5-fold Shuriken Tiling

Discovered by


A substitution rule that gives rise to an aperiodic tiling with dense tile orientations and 5-fold rotational symmetry. The inflation factor is $\sqrt{6+\sqrt{5}}$. The tiling has finite local complexity with respect to rigid motions.

Substitution Rule

Rule 5-fold Shuriken Tiling


Patch 5-fold Shuriken Tiling download vectorformat 5-fold Shuriken Tiling


Frettlöh, D and Say-awen, A. L. D. and de las Peñas, M. L. A. N.
Substitution tilings with dense tile orientations and n-fold rotational symmetry.
Indagationes Mathematicae 2017, 28(1), pp. 120-131, arxiv 1602.00518