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

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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.",

keywords = "Convex bodies, Polytopes, Similarities, Tilings",

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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AB - 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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KW - Polytopes

KW - Similarities

KW - Tilings

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Characterization of Polytopes via Tilings with Similar Pieces

Abstract

Bibliographical note

Keywords

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