On these pages we present software and publications that treat crystallographic space and point groups using Geometric Algebra. The algebra allows us to represent symmetries without the need to refer to a particular basis or origin. This method to describe point and space groups was first introduced by David Hestenes.
Eckhard Hitzer and Christian Perwass worked on visualising point and space groups using the visualisation tool CLUCalc.This software implements Geometric Algebra, which allows for a direct implementation of symmetry operators in the algebra.
There exist 230 symmetry space groups in 3D space, which are shown as 2D projections in the ITC Tables Volume A. The SpaceGroupVisualizer is a visualisation software that is the perfect addition to the ITC Tables Volume A, as it visualizes all 230 space groups in 3D, lets you freele rotate and move the crystal cells, offers real 3D impressions with Green/Magenta or Red/Cyan glasses, lets you select subsets of symmetries and animates the effect of symmetries on the unique cell elements. The SpaceGroupVisualizer therefore allows you to get a good grasp on the symmetry structure of a space group much more easily.