Inflation rules of square-triangle tilings: From approximants to dodecagonal liquid quasicrystals

X. Zeng; G. Ungar

doi:10.1080/14786430500363148

Inflation rules of square-triangle tilings: From approximants to dodecagonal liquid quasicrystals

X. Zeng
, G. Ungar

University of Sheffield

Research output: Contribution to journal › Review article › peer-review

18 Scopus citations

Abstract

An inflation rule for square-triangle tilings is presented and its properties described. Its relationship to other previously found inflation rules, used to generate models of dodecagonal quasicrystals, is discussed. The rule is applied to generate a series of approximants of dodecagonal quasicrystal, including the well-known and P 4 2 / mnm structures. The bigger the unit cell dimensions, the closer the structures of these approximants are to that of the dodecagonal quasicrystal.

Original language	English
Pages (from-to)	1093-1103
Number of pages	11
Journal	Philosophical Magazine
Volume	86
Issue number	6-8
DOIs	https://doi.org/10.1080/14786430500363148
State	Published - 21 Feb 2006
Externally published	Yes

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10.1080/14786430500363148

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abstract = "An inflation rule for square-triangle tilings is presented and its properties described. Its relationship to other previously found inflation rules, used to generate models of dodecagonal quasicrystals, is discussed. The rule is applied to generate a series of approximants of dodecagonal quasicrystal, including the well-known and P 4 2 / mnm structures. The bigger the unit cell dimensions, the closer the structures of these approximants are to that of the dodecagonal quasicrystal.",

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AU - Ungar, G.

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N2 - An inflation rule for square-triangle tilings is presented and its properties described. Its relationship to other previously found inflation rules, used to generate models of dodecagonal quasicrystals, is discussed. The rule is applied to generate a series of approximants of dodecagonal quasicrystal, including the well-known and P 4 2 / mnm structures. The bigger the unit cell dimensions, the closer the structures of these approximants are to that of the dodecagonal quasicrystal.

AB - An inflation rule for square-triangle tilings is presented and its properties described. Its relationship to other previously found inflation rules, used to generate models of dodecagonal quasicrystals, is discussed. The rule is applied to generate a series of approximants of dodecagonal quasicrystal, including the well-known and P 4 2 / mnm structures. The bigger the unit cell dimensions, the closer the structures of these approximants are to that of the dodecagonal quasicrystal.

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JO - Philosophical Magazine

JF - Philosophical Magazine

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ER -

Inflation rules of square-triangle tilings: From approximants to dodecagonal liquid quasicrystals

Abstract

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