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Article Dans Une Revue Ferroelectrics Année : 2004

An example of symmetry space group for a quasicrystal

Résumé

We present the construction of a symmetry plane-group for a quasiperiodic point-set in the plane named τ-lattice, τ being the golden-ratio. The τ-lattice generalizes the notion of periodic lattice to quasiperiodicity. The algebraic framework is issued from the counting system of τ-integers. The set of τ-integers can be equipped with an abelian group structure and an internal multiplicative law. These arithmetic structures lead to a freely generated symmetry plane-group for the τ-lattice, based on repetitions of discrete “τ-rotations” and “τ-translations” in the plane. Hence the τ-lattice, endowed with these adapted rotations and translations, can be viewed as a lattice with “rotational” symmetries.
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hal-03136727 , version 1 (13-02-2021)

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A. Elkharrat, C. Frougny, J.-P. Gazeau, Jean-Louis Verger-Gaugry. An example of symmetry space group for a quasicrystal. Ferroelectrics, 2004, 305 (1), pp.9-13. ⟨10.1080/00150190490462243⟩. ⟨hal-03136727⟩
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