Meyer Sets and the Finite Generation of Quasicrystals

  • R. V. Moody


A monk saw a turtle walking in the garden of Ta-sui’s monastery and asked his teacher “ All beings cover their bones with flesh and skin. Why does this being cover its flesh and skin with bones?” Ta-sui, the master, took off one of his sandals and covered the turtle with it. ----- The Iron Flute




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  1. [CMP]
    Chen, L., Moody, R. V., and Patera, J., Non-crystallographic root systems and quasicrystals (to appear).Google Scholar
  2. [De]
    Deodhar, V., On the root system of a Coxeter group, Comm. in Algebra 10 (1982), 611.MathSciNetMATHCrossRefGoogle Scholar
  3. [ES]
    Elser, V. and Sloane, N. J. A., A highly symmetric four-dimensional quasicrystal,J. Phys. A: Math. Gen. 20 (1987), 6161.MathSciNetADSMATHCrossRefGoogle Scholar
  4. [Hu]
    Humphreys, J.E., Relection groups and Coxeter groups, Cambridge Univ. Press, 1990.CrossRefGoogle Scholar
  5. [Ja]
    Janot, C., Quasicrystals: A Primer, Monographs on the Physics and Chemistry of Materials, vol. 48, Clarendon Press, Oxford, 1992.Google Scholar
  6. [KMP]
    Kramer, P., Papadopolis, Z., and Moody, R. V., A growth mechanism for the T(2F)-tiling (to appear).Google Scholar
  7. [KN]
    Kramer, P. and Nori, R., On periodic and no-periodic space fillings obtained by projections, Acta Cryst. A40 (1984), 580.Google Scholar
  8. [LP]
    Lunnon, W. F. and Pleasants, P., Quasicrystallographic tilings, J. Math. pures et appl. 66 (1987), 217.MathSciNetMATHGoogle Scholar
  9. [Mel]
    Meyer, Y., Algebraic numbers and harmonic analysis, North-Holland Publ., Amsterdam, 1972.MATHGoogle Scholar
  10. [Me2]
    Meyer, Y., Quasicrystals, diophantine approximation, and algebraic numbers (1994), Beyond Quasicrystals, Les Houches,1994.Google Scholar
  11. [MP1]
    Moody, R. V. and Patera, J., Quasicrystals and icosians, J.Phy.A:Math.GEn. 26 (1993), 2829.MathSciNetADSMATHCrossRefGoogle Scholar
  12. [MP2]
    Moody, R. V. and Patera, J., Local dynamical generation of quasicrystals (to appear).Google Scholar
  13. [Sc]
    Schechtman, D., Blech, I., and Gratias, D., Metallic phase with long-range orientational order and no translational symmetry, Phys. Rev. Lett. 53 (1984), 1951.ADSCrossRefGoogle Scholar
  14. [Se]
    Senechal, M., Quasicrystals and Geometry, Cambrdige Univ. Press (to appear1995).Google Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • R. V. Moody
    • 1
  1. 1.Department of MathematicsUniversity of AlbertaEdmonton, AlbertaCanada

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