Geometrical symbols for all crystallographic symmetry groups up to three dimensions
Abstract
<h2>Acta Crystallographica</h2><h3></h3><h3>0365-110X</h3> <h2>research papers</h2> Volume 23 Part 6 Pages 913-933 December 1967 <h2>Geometrical symbols for all crystallographic symmetry groups up to three dimensions</h2> J. Bohm and K. Dornberger-Schiff Acta Cryst. (1967). 23, 913 Geometrical Symbols for All Crystallographic Symmetry Groups up to Three Dimensions BY J. BOHM AND K. DORNBERGER- SCHIFF Deutsche Akademie der Wissenschaften zu Berlin, II. Physikalisch-Technisches lnstitut and lnstitut fiir Strukturforschung, Berlin-Adlershof, Germany (DDR) (Received 20 March 1967) A complete list of the individual symmetry groups belonging to all sets of such groups up to three dimensions is given, each set being characterized by symbols as agreed upon by the Commission on International Tables and each symmetry group by a symbol closely connected with the international space group symbols. Each set is characterized by the reducibility of the matrices of the transformations of space corresponding to the symmetry operations. As pointed out elsewhere (Bohm & Dornberger-Schiff, 1966) the different kinds of symmetry group - not only the purely geometrical groups but also those including antisymmetry and other generalized symmetry - may be described and symbolized as geometrical symmetry groups. It is of advantage to have easily understand- able symbols for the different sets of symmetry