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Study of Penrose Tiling Using Parameterization Method

  • THEORY OF CRYSTAL STRUCTURES
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Abstract

A new description of Penrose tiling, based on parameterization of tiling rhombuses, has been obtained. A method making it possible to describe clusters and coordination environments in Penrose tiling in terms of parameters is developed. The parameters of all possible types of the first coordination environments in Penrose tiling are found. A new proof is obtained that the form of layer-by-layer growth of Penrose tiling is a regular decagon, and the vertices of this decagon are calculated.

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ACKNOWLEDGMENTS

This study was supported by the Russian Foundation for Basic Research, project nos. 14-01-00360-a, 17-02-00835-a and 17-42-330787-ra.

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Authors and Affiliations

  1. Vladimir State University, 600000, Vladimir, Russia

    A. V. Shutov & A. V. Maleev

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  1. A. V. Shutov
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  2. A. V. Maleev
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Correspondence to A. V. Maleev.

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Translated by Yu. Sin’kov

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Shutov, A.V., Maleev, A.V. Study of Penrose Tiling Using Parameterization Method. Crystallogr. Rep. 64, 376–385 (2019). https://doi.org/10.1134/S1063774519030234

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