Some indecomposable polyhedra

Author: Yost, D.

Source: Optimization, Volume 56, Numbers 5-6, October 2007 , pp. 715-724(10)

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Abstract:

We complete the classification, in terms of decomposability, of all combinatorial types of polytopes with 14 or fewer edges. Recall that a polytope P is said to be decomposable if it is equal to a Minkowski sum [image omitted] of two polytopes Q and R which are not similar to P. Our main contribution here is to consider the 42 types of polyhedra with 8 faces and 8 vertices. It turns out that 34 of these are always indecomposable, and 5 are always decomposable. The remaining 3 are ambiguous, i.e. each of them has both decomposable and indecomposable geometric realizations.

Keywords: Mathematics Subject Classifications 2000:; 52B11; 52B12

Document Type: Research article

DOI: http://dx.doi.org/10.1080/02331930701617304

Affiliations: 1: School of Information Technology and Mathematical Sciences, University of Ballarat, Ballarat, Victoria, Australia

Publication date: 2007-10-01