Visualization of Time-Reversal Symmetry in Magnetic Point Groups

Abstract

The direct visualization of crystallographic and magnetic point group symmetry by means of computer graphics simplifies the teaching of point group symmetry at the undergraduate and graduate levels. Still images and animated movies for all 32 crystallographic point groups, and for the 122 magnetic point groups, are presented. For each point group, the action of the symmetry operators on scalar and pseudo-scalar objects, as well as on polar and axial vectors, is represented as a three-dimensional rendered image. All images and movies are made available as supplementary educational material via a dedicated web site.