Michael Baake et al 1997 J. Phys. A: Math. Gen. 30 3029 doi:10.1088/0305-4470/30/9/016
The torus parametrization of quasiperiodic LI-classes
Michael Baake
, Joachim Hermisson and Peter A B Pleasants
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.
- PACS
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61.50.Ah Theory of crystal structure, crystal symmetry; calculations and modeling
- MSC
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11B39 Fibonacci and Lucas numbers and polynomials and generalizations
- Subjects
- Dates
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Issue 9 (7 May 1997)
Received 9 August 1996
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The torus parametrization of quasiperiodic LI-classes
Michael Baake et al 1997 J. Phys. A: Math. Gen. 30 3029
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