Symmetry properties of Penrose type tilings

Nicolae Cotfas (1)

1 Faculty of Physics

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, -τ, (-τ)², (-τ)³, ... , where τ = (1+√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.

Mots clés: Physical Sciences

Nicolae Cotfas. Symmetry properties of Penrose type tilings. Philosophical Magazine, 2008, 88 (13-15), pp.2017-2023. ⟨10.1080/14786430802035691⟩. ⟨hal-00513883⟩