An Effective Construction for Cut-And-Project Rhombus Tilings with Global n-Fold Rotational Symmetry

Abstract

We give an explicit and effective construction for rhombus cut-and-project tilings with global n-fold rotational symmetry for any n. This construction is based on the dualization of regular n-fold multigrids. The main point is to prove the regularity of these multigrids, for this we use a result on trigonometric diophantine equations. A SageMath program that computes these tilings and outputs svg files is publicly available in [7]. 2012 ACM Subject Classification Mathematics of computing → Discrete mathematics; Mathematics of computing → Combinatorics