International
Tables for Crystallography Volume A Spacegroup symmetry Edited by Th. Hahn © International Union of Crystallography 2006 
International Tables for Crystallography (2006). Vol. A, ch. 2.1, p. 14
Section 2.1.2. Spacegroup classification^{a}Institut für Kristallographie, RheinischWestfälische Technische Hochschule, Aachen, Germany, and ^{b}Laboratorium voor Chemische Fysica, Rijksuniversiteit Groningen, The Netherlands 
In this volume, the plane groups and space groups are classified according to three criteria:

For three dimensions, this applies to the triclinic, monoclinic, orthorhombic, tetragonal and cubic systems. The only complication exists in the hexagonal crystal family for which several subdivisions into systems have been proposed in the literature. In this volume, as well as in IT (1952), the space groups of the hexagonal crystal family are grouped into two `crystal systems' as follows: all space groups belonging to the five crystal classes 3, , 32, 3m and , i.e. having 3, , or as principal axis, form the trigonal crystal system, irrespective of whether the Bravais lattice is hP or hR; all space groups belonging to the seven crystal classes 6, , 622, 6mm, 2m and , i.e. having 6, , , , , or as principal axis, form the hexagonal crystal system; here the lattice is always hP (cf. Section 8.2.8 ). The crystal systems, as defined above, are listed in column 3 of Table 2.1.2.1.
A different subdivision of the hexagonal crystal family is in use, mainly in the French literature. It consists of grouping all space groups based on the hexagonal Bravais lattice hP (lattice point symmetry ) into the `hexagonal' system and all space groups based on the rhombohedral Bravais lattice hR (lattice point symmetry ) into the `rhombohedral' system. In Section 8.2.8 , these systems are called `Lattice systems'. They were called `Bravais systems' in earlier editions of this volume.
The theoretical background for the classification of space groups is provided in Chapter 8.2 .
References
International Tables for Crystallography (2004). Vol. C, 3rd ed., edited by A. J. C. Wilson & E. Prince. Dordrecht: Kluwer Academic Publishers.International Tables for Xray Crystallography (1952). Vol. I, edited by N. F. M. Henry & K. Lonsdale. Birmingham: Kynoch Press. [Revised editions: 1965, 1969 and 1977. Abbreviated as IT (1952).]
Wolff, P. M. de, Belov, N. V., Bertaut, E. F., Buerger, M. J., Donnay, J. D. H., Fischer, W., Hahn, Th., Koptsik, V. A., Mackay, A. L., Wondratschek, H., Wilson, A. J. C. & Abrahams, S. C. (1985). Nomenclature for crystal families, Bravaislattice types and arithmetic classes. Report of the International Union of Crystallography Adhoc Committee on the Nomenclature of Symmetry. Acta Cryst. A41, 278–280.