International Tables for Crystallography

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Bases, lattices, Bravais lattices and other classifications
H. Burzlaff and H. Zimmermann. International Tables for Crystallography (2006). Vol. A, ch. 9.1, pp. 742-749  [ doi:10.1107/97809553602060000517 ]

Abstract

In this chapter, the symmetry and some topological aspects of lattices are considered. Different classifications of lattices into five Voronoi types, 24 Symmetrische Sorten and 14 Bravais lattices are described. Conventional lattice bases and their cells are defined and illustrated. Extensive tabulations for the two- and three-dimensional Bravais lattices are provided. Further classifications use reduction theory; details of the Delaunay reduction are given.


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About International Tables for Crystallography

International Tables for Crystallography is the definitive resource and reference work for crystallography. The multi-volume series comprises articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials.