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Affine symmetry groups in 2D-quasicrystals

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This paper is devoted to the mathematical description of possible finite affine symmetry groups in two-dimensional quasicrystals.

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References

  1. V. A. Artamonov, “On symmetries of quasicrystals,” in: J. A. de la Pena, E. Vallejo, and N. Atakishiev, eds., Algebraic Structures and Their Representation: XV Colloquio Latinoamericano de Álgebra, Cocoyoc, Morelos, Mexico, July 20–26, 2003, Amer. Math. Soc., Providence (2005), Contemp. Math., Vol. 376, pp. 175–188.

    Google Scholar 

  2. V. A. Artamonov and S. Sanchez, “Remarks on symmetries of 2D-quasicrystals,” in: Proc. of the Conf. on Computation and Mathematical Methods in Science and Engineering (CMMSE-2006), Univ. Rey Juan Carlos, Madrid, Spain, September 21–25, 2006, pp. 59–70.

  3. V. A. Artamonov and Yu. L. Slovokhotov, Groups and Their Applications in Physics, Chemistry, and Crystallography, Akademia, Moscow (2005).

    Google Scholar 

  4. B. Delone, N. Padurov, and A. Aleksandrov, Mathematical Foundations of the Structural Analysis of Crystals [in Russian], Moscow (1934).

  5. E. S. Fedorov, The Symmetry and Structure of Crystals. Fundamental Works [in Russian], Moscow (1949).

  6. A. Schönflies, Kristallsysteme und Kristallstruktur, Leipzig (1891).

  7. D. Shechtman et al., “Metallic phase with long-range orientational order and no translational symmetry,” Phys. Rev. Lett., 53, 1951–1953 (1984).

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Authors and Affiliations

  1. Moscow State Industrial University, Moscow, Russia

    B. A. Dolgikh

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  1. B. A. Dolgikh
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Correspondence to B. A. Dolgikh.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 2, pp. 117–122, 2007.

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Dolgikh, B.A. Affine symmetry groups in 2D-quasicrystals. J Math Sci 154, 204–207 (2008). https://doi.org/10.1007/s10958-008-9158-4

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  • DOI: https://doi.org/10.1007/s10958-008-9158-4

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