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1998 J. Phys. A: Math. Gen. 31 7273-7277 doi: 10.1088/0305-4470/31/35/008
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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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