Characterization of polytopes via tilings with similar pieces
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.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2010
- DOI:
- arXiv:
- arXiv:1011.4651
- Bibcode:
- 2010arXiv1011.4651A
- Keywords:
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- Mathematics - Metric Geometry;
- Mathematics - Combinatorics
- E-Print:
- accepted for publication in Discrete and Computational Geometry