A007021 Number of 4-connected simplicial polyhedra with n nodes.

1, 1, 1, 1, 1, 2, 4, 10, 25, 87, 313, 1357, 6244, 30926, 158428, 836749, 4504607, 24649284, 136610879, 765598927, 4332047595, 24724362117, 142205424580, 823687567019, 4801749063379

Offset: 3

Author

N. J. A. Sloane

Keywords

• nonn
• more

Comments

Also the number of 4-connected triangulations on n vertices. - Manfred Scheucher, Mar 17 2023

References

• M. B. Dillencourt, Polyhedra of small orders and their Hamiltonian properties. Tech. Rep. 92-91, Info. and Comp. Sci. Dept., Univ. Calif. Irvine, 1992.
• H. Heesch, Ein zum Vierfarbensatz aquivalenter Satz der Panisochromie [ A theorem of panisochromaticity equivalent to the four color theorem ], pp. 229-253 of Graph Theory in Memory of G. A. Dirac (Sandbjerg, 1985). Edited by L. D. Andersen et al., Annals of Discrete Mathematics, 41. North-Holland Publishing Co., Amsterdam-New York, 1989.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Gunnar Brinkmann and Brendan McKay, Guide to using plantri
• Gunnar Brinkmann and Brendan McKay, Guide to using plantri [Cached copy, with permission]
• S. Butler et al., Irreducible Apollonian configurations and packings, Discrete and Computational Geometry, 44 (2010), 487-507.
• CombOS - Combinatorial Object Server, generate planar graphs
• Paul Jungeblut, Edge Guarding Plane Graphs, Master Thesis, Karlsruhe Institute of Technology (Germany, 2019).
• Irene Pivotto and Gordon Royle, Highly-connected planar cubic graphs with few or many Hamilton cycles, arXiv:1901.10683 [math.CO], 2019.
• Manfred Scheucher, Hendrik Schrezenmaier, and Raphael Steiner, A Note On Universal Point Sets for Planar Graphs, arXiv:1811.06482 [math.CO], 2018.

Crossrefs

Cf. A000109, A007027, A111358.

Extensions

More terms generated with plantri by Moritz Firsching, Aug 20 2015