Abstract
Tilings provide generalized frames of coordinates and as such they are used in different areas of physics. The aim of the present paper is to present a unified and systematic description of a class of tilings which have appeared in contexts as disconnected as crystallography and dynamical systems. The tilings of this class show periodic or quasiperiodic ordering and the tiles are related to the unit cube through affine transformations. We present a section procedure generating canonical quasiperiodic tilings and we prove that true tilings are indeed obtained. Moreover, the procedure provides a direct and simple characterization of quasiperiodicity which is suitable for tilings but which does not refer to Fourier transform.
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Communicated by A. Jaffe
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Oguey, C., Duneau, M. & Katz, A. A geometrical approach of quasiperiodic tilings. Commun.Math. Phys. 118, 99–118 (1988). https://doi.org/10.1007/BF01218479
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DOI: https://doi.org/10.1007/BF01218479