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Sub Rosa, A System of Quasiperiodic Rhombic Substitution Tilings with n-Fold Rotational Symmetry

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Abstract

In this paper we prove the existence of quasiperiodic rhombic substitution tilings with 2n-fold rotational symmetry, for any n. The tilings are edge-to-edge and use \(\lfloor {\frac{n}{2}\rfloor }\) rhombic prototiles with unit length sides. We explicitly describe the substitution rule for the edges of the rhombuses, and prove the existence of the corresponding tile substitutions by proving that the interior can be tiled consistently with the given edge substitutions.

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Acknowledgments

We would like to thank Henna Helander for editing the images and Reino Niskanen for many helpful comments and suggestions. This research was supported during 2012 by a grant from the Kone Foundation.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Turku, 20014, Turku, Finland

    Jarkko Kari

  2. Töölönkatu 11 A 130, 00100, Helsinki, Finland

    Markus Rissanen

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  1. Jarkko Kari
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  2. Markus Rissanen
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Correspondence to Jarkko Kari.

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Editor in Charge: Kenneth Clarkson

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Kari, J., Rissanen, M. Sub Rosa, A System of Quasiperiodic Rhombic Substitution Tilings with n-Fold Rotational Symmetry. Discrete Comput Geom 55, 972–996 (2016). https://doi.org/10.1007/s00454-016-9779-1

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  • DOI: https://doi.org/10.1007/s00454-016-9779-1

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