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arXiv · 1804.09920

Multi-tiling and equidecomposability of polytopes by lattice translates

Nir Lev·Bochen Liu
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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.

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Nir Lev, Bochen Liu. 2019-09-17. Multi-tiling and equidecomposability of polytopes by lattice translates. https://doi.org/10.1112/blms.12297

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