E.S.M. Hitzer, C. Perwass, D. Ichikawa

**Interactive 3D Space Group Visualization with CLUCalc and
Crystallographic Subperiodic Groups in Geometric Algebra**

in G. Scheuermann, E. Bayro-Corrochano (eds.),
*Geometric Algebra Computing*,
Springer, New York, 2010, pp. 385-400.

**Abstract:**
The Space Group Visualizer (SGV) for all 230 3D space groups is a standalone
PC application based on the visualization software CLUCalc. We first explain
the unique geometric algebra structure behind the SGV. In the second part
we review the main features of the SGV: The GUI, group and symmetry selection,
mouse pointer interactivity, and visualization options.We further introduce the joint
use with the International Tables of Crystallography, Vol. A [7]. In the third part
we explain how to represent the 162 socalled subperiodic groups of crystallography
in geometric algebra. We construct a new compact geometric algebra group representation
symbol, which allows to read off the complete set of geometric algebra
generators. For clarity we moreover state explicitly what generators are chosen. The
group symbols are based on the representation of point groups in geometric algebra
by versors.

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