THE SYMMETRY OF QUASI-PERIODIC CRYSTALS

Experimentally observed crystals range from periodic crystals, through incommensurately modulated crystals and composite crystals, to quasic rystals and even modulated quasicrystals. How does one characterize in a unified manner the symmetry of all these types of crystals? How doe s one classify all crystals according to their symmetry? These questio ns are answered through a review of the Fourier-space approach to crys tal symmetry of Rokhsar, Wright, and Mermin. The notion of indistingui shability, which is central to the approach, is introduced and used as the basis for a generalization of the traditional space-group classif ication scheme, applicable to all types of crystals known to date.