Teaching crystallographic and magnetic point group symmetry using three-dimensional rendered visualizations

Marc De Graef

Department of Materials Science and Engineering, Carnegie Mellon University

Teaching aims

To provide teachers with a new tool for the teaching of crystallographic and magnetic point groups; to provide students with a new way to learn about point groups.


This pamphlet can be used at the undergraduate level by students with some prior exposure to symmetry. This pamphlet would be useful for students in the fields of physics, chemistry, geology, and materials science and engineering.


Prior exposure to crystallography and symmetry is desirable.

Practical resources

A list of references is given at the end of the pamphlet. Web-based resources can be found on the site http://mpg.web.cmu.edu; these resources can be used by teachers and students alike.

Time required for teaching

This material can be taught in a two-hour lecture.