N-dimensional space groups and regular point systems

Abstract

The concept of symmetrically-nonequivalent (i.e. different in their symmetry) regular point systems (SNRPS) of the n-dimensional space groups of symmetry was introduced. The group-theoretical algorithm for derivation of these groups was suggested. The number of SNRPS was determined to be 13,166 and 3684 for n = 2, 3, 4 accordingly. For three-dimensional space groups 58 locally-centrosymmetric space groups (LCSG) were considered, each regular point system of which is symmetric with respect to some inversion center. It was estimated that for the crystals with LCSG a tendency to a decrease in the absolute values of piezoelectric and electrooptic coefficients has been observed with the increasing atomic number of the most heavy atom of the structure.