E. Hitzer, C. Perwass

**
Crystallogaphic space groups:
Representation and interactive visualization by geometric algebra
**

submitted to:
Proceedings of *the 26th Int. Conference on Group Theoretical
Methods in Physics, New York, USA, 2006.*

**Abstract:**
We treat the symmetries of crystal space lattices in geometric algebra
(GA)[1].
All crystal cell
point groups are
generated by geometric multiplication of two or three physical cell vectors.
Only one or two relative angles
subtended by these vectors need to be known.
This treatment extends to space groups by
including translations.
GA helps to identify optimal multivector generators.
As example we take the monoclinic case.
New free interactive
OpenGL and GA based software
visualizes these symmetries.

[1]
Hestenes, D. 2002,
*Point
groups and space groups in geometric algebra*,
in ed. Dorst, L, etal,
*Applications
of Geometric Algebra in Computer Science and Engineering*
(Basel: Birkhauser) pp. 3-34.
Hestenes, D. and Holt, J. 2006,
*The crystallographic
space groups in geometric algebra*,
J. Math. Phys. 48, 023514 (2007);
doi10.1063/1.2426416.

[PDF] 2600 kb

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