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arXiv · 2010.01879

Substitution discrete plane tilings with $2n$-fold rotational symmetry for odd n

Jarkko Kari·Victor H. Lutfalla
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Abstract

We study substitution tilings that are also discrete plane tilings, that is, satisfy a relaxed version of cut-and-projection. We prove that the Sub Rosa substitution tilings with a 2n-fold rotational symmetry for odd n greater than 5 defined by Kari and Rissanen are not discrete planes, and therefore not cut-and-project tilings either. We then define new Planar Rosa substitution tilings with a 2n-fold rotational symmetry for any odd n, and show that these satisfy the discrete plane condition. The tilings we consider are edge-to-edge rhombus tilings. We give an explicit construction for the 10-fold case, and provide a construction method for the general case of any odd n.

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Jarkko Kari, Victor H. Lutfalla. 2020-10-05. Substitution discrete plane tilings with $2n$-fold rotational symmetry for odd n. https://doi.org/10.1007/s00454-022-00390-z

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