A Quasiperiodic Tiling With 12-Fold Rotational Symmetry and Inflation Factor 1 + Sqrt(3)

Abstract

We show how we found substitution rules for a quasiperiodic tiling with local rotational symmetry and inflation factor 1 + sqrt(3). The base tiles are a square, a rhomb with an acute angle of 30 degrees, and equilateral triangles that are cut in half. These half-triangles follow three different substitution rules and can be recombined into equilateral triangles in nine different ways to make minor variations of the tiling. The tiling contains quasiperiodically repeated 12-fold rosettes. A central rosette can be enlarged to make an arbitrarily large tiling with 12-fold rotational symmetry. An online computer program is provided that allows the user to explore the tiling.