Welcome to the magnetic point groups web site!
This site provides a series of still images and movies showing the regular and magnetic point groups as 3D rendered objects. To generate the images, we use the POVray rendering package; all scripts used to create the images/movies, as well as all the scripts needed to create this entire website, are available from GitHub; simply fork the repository, clone it to your own computer, install a few programs and execute the top scripts described in the README file.
For details on the underlying math and physics, please refer to the following paper: M. De Graef, Visualization of time-reversal symmetry in magnetic point groups, Met. Mat. Trans. A, 41, pp. 1321-1329 (2010). A similar article was published as Teaching Pamphlet #23 by the International Union of Crystallography.
For each point group, there are a number of rendering options available: [CPG=crystallographic point group, MPG=magnetic point group]
- raw stills: These images only show the symmetry elements, without any objects, for the 32 CPGs.
- scalar stills: 32 CPGs with a scalar object, i.e., a sphere
- scalar movies: Similar to scalar stills, but with the whole object rotating around its axis
- anaglyph stills: 32 CPGs with a scalar object rendered as red/blue stereo anaglyphs
- pseudoscalar stills: 32 CPGs with a pseudoscalar object, i.e., a righthanded helix
- pseudoscalar movies: Similar to pseudoscalar stills, but with the whole object rotating around its axis
- polar stills: 32 CPGs with a polar object, i.e., an arrow
- polar movies: Similar to polar stills, but with the whole object rotating around its axis
- axial stills: 122 MPGs with an axial object, i.e., an arrow
- axial movies: Similar to axial stills, but with the whole object rotating around its axis
All still images and movies are available in tar.gzip compressed format via the "Archives" menu link.
This material is based upon work initially funded by the National Science Foundation under Grant Nos. DMR-0809048 and DMR-1005330; this latest version, rendered with POVray and fully open source on GitHub, was supported by NSF DMR-1564550. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author.