Skeleton
In algebraic topology, a p-skeleton is a simplicial subcomplex of K that is the collection of all simplices of K of dimension at most p, denoted K^((p)).
PlatonicGraphs
The graph obtained by replacing the faces of a polyhedron with its edges and vertices is therefore the skeleton of the polyhedron. The polyhedral graphs corresponding to the skeletons of Platonic solids are illustrated above. The number of topologically distinct skeletons N(n) with n graph vertices for n=4, 5, 6, ... are 1, 2, 7, 18, 52, ... (OEIS A006869).
See also
Polyhedral Graph, Schlegel GraphExplore with Wolfram|Alpha
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References
Gardner, M. Martin Gardner's New Mathematical Diversions from Scientific American. New York: Simon and Schuster, p. 233, 1966.Hatcher, A. Algebraic Topology. Cambridge, England: Cambridge University Press, 2002.Munkres, J. R. Elements of Algebraic Topology. New York: Perseus Books Pub., 1993.Sloane, N. J. A. Sequence A006869/M1748 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
SkeletonCite this as:
Weisstein, Eric W. "Skeleton." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Skeleton.html