More Indecomposable Polyhedra

Authors

  • Krzysztof Przeslawski Wydzial Matematyki, Informatyki i Ekonometrii, Uniwersytet Zielonogórski, ul. prof. Z. Szafrana 4a, 65 − 516 Zielona Góra, Poland
  • David Yost Centre for Informatics and Applied Optimization, Faculty of Science and Technology, Federation University, PO Box 663, Ballarat, Vic. 3353, Australia

Keywords:

Polytope, decomposable

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 d2 + d/2 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.

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References

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Published

2016-12-01

Issue

Section

Convex Geometry