Non-commutative Models for Quasicrystals

  • P. Kramer
  • J. Garcia-Escudero
Conference paper
Part of the Centre de Physique des Houches book series (LHWINTER, volume 3)


A powerful approach to quasicrystals arises from the use of n-dimensional crystallography: Given a non-crystallographic point group H in R 3, look for the lattice Γ of minimal dimension n which has H as (part of) its point group. The n-dimensional representation of H must be reducible and contain a 3D representation. Split R n into this representation space R 3 and its orthogonal complement, construct discrete quasiperiodic patterns by projection from the lattice to R 3 and use the orthogonal complement for windows and for coding. Periodicity and tranlational symmetry in R 3 are absent by construction. This scheme allows to treat diffraction properties by lifting the Fourier coefficients to the reciprocal lattice Γ R .


Propa Lentin 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • P. Kramer
    • 1
  • J. Garcia-Escudero
    • 2
  1. 1.Institut für Theoretische PhysikUniversität TübingenTübingenGermany
  2. 2.Departamento de FisicaUniversidad de OviedoOviedoSpain

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