Characterization of Polytopes via Tilings with Similar Pieces

Karim Adiprasito*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 cannot be improved.

Original languageAmerican English
Pages (from-to)424-429
Number of pages6
JournalDiscrete and Computational Geometry
Issue number2
StatePublished - Mar 2012
Externally publishedYes

Bibliographical note

Funding Information:
The final preparation of this paper was supported by the Deutsche Forschungsgemeinschaft within the research training group ‘Methods for Discrete Structures’ (GRK1408).


  • Convex bodies
  • Polytopes
  • Similarities
  • Tilings


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