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Substitution planar tilings with $n$-fold rotational symmetry

Authors
  • Kari, Jarkko
  • Lutfalla, Victor H.
Type
Preprint
Publication Date
Oct 18, 2020
Submission Date
Oct 05, 2020
Source
University of Michigan Library Repository
License
Yellow
External links

Abstract

We prove that the SubRosa substitution tilings with $2n$-fold rotational symmetry defined by Kari and Rissanen are not planar for odd $n$. However we prove the existence of planar substitution tilings with $2n$-fold rotational symmetry for any odd $n$. The tilings we consider are rhombic and edge-to-edge. We give an explicit 10-fold substitution planar tiling and we give a construction method for the general case of $2n$-fold with odd $n$.

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