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

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

Keywords

Convex bodies
Polytopes
Similarities
Tilings

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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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).",

year = "2012",

month = mar,

doi = "10.1007/s00454-011-9331-2",

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AU - Adiprasito, Karim

N1 - Funding Information: The final preparation of this paper was supported by the Deutsche Forschungsgemeinschaft within the research training group ‘Methods for Discrete Structures’ (GRK1408).

PY - 2012/3

Y1 - 2012/3

N2 - 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.

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.

KW - Convex bodies

KW - Polytopes

KW - Similarities

KW - Tilings

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U2 - 10.1007/s00454-011-9331-2

DO - 10.1007/s00454-011-9331-2

M3 - مقالة

SN - 0179-5376

VL - 47

SP - 424

EP - 429

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

IS - 2

ER -

Characterization of Polytopes via Tilings with Similar Pieces

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

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