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arXiv · 2203.08856

Planar Rosa : a family of quasiperiodic substitution discrete plane tilings with $2n$-fold rotational symmetry

Jarkko Kari·Victor Lutfalla
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Abstract

We present Planar Rosa, a family of rhombus tilings with a $2n$-fold rotational symmetry that are generated by a primitive substitution and that are also discrete plane tilings, meaning that they are obtained as a projection of a higher dimensional discrete plane. The discrete plane condition is a relaxed version of the cut-and-project condition. We also prove that the Sub Rosa substitution tilings with $2n$-fold rotational symmetry defined by Kari and Rissanen do not satisfy even the weaker discrete plane condition. We prove these results for all even $n\geq 4$. This completes our previously published results for odd values of $n$.

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Jarkko Kari, Victor Lutfalla. 2022-03-16. Planar Rosa : a family of quasiperiodic substitution discrete plane tilings with $2n$-fold rotational symmetry. https://doi.org/10.1007/s11047-022-09929-8

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