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

03/16/2022

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by   Jarkko Kari, et al.

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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 our results for all even n≥ 4. This completes our previously published results for odd values of n.