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Fifty-Nine Icosahedra

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There are 59 stellations of the icosahedron. The faces of the stellations lie in one of 20 planes through the faces of the original icosahedron. Each stellation consists of a set of facets subjected to connectivity constraints (no holes).

Contributed by: Roman E. Maeder (September 2007)
Open content licensed under CC BY-NC-SA

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The combinatorial analysis of the icosahedral stellations is by H. S. M. Coxeter, P. Du Val, H. T. Flather, and J. F. Petrie, The Fifty-Nine Icosahedra, New York: Springer-Verlag, 1982. (Originally published by Univ. of Toronto Press, 1938.) The Mathematica code was originally developed for R. E. Maeder, The Mathematica Programmer, Boston: AP Professional, 1994.

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