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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.doi:10.1080/14786430802035691 fatcat:dfujardwizb6zj4apb4vjkv5ka