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Tiling approach for the description of the sevenfold symmetry in quasicrystals

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He from the centre of the realm upraised a Behistun, from which that of Farhad fled.

In such a Behistun, which seven columns had, he raised up to the heavens seven domes.

And in those walls, which touched upon the sky, he saw a rampart round the lofty spheres.

He saw seven domes within those walls built up after the nature of the planets seven.

Nizami Ganjavi, “The Seven Beauties”.

Abstract

An example of substitution rules for the construction of heptagonal rhombic tilings is proposed. Rigorous inflation/deflation rules make it possible to expand the tiling up to infinity without additional ad hoc rearrangements. The derived tilings are self-similar and consist of characteristic patterns with seven-pointed stars surrounded by similar seven-pointed stars.

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Acknowledgments

I thank Jelena R. Kambak for proofreading and writing assistance.

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Authors and Affiliations

  1. Admiral Makarov State University of Maritime and Inland Shipping, ul. Dvinskaya 5/7, Saint-Petersburg, Russia, 198035

    A. E. Madison

  2. Center for Advanced Studies, Peter the Great St. Petersburg Polytechnic University, ul. Polytechnicheskaya 29, Saint-Petersburg, Russia, 195251

    A. E. Madison

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  1. A. E. Madison
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Correspondence to A. E. Madison.

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Dedicated to Professor Alan L. Mackay on the occasion of his 90th birthday.

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Madison, A.E. Tiling approach for the description of the sevenfold symmetry in quasicrystals. Struct Chem 28, 57–62 (2017). https://doi.org/10.1007/s11224-016-0793-y

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  • DOI: https://doi.org/10.1007/s11224-016-0793-y

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