E.S.M. Hitzer
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).

Abstract: 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 Classi cation (2000). Primary 20H15; Secondary 15A66, 74N05, 76M27, 20F55.

Keywords. Crystallography, Grassmann algebra, Cli ord geometric algebra, Visualization, Computer graphics.

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