Physical Sciences and Mathematics Commons^™

Primitive Substitution Tilings With Rotational Symmetries, April Lynne D. Say-Awen, Ma. Louise Antonette N. De Las Peñas, Dirk Frettlöh

Mathematics Faculty Publications

This work introduces the idea of symmetry order, which describes the rotational symmetry types of tilings in the hull of a given substitution. Definitions are given of the substitutions σ6 and σ7 which give rise to aperiodic primitive substitution tilings with dense tile orientations and which are invariant under six- and sevenfold rotations, respectively; the derivation of the symmetry orders of their hulls is also presented.