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Convex bodies which tile space by translation

  • P. McMullen (a1)
Abstract
Abstract

It is shown that a convex body K tiles Ed by translation if, and only if, K is a centrally symmetric d-polytope with centrally symmetric facets, such that every belt of K (consisting of those of its facets which contain a translate of a given (d – 2)-face) has four or six facets. One consequence of the proof of this result is that, if K tiles Ed by translation, then K admits a face-to-face, and hence a lattice tiling.

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Mathematika
  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
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