Characterization of polytopes via tilings with similar pieces

Details Characterization of polytopes via tilings with similar pieces Characterization of polytopes via tilings with similar pieces

2010-11-21

arxiv.org/abs/1011.4651v4

Mathematics

Metric Geometry

accepted for publication in Discrete and Computational Geometry

Scientific paper

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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