A Method to Generate Polyominoes and Polyiamonds for Tilings with Rotational Symmetry

Abstract

We show a simple method to generate polyominoes and polyiamonds that produce isohedral tilings with p3, p4 or p6 rotational symmetry by using n line segments between lattice points on a regular hexagonal, square and triangular lattice, respectively. We exhibit all possible tiles generated by this algorithm up to n = 9 for p3, n = 8 for p4, and n = 13 for p6. In particular, we determine for n ≤ 8 all n-ominoes that are fundamental domains for p4 isohedral tilings.