Space-group symbols and their use

The three main kinds of point-group symbols in use today (Schoenflies symbols, Shubnikov symbols and Hermann–Mauguin symbols) are described and listed. International (Hermann–Mauguin) and Shubnikov symbols for symmetry elements and representatives for the lattice symmetry directions in the different crystal families are tabulated. It is then explained how space-group symbols can be obtained by a modification of point-group symbols. The standard Schoenflies, Shubnikov and short and full international space-group symbols used in the present edition and the 1935 edition of International Tables are discussed and extensively tabulated. Examples are given of how to derive the space group from the short international symbol and how to derive the full symbol from the short symbol. The derivation of symmetry elements that are not given explicitly in the full symbol is described. Standardization rules for the short symbols are given, and systematic absences and generalized symmetry (e.g. colour groups) are briefly discussed. Finally, it is noted that the original Hermann–Mauguin symbols used in the first edition of International Tables in 1935 were changed considerably in the 1952 edition. Further changes were made in the 1983 and 1995 editions. The changes made since 1935 are described.