Nespolo Massimo
LCM3B UMR-CNRS 7036, Nancy Université, BP 239, F-54506 Vandoeuvre-lès-Nancy CEDEX, France.
Acta Crystallogr A. 2008 Jan;64(Pt 1):96-111. doi: 10.1107/S0108767307044625. Epub 2007 Dec 21.
Mathematical crystallography is the branch of crystallography dealing specifically with the fundamental properties of symmetry and periodicity of crystals, topological properties of crystal structures, twins, modular and modulated structures, polytypes and OD structures, as well as the symmetry aspects of phase transitions and physical properties of crystals. Mathematical crystallography has had its most evident success with the development of the theory of space groups at the end of the XIX century; since then, it has greatly enlarged its applications, but crystallographers are not always familiar with the developments that followed, partly because the applications sometimes require some additional background that the structural crystallographer does not always possess (as is the case, for example, in graph theory). The knowledge offered by mathematical crystallography is at present only partly mirrored in International Tables for Crystallography and is sometimes still enshrined in more specialist texts and publications. To cover this communication gap is one of the tasks of the IUCr Commission on Mathematical and Theoretical Crystallography (MaThCryst).
数学晶体学是晶体学的一个分支，专门研究晶体的对称性和周期性的基本性质、晶体结构的拓扑性质、孪晶、模块化和调制结构、多型体和OD结构，以及相变的对称性方面和晶体的物理性质。随着19世纪末空间群理论的发展，数学晶体学取得了最显著的成功；从那时起，它的应用范围大大扩展，但晶体学家并不总是熟悉其后的发展，部分原因是这些应用有时需要一些结构晶体学家并不总是具备的额外背景知识（例如在图论中就是这种情况）。目前，数学晶体学所提供的知识在《国际晶体学表》中只是部分体现，有时仍收录在更专业的文本和出版物中。弥补这一沟通差距是国际晶体学联盟数学与理论晶体学委员会（MaThCryst）的任务之一。
