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A000109 Number of simplicial polyhedra with n nodes; simple planar graphs with 3n-6 edges; maximal simple planar graphs; 3-connected planar triangulations; 3-connected triangulations of the sphere; 3-connected cubic planar graphs.
(Formerly M1469 N0580)
1, 1, 1, 2, 5, 14, 50, 233, 1249, 7595, 49566, 339722, 2406841, 17490241, 129664753, 977526957, 7475907149, 57896349553, 453382272049, 3585853662949, 28615703421545 (list; graph; refs; listen; history; text; internal format)



J. Bokowski and P. Schuchert, Equifacetted 3-spheres as topes of nonpolytopal matroid polytopes. Discrete Comput. Geom. 13 (1995), no. 3-4, 347-361.

R. Bowen and S. Fisk, Generation of triangulations of the sphere, Math. Comp., 21 (1967), 250-252.

G. Brinkmann and Brendan McKay, in preparation.

M. Deza, M. Dutour and P. W. Fowler, Zigzags, railroads and knots in fullerenes, J. Chem. Inf. Comput. Sci., 44 (2004), 1282-1293.

M. B. Dillencourt, Polyhedra of small orders and their Hamiltonian properties. Tech. Rep. 92-91, Info. and Comp. Sci. Dept., Univ. Calif. Irvine, 1992.

C. F. Earl and L. J. March, Architectural applications of graph theory, pp. 327-355 of R. J. Wilson and L. W. Beineke, editors, Applications of Graph Theory. Academic Press, NY, 1979.

P. J. Federico, Enumeration of polyhedra: the number of 9-hedra, J. Combin. Theory, 7 (1969), 155-161.

Fukuda, Komei; Miyata, Hiroyuki; Moriyama, Sonoko. Complete Enumeration of Small Realizable Oriented Matroids. Discrete Comput. Geom. 49 (2013), no. 2, 359--381. MR3017917. - From N. J. A. Sloane, Feb 16 2013

B. Gr├╝nbaum, Convex Polytopes. Wiley, NY, 1967, p. 424.

J. Lederberg, Hamilton circuits of convex trivalent polyhedra (up to 18 vertices), Am. Math. Monthly, 74 (1967), 522-527.

Sciriha, I. and Fowler, P.W., Nonbonding Orbitals in Fullerenes: Nuts and Cores in Singular Polyhedral Graphs J. Chem. Inf. Model., 47, 5, 1763 - 1775, 2007.

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).


David Wasserman, Table of n, a(n) for n = 3..23

R. Bowen and S. Fisk, Generation of triangulations of the sphere [Annotated scanned copy]

F. H. Lutz, Triangulated manifolds with few vertices: Combinatorial Manifolds

B. D. McKay, Plantri

G. P. Michon, Counting Polyhedra

Thom Sulanke, Generating triangulations of surfaces (surftri), (also subpages).

Eric Weisstein's World of Mathematics, Cubic Polyhedral Graph

Eric Weisstein's World of Mathematics, Simple Polyhedron

Eric Weisstein's World of Mathematics, Triangulated Graph

Index entries for "core" sequences


Cf. A005964, A058378.

Sequence in context: A022562 A245883 A115340 * A049338 A115275 A000679

Adjacent sequences:  A000106 A000107 A000108 * A000110 A000111 A000112




N. J. A. Sloane


Extended by Brendan McKay and Gunnar Brinkmann (Gunnar.Brinkmann(AT)ugent.be) using their program "plantri", Dec 19 2000



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Last modified May 24 02:08 EDT 2016. Contains 273226 sequences.