The following five videos on YouTube give an explanation and demonstration of the interactive Space Group Visualizer software, visualizing and animating all 230 crystallographic space groups in three dimensions. The videos are parts of an invited presentation given by E. Hitzer (with co-author) C. Perwass at the ICCA8 conference in Las Campinas, Brazil in 2008. The full video is available for download here. The presentation slides are here. The conference paper is here. (Update: 06 Mar. 2012)
Video 1: Explanation of: Crystal classes and point groups. Geometric algebra approach to point groups in 2 and 3 dimensions. Geometric notation (Hestenes and Coxeter). Example: Holohedry (maximum order point group) of hexagonal crystal cell. Space groups in 2 and 3 dimensions. Use of conformal geometric algebra model for space group representation.
Video 2: Crystallographic space group transformations in conformal geometric algebra. 3D space group notation. Symmetry elements in computer graphics of space group visualizer. Interactive software implementation. Help function. View of Space Group Visualizer GUI. How to use the GUI for manipulating the view of a space group. How to select a space group. Selection of symmetry elements by type, by properties, by generator expression. 3D mouse interactivity. 3D mouse. Drop down menu options. Pairallel view with International Tables of Crystallography online. Point group visualizer. Wallpaper visualizer.
Video 3: Life demonstration of free space group visualizer. Here: monoclinic, triclinic, tetragonal, trigonal, hexagonal crystal classes.
Video 4: Life demonstration of free space group visualizer. Cubic space group No. 225, Fm3barm, geometric name: F43. Demonstration of lighting, background choice, 3D 2-color coded stereographic view, 1 cluster view (point group), reflection planes, pick and activate symmetry elements, inversion centers.
Video 5: Life demonstration of free space group visualizer. Cubic space group No. 225, Fm3barm, geometric name: F43. Demonstration of rotations, selection by angle, orthographic view, srew transformations, mouse interactive symmetry selection and animation, enantiomorphic symmetry elements, roto-inversions (roto-reflections), multi cell view. Question.