Space Group Visualizer – New Free Release for all 230 Space Groups

Welcome to the space group web site!

New (06 March 2012): full software download | tutorial videos | tutorial presentation | introduction paper

The latest (10. August 2011):
A new release version (2.3.1) of the SpaceGroupVisualizer is now available. This version has all 230 space groups enabled.

On these pages we present fully interactive 3D software and publications that treat crystallographic space and point groups using W.K. Clifford’s 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 W.K. Clifford’s Geometric Algebra, which allows for a direct implementation of symmetry operators in the algebra. Follow the link to download publications and fully interactive software for the different topics.

In particular note the space group visualisation project, which started at the end of 2005. In January 2010 the first release version was available. The latest version has all 230 space groups enabled, including a wide variety of crystallographic cell choices.

We would be glad to hear your comments and suggestions. Just send us an email to

Christian Perwass, Eckhard Hitzer, August 2011


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