Symmetry properties of Penrose type tilings

Details Symmetry properties of Penrose type tilings Symmetry properties of Penrose type tilings

2007-10-20

arxiv.org/abs/0710.3845v2

Philosophical Magazine 88 (2008) 2017-2023

Physics

Mathematical Physics

Paper submitted to Phil. Mag. (for Proceedings of Quasicrystals: The Silver Jubilee, Tel Aviv, 14-19 October, 2007)

Scientific paper

10.1080/14786430802035691

The Penrose tiling is directly related to the atomic structure of certain decagonal quasicrystals and, despite its aperiodicity, is highly symmetric. It is known that the numbers 1, $-\tau $, $(-\tau)^2$, $(-\tau)^3$, ..., where $\tau =(1+\sqrt{5})/2$, are scaling factors of the Penrose tiling. We show that the set of scaling factors is much larger, and for most of them the number of the corresponding inflation centers is infinite.

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