphs) with n nodes.
0, 0, 0, 1, 2, 7, 34, 257, 2606, 32300, 440564, 6384634, 96262938, 1496225352, 23833988129, 387591510244, 6415851530241, 107854282197058
Offset: 1
References
- H. T. Croft, K. J. Falconer and R. K. Guy, Unsolved Problems in Geometry, B15.
- M. B. Dillencourt, Polyhedra of small orders and their Hamiltonian properties. Tech. Rep. 92-91, Info. and Comp. Sci. Dept., Univ. Calif. Irvine, 1992.
- B. Grünbaum, Convex Polytopes. Wiley, NY, 1967, p. 424.
- Y. Y. Prokhorov, ed., Mnogogrannik [Polyhedron], Mathematical Encyclopedia Dictionary, Soviet Encyclopedia, 1988.
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
- G. M. Ziegler, Questions about polytopes, pp. 1195-1211 of Mathematics Unlimited - 2001 and Beyond, ed. B. Engquist and W. Schmid, Springer-Verlag, 2001.
Links
- Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph.
- Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph [Cached copy, pdf file only, no active links, with permission]
- CombOS - Combinatorial Object Server, generate planar graphs
- A. J. W. Duijvestijn and P. J. Federico, The number of polyhedral (3-connected planar) graphs, Math. Comp. 37 (1981), no. 156, 523-532. MR0243424 (39 #4746).
- P. J. Federico, Enumeration of polyhedra: the number of 9-hedra, J. Combin. Theory, 7 (1969), 155-161.
- Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018.
- Lukas Finschi, A Graph Theoretical Approach for Reconstruction and Generation of Oriented Matroids, A dissertation submitted to the Swiss Federal Institute of Technology, Zurich for the degree of Doctor of Mathematics, 2001. See p. 155.
- Moritz Firsching, Realizability and inscribability for simplicial polytopes via nonlinear optimization. Math. Program. 166, No. 1-2 (A), 273-295 (2017). Table 1
- Komei Fukuda, Hiroyuki Miyata, and Sonoko Moriyama, Complete Enumeration of Small Realizable Oriented Matroids, arXiv:1204.0645 [math.CO], 2012; Discrete Comput. Geom. 49 (2013), no. 2, 359--381. MR3017917. - From _N. J. A. Sloane_, Feb 16 2013
- Jorik Jooken, Computer-assisted graph theory: a survey, arXiv:2508.20825 [math.CO], 2025. See Ref. 196 at p. 5.
- A. B. Korchagin, Ordering Cellular Spaces with Application to Curves and Knots, Discrete Comput. Geom., 40 (2008), 289-311.
- G. P. Michon, Counting Polyhedra
- Eric Weisstein's World of Mathematics, Polyhedral Graph
Extensions
More terms from Brendan McKay
a(18) from Brendan McKay, Jun 02 2006