E.S.M. Hitzer, C. Perwass

**Visualization of fundamental symmetries in nature**

Proceedings of
*Fuzzy System Symposium (FSS 2009)*,
Tsukuba, Japan, 14-16 Jul. 2009.

**Abstract:**
Most matter in nature and technology is composed of crystals and crystal grains. A full
understanding of the inherent symmetry is vital. A new interactive software tool is demonstrated, that
visualizes 3D space group symmetries. The software computes with Clifford (geometric) algebra. The space
group visualizer (SGV) is a script for the open source visual CLUCalc, which fully supports geometric
algebra computation. In our presentation we will first give some insights into the geometric algebra
description of space groups. The symmetry generation data are stored in an XML file, which is read by
a special CLUScript in order to generate the visualization. Then we will use the Space Group Visualizer
to demonstrate space group selection and give a short interactive computer graphics presentation on how
reflections combine to generate all 230 three-dimensional space groups.

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[Geometric Calculus Japan index]