Islamic star patterns from polygons in contact

Abstract

We present a simple method for rendering Islamic star patterns based on Hankin's polygons-in-contact technique. The method builds star patterns from a tiling of the plane and a small number of intuitive parameters. We show how this method can be adapted to construct Islamic designs reminiscent of Huff's parquet deformations. Finally, we introduce a geometric transformation on tilings that expands the range of patterns accessible using our method. This transformation simplifies construction techniques given in previous work, and clarifies previously unexplained relationships between certain classes of star patterns.