The Brillouin-zone database of theBilbao Crystallographic Server(http://www.cryst.ehu.es) offersk-vector tables and figures which form the background of a classification of the irreducible representations of all 230 space groups. The symmetry properties of the wavevectors are described by the so-called reciprocal-space groups and this classification scheme is compared with the classification of Cracknellet al.[Kronecker Product Tables, Vol. 1,General Introduction and Tables of Irreducible Representations of Space Groups(1979). New York: IFI/Plenum]. The compilation provides a solution to the problems of uniqueness and completeness of space-group representations by specifying the independent parameter ranges of general and specialkvectors. Guides to thek-vector tables and figures explain the content and arrangement of the data. Recent improvements and modifications of the Brillouin-zone database, including new tables and figures for the trigonal, hexagonal and monoclinic space groups, are discussed in detail and illustrated by several examples.
