New views of crystal symmetry guided by profound admiration of the extraordinary works of Grassmann and Clifford
in Petsche, H.-J.; Lewis, A.C.; Liesen, J.; Russ, S. (eds.), From Past to Future: Grasmann's Work in Context, Grasmann Bicentennial Conference, September 2009, Springer, Basel, pp. 413 - 422 (2010).
This paper shows how beginning with Justus Grassmann's work,
Hermann Grassmann was influenced in his mathematical thinking by crystal-
lography. H. Grassmann's Ausdehnungslehre in turn had a decisive influence
on W.K. Clifford in the genesis of geometric algebras. Geometric algebras
have been expanded to conformal geometric algebras, which provide an ideal
framework for modern computer graphics. Within this framework a new
visualization of three-dimensional crystallographic space groups has been created.
The complex beauty of this new visualization is shown by a range of images
of a diamond cell. Mathematical details are given in an appendix.
Mathematics Subject Classication (2000). Primary 20H15; Secondary 15A66, 74N05, 76M27, 20F55.
Keywords. Crystallography, Grassmann algebra, Cliord geometric algebra, Visualization, Computer graphics.
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