Characterization of Polytopes via Tilings with Similar Pieces

Karim Adiprasito

doi:10.1007/s00454-011-9331-2

Characterization of Polytopes via Tilings with Similar Pieces

Karim Adiprasito^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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 cannot be improved.

Original language	English
Pages (from-to)	424-429
Number of pages	6
Journal	Discrete and Computational Geometry
Volume	47
Issue number	2
DOIs	https://doi.org/10.1007/s00454-011-9331-2
State	Published - Mar 2012
Externally published	Yes

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).

Keywords

Convex bodies
Polytopes
Similarities
Tilings

Access to Document

10.1007/s00454-011-9331-2

Cite this

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title = "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 cannot be improved.",

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author = "Karim Adiprasito",

note = "Funding Information: The final preparation of this paper was supported by the Deutsche Forschungsgemeinschaft within the research training group {\textquoteleft}Methods for Discrete Structures{\textquoteright} (GRK1408).",

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KW - Similarities

KW - Tilings

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Characterization of Polytopes via Tilings with Similar Pieces

Abstract

Bibliographical note

Keywords

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