Noncrystallographic symmetry and the sampling theorem

Abstract

Abstract When the asymmetric unit of a crystal structure expresses some noncrystallographic symmetry it is often found that these local symmetry elements involve only proper rotations. Under these conditions the relations between the structure factors resulting from this repetition within the crystallographic asymmetric unit reduce to a statement of the Whittaker-Shannon sampling theorem, and thereby suggest the real space method for solution. A simple model structure is solved as an example.