Concerning the use of 4-dimensional space group symmetry for the derivation of 3-dimensionalp-coloured point groups (p=1,2,3,4,6)

Abstract

The four-dimensional space symmetry groups of the lower systems previously obtained by the authors (Kristallografiya (1971). 16, 5, 268) are used for the independent derivation of 660 Shubnikov groups of triclinic, monoclinic, and orthorhombic systems, and also 179 antisymmetry groups of two-sided infinite bands in three-dimensional space. The crystallographic symmetry groups have been derived for four-dimensional polar and non-polar rods which, in particular, are used for deriving 126 three-dimensional p-coloured point groups (p = 1, 2, 3, 4, 6).