TOPICS
Search

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 Graph

Explore with Wolfram|Alpha

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

Skeleton

Cite this as:

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

Subject classifications