Hexahedral Graph


A hexahedral graph is a polyhedral graph on six vertices. There are seven distinct hexahedral graphs (illustrated above) which, through duality, correspond to seven convex hexahedra. The hexahedral graphs were first enumerated by Steiner (1828; Duijvestijn and Federico 1981).

Three of the hexahedral graphs correspond to the skeletons of the pentagonal pyramid (i.e., the wheel graph W_6), triangular prism, and octahedron (square dipyramid, triangular antiprism). An additional hexahedron can be obtained by truncation of two of the four apexes of the tetrahedron, producing a solid composed of 2 triangles, 2 quadrilaterals, and two pentagons which, like the cube, has 6 faces, 8 vertices, 12 edges and cubic connectivity.

See also

Hexahedron, Polyhedral Graph

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Duijvestijn, A. J. W. and Federico, P. J. "The Number of Polyhedral (3-Connected Planar) Graphs." Math. Comput. 37, 523-532, 1981.Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, 1994.Steiner, J. "Problème de situation." Ann. de Math 19, 36, 1828. Reprinted in Jacob Steiner's gesammelte Werke, Band I. Bronx, NY: Chelsea, p. 227, 1971.

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Hexahedral Graph

Cite this as:

Weisstein, Eric W. "Hexahedral Graph." From MathWorld--A Wolfram Web Resource.

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