A Quasiperiodic Tiling With 12-Fold Rotational Symmetry and Inflation Factor 1 + Sqrt(3)
History and Overview
2021-02-12 v1
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.
Keywords
Cite
@article{arxiv.2102.06046,
title = {A Quasiperiodic Tiling With 12-Fold Rotational Symmetry and Inflation Factor 1 + Sqrt(3)},
author = {Theo P. Schaad and Peter Stampfli},
journal= {arXiv preprint arXiv:2102.06046},
year = {2021}
}
Comments
16 pages, 10 figures