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1997 J. Phys. A: Math. Gen. 30 3029-3056 doi: 10.1088/0305-4470/30/9/016
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Institut für Theoretische Physik, Universität Tübingen, Auf der Morgenstelle 14, D-72076 Tübingen, Germany Department of Mathematics, Macquarie University, Sydney, NSW 2109, AustraliaAbstract. The torus parametrization of quasiperiodic local isomorphism classes is introduced and used to determine the number of elements in such a class with special symmetries or inflation properties. The method is explained in an illustrative fashion for some widely used tiling classes with golden mean rescaling, namely for the Fibonacci chain (one-dimensional), the triangle and Penrose patterns (two-dimensional) and for Kramer's and Danzer's icosahedral tilings (three-dimensional). We obtain a rather complete picture of the orbit structure within these classes, and also discuss various general results.
Print publication: Issue 9 (7 May 1997) |
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