64 research outputs found
More indecomposable polyhedra
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 , we show that of all the polytopes with 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.Comment: PDFLaTeX, 21 pages, 6 figure
More indecomposable polyhedra
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 dâ 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.peerReviewe
On the number of minimal partitions of a box into boxes
AbstractThe number of minimal partitions of a box into proper boxes is examined
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