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.


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