Crystals and Quasicrystals

Authored by: Marjorie Senechal

Discrete and Computational Geometry

Print publication date:  April  2004
Online publication date:  April  2004

Print ISBN: 9781584883012
eBook ISBN: 9781420035315
Adobe ISBN:

10.1201/9781420035315.ch62

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Abstract

Mathematical crystallography is the branch of discrete geometry that deals with the structure and form of crystals. For over a century the field has been a meeting ground for polytopes, lattices, tilings, and groups. Today, stimulated both by developments internal to mathematics and by the discovery of quasicrystals, the subject is broadening rapidly, and modeling the geometry of crystals requires an ever-expanding mathematical toolbag. In Section 62.1 we survey the classical foundations of the subject; in Section 62.2 we indicate how these foundations are being redesigned to encompass recent developments. We assume that the reader is familiar with the terminology and results of Chapter 3 of this Handbook.

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