author : Marjorie Senechal

The discovery in 1984 of crystals with ‘forbidden’ symmetry posed fascinating and challenging problems in many fields of mathematics, as well as in the solid state sciences. By demonstrating that ‘order’ need not be synonymous with periodicity, it raised the question of what we mean by ‘order’, and how orderliness in a geometric structure is reflected in measures of order such as diffraction spectra. Increasingly, mathematicians and physicists are becoming intrigued by the quasicrystal phenomenon, and the result has been an exponential growth in the literature on the geometry of diffraction patterns, the behavior of the Fibonacci and other nonperiodic sequences, and the fascinating properties of the Penrose tilings and their many relatives.

This detailed account of quasicrystal geometry will be of great value to mathematicians at all levels with an interest in quasicrystals and geometry, and will also be of interest to graduate students and researchers in solid state physics, crystallography and materials science.