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.
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. London12, 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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