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.
pentahedron degree sequence V E
triangular
prism 3, 3, 3, 3, 3, 3 6 9
square pyramid 3, 3, 3, 3, 4 5 8
See also
Pentahedron, Polyhedral Graph, Square Pyramid, Triangular DipyramidExplore with Wolfram|Alpha
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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.Referenced on Wolfram|Alpha
Pentahedral GraphCite this as:
Weisstein, Eric W. "Pentahedral Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PentahedralGraph.html