Line groups structure

Abstract

Line groups are introduced as symmetry groups of the system periodic in a single direction, with periodicity being not restricted to the translational one. Their structure is a weak direct product of the intrinsic symmetry of monomer and the group of generalized translations, arranging these monomers along the direction of periodicity. Continuously many of these groups are classified into 13 infinite families. Only 75 of the line groups are subgroups of the space groups and they are known as rod groups. © 2010 Springer-Verlag Berlin Heidelberg.