Characterization of polytopes via tilings with similar pieces
Metric Geometry
2011-05-17 v4 Combinatorics
Abstract
Generalizing results by Valette, Zamfirescu and Laczkovich, we will prove that a convex body is a polytope if there are sufficiently many tilings which contain a tile similar to . Furthermore, we give an example that this can not be improved.
Cite
@article{arxiv.1011.4651,
title = {Characterization of polytopes via tilings with similar pieces},
author = {Karim Adiprasito},
journal= {arXiv preprint arXiv:1011.4651},
year = {2011}
}
Comments
accepted for publication in Discrete and Computational Geometry