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Convex bodies which tile space by translation

Published online by Cambridge University Press:  26 February 2010

P. McMullen
P. McMullen
Affiliation:
University College London, Gower Street, London WC1E 6BT.
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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.

Type
Research Article
Information
Mathematika , Volume 27 , Issue 1 , June 1980 , pp. 113 - 121
Copyright
Copyright © University College London 1980

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