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Pentahedral Graph


PentahedralGraph

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 V-E=-3, as required by the polyhedral formula.

pentahedrondegree sequenceVE
triangular prism3, 3, 3, 3, 3, 369
square pyramid3, 3, 3, 3, 458

See also

Pentahedron, Polyhedral Graph, Square Pyramid, Triangular Dipyramid

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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.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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Pentahedral Graph

Cite this as:

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

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