Substitution planar tilings with n-fold rotational symmetry

10/05/2020

∙

by   Jarkko Kari, et al.

∙

0

∙

share

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.