On the affine self-similarities of the three-dimensional Penrose pattern

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, , Citation Nicolae Cotfas 1998 J. Phys. A: Math. Gen. 31 7273 DOI 10.1088/0305-4470/31/35/008

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1 Department of Mathematics, Faculty of Physics, University of Bucharest, PO Box 76-54, Bucharest 76, Romania

Dates

  1. Received 16 April 1998

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0305-4470/31/35/7273

Abstract

We prove that the vertex set of the usual three-dimensional Penrose tiling admits an infinite number of independent scaling factors and an infinite number of inflation centres. More exactly, we prove that there exist an infinite number of real numbers and an infinite number of points such that .

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