Transformational space-group symbols

Ambiguities present in space-group construction from the Hermann-Mauguin (H-M) symbols enforce the use of other space-group designations or H-M symbol modifications. Therefore, a transformational space-group symbol (TSG) composed of the well defined standard space-group identifier, an axis-system transformation and origin shift is proposed as a symbol of any space-group description. The first description given in International Tables for Crystallography [(1983), Vol. A, Space-Group Symmetry, edited by Th. Hahn. Dordrecht: Reidel (ITA83)] or the second one for space groups with two origins is suggested here as a reference description. For standard descriptions based on the ITA generators and compiled list of the TSG symbols, all conventional space-group settings listed in ITA83 can be reconstructed.