Bases, lattices, Bravais lattices and other classifications
Hans Burzlaff, Herbert Zimmermann · International Tables for Crystallography · 2006
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.