

A000109


Number of simplicial polyhedra with n nodes; simple planar graphs with 3n6 edges; maximal simple planar graphs; 3connected planar triangulations; 3connected triangulations of the sphere; 3connected cubic planar graphs.
(Formerly M1469 N0580)


15



1, 1, 1, 2, 5, 14, 50, 233, 1249, 7595, 49566, 339722, 2406841, 17490241, 129664753, 977526957, 7475907149, 57896349553, 453382272049, 3585853662949, 28615703421545
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OFFSET

3,4


REFERENCES

G. Brinkmann and Brendan McKay, in preparation. [Looking at http://users.cecs.anu.edu.au/~bdm/publications.html,there are a few papers with Brinkmann that seem relevant, in particular #126 but also #97, 81, 158. Perhaps the right one is 126.]
M. B. Dillencourt, Polyhedra of small orders and their Hamiltonian properties. Tech. Rep. 9291, Info. and Comp. Sci. Dept., Univ. Calif. Irvine, 1992.
C. F. Earl and L. J. March, Architectural applications of graph theory, pp. 327355 of R. J. Wilson and L. W. Beineke, editors, Applications of Graph Theory. Academic Press, NY, 1979.
B. Grünbaum, Convex Polytopes. Wiley, NY, 1967, p. 424.
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).


LINKS

David Wasserman, Table of n, a(n) for n = 3..23
J. Bokowski and P. Schuchert, Equifacetted 3spheres as topes of nonpolytopal matroid polytopes, Discrete Comput. Geom. 13 (1995), no. 34, 347361.
R. Bowen and S. Fisk, Generation of triangulations of the sphere [Annotated scanned copy]
R. Bowen and S. Fisk, Generation of triangulations of the sphere, Math. Comp., 21 (1967), 250252.
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]
M. Deza, M. Dutour and P. W. Fowler, Zigzags, railroads and knots in fullerenes, J. Chem. Inf. Comput. Sci., 44 (2004), 12821293.
C. F. Earl and L. J. March, Architectural applications of graph theory, pp. 327355 of R. J. Wilson and L. W. Beineke, editors, Applications of Graph Theory. Academic Press, NY, 1979. (Annotated scanned copy)
P. J. Federico, Enumeration of polyhedra: the number of 9hedra, J. Combin. Theory, 7 (1969), 155161.
Komei Fukuda, Hiroyuki Miyata, Sonoko Moriyama, Complete Enumeration of Small Realizable Oriented Matroids. Discrete Comput. Geom. 49 (2013), no. 2, 359381. MR3017917. Also arXiv:1204.0645.  From N. J. A. Sloane, Feb 16 2013
R. K. Guy, The Second Strong Law of Small Numbers, Math. Mag, 63 (1990), no. 1, 320. [Annotated scanned copy]
J. Lederberg, Hamilton circuits of convex trivalent polyhedra (up to 18 vertices), Am. Math. Monthly, 74 (1967), 522527.
F. H. Lutz, Triangulated manifolds with few vertices: Combinatorial Manifolds
G. P. Michon, Counting Polyhedra
I. Sciriha and P. W. Fowler, Nonbonding Orbitals in Fullerenes: Nuts and Cores in Singular Polyhedral Graphs, J. Chem. Inf. Model., 47, 5, 1763  1775, 2007.
A. Stoimenow, A theorem on graph embedding with a relation to hyperbolic volume, Combinatorica, October 2016, Volume 36, Issue 5, pp 557589.
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


CROSSREFS

Cf. A005964, A058378.
Sequence in context: A022562 A245883 A115340 * A049338 A115275 A000679
Adjacent sequences: A000106 A000107 A000108 * A000110 A000111 A000112


KEYWORD

nonn,nice,hard,more,core


AUTHOR

N. J. A. Sloane


EXTENSIONS

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


STATUS

approved



