Multi-tiling and equidecomposability of polytopes by lattice translates

Abstract

We characterize the polytopes in ${\mathbb{R}}^d$ (not necessarily convex or connected ones) which multi-tile the space by translations along a given lattice. We also give a necessary and sufficient condition for two polytopes in ${\mathbb{R}}^d$ to be equidecomposable by lattice translations.

arXiv commentTo appear in the Bulletin of the London Mathematical Society

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