A polyhedral graph on five nodes. There are two topologically distinct pentahedral graphs which, through duality,
correspond to the skeletons of the square pyramid
(left figure) and triangular dipyramid (right
figure). The pentahedral graphs were first enumerated by Steiner (1828; Duijvestijn
and Federico 1981). The following table gives the convex pentahedra, which have , as required by the polyhedral
formula.

Duijvestijn, A. J. W. and Federico, P. J. "The Number of Polyhedral (3-Connected Planar) Graphs." Math. Comput.37,
523-532, 1981.Steiner, J. "Problème de situation."
Ann. de Math19, 36, 1828. Reprinted in Jacob
Steiner's gesammelte Werke, Band I. Bronx, NY: Chelsea, p. 227, 1971.