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Heptahedral Graph


HeptahedralGraphs

A heptahedral graph is a polyhedral graph on seven nodes. There are 34 nonisomorphic heptahedral graphs, as first enumerated by Kirkman (1862-1863) and Hermes (1899ab, 1900, 1901; Federico 1969; Duijvestijn and Federico 1981). Three are the 7-node self-dual graphs and another is the wheel graph W_7.


See also

Heptahedron, Polyhedral Graph

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References

Duijvestijn, A. J. W. and Federico, P. J. "The Number of Polyhedral (3-Connected Planar) Graphs." Math. Comput. 37, 523-532, 1981.Federico, P. J. "Enumeration of Polyhedra: The Number of 9-Hedra." J. Combin. Th. 7, 155-161, 1969.Grünbaum, B. Convex Polytopes. New York: Wiley, pp. 288 and 424, 1967.Hermes, O. "Die Formen der Vielflache. I." J. reine angew. Math. 120, 27-59, 1899a.Hermes, O. "Die Formen der Vielflache. II." J. reine angew. Math. 120, 305-353, 1899b.Hermes, O. "Die Formen der Vielflache. III." J. reine angew. Math. 122, 124-154, 1900.Hermes, O. "Die Formen der Vielflache. IV." J. reine angew. Math. 123, 312-342, 1901.Kirkman, T. P. "Application of the Theory of the Polyhedra to the Enumeration and Registration of Results." Proc. Roy. Soc. London 12, 341-380, 1862-1863.Pegg, E. Jr. "The 34 Convex Heptahedra and Their Characteristic Polynomials." http://www.mathpuzzle.com/charpoly.htm.

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Heptahedral Graph

Cite this as:

Weisstein, Eric W. "Heptahedral Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HeptahedralGraph.html

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