Teaching Point-Group Symmetry with Three-Dimensional Models

Three tools for teaching symmetry in the context of an upper-level undergraduate or introductory graduate course on the chemical applications of group theory are presented. The first is a collection of objects that have the symmetries of all the low-symmetry and high-symmetry point groups and the point groups with rotational symmetries from 2-fold to 6-fold. Students can sort the objects by point group and can also see similarities and differences between point groups. The second is a magnet-backed mirror onto which are placed molecular models that have been modified to rest on the mirror and represent atoms and bonds that are on the mirror plane. The third is a frame to show the perpendicular C2 axes that are a feature of all the Dnh, Dnd, and Dn point groups.