Quasicrystals and Geometry

Quasicrystals and Geometry is a book on quasicrystals and aperiodic tiling by Marjorie Senechal, published in 1995 by Cambridge University Press (ISBN 0-521-37259-3). One of the main themes of the book is to understand how the mathematical properties of aperiodic tilings such as the Penrose tiling, and in particular the existence of arbitrarily large patches of five-way rotational symmetry throughout these tilings, correspond to the properties of quasicrystals including the five-way symmetry of their Bragg peaks. Neither kind of symmetry is possible for a traditional periodic tiling or periodic crystal structure, and the interplay between these topics led from the 1960s into the 1990s to new developments and new fundamental definitions in both mathematics and crystallography. rdf:langString