The adjunction of antiidentity operations to point groups, including a derivation of the magnetic point groups

Abstract

AbstractThe theoretical basis for an iterative procedure for adjoining antiidentity operations to point groups is presented. The theory is stated in a general context and is then applied to point groups yielding the crystallographic point groups from the proper crystallographic point groups and yielding the antisymmetry groups (including the magnetic point groups) from the crystallographic point groups.A method for constructing point groups that describe the symmetry of an object having a number of two-mode properties (positive-negative, black-white etc.) is discussed. Finally, a physical interpretation of the crystallographic point groups involved in the construction of a given magnetic point group is presented.