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arXiv · 1011.4651

Characterization of polytopes via tilings with similar pieces

Karim Adiprasito
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Abstract

Generalizing results by Valette, Zamfirescu and Laczkovich, we will prove that a convex body $K$ is a polytope if there are sufficiently many tilings which contain a tile similar to $K$. Furthermore, we give an example that this can not be improved.

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Karim Adiprasito. 2011-05-16. Characterization of polytopes via tilings with similar pieces. https://arxiv.org/abs/1011.4651

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