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Multi-tiling and equidecomposability of polytopes by lattice translates
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math.COmath.CAmath.MG
keywords
latticepolytopesmathbbtranslationsalongcharacterizeconditionconnected
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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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