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Title: More indecomposable polyhedra
Authors: PrzesŁawski, Krzysztof
Yost, David
Keywords: Polytope;Decomposable;Politopo;Descomponible
Issue Date: 2016
Publisher: Universidad de Extremadura
Abstract: We apply combinatorial methods to a geometric problem: the classification of polytopes, in terms of Minkowski decomposability. Various properties of skeletons of polytopes are exhibited, each sufficient to guarantee indecomposability of a significant class of polytopes. We illustrate further the power of these techniques, compared with the traditional method of examining triangular faces, with several applications. In any dimension d≠2, we show that of all the polytopes with d^2 + ½d or fewer edges, only one is decomposable. In 3 dimensions, we complete the classification, in terms of decomposability, of the 260 combinatorial types of polyhedra with 15 or fewer edges.
Appears in Collections:Extracta Mathematicae Vol. 31, nº 2 (2016)

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