  This paper shows how beginning with Justus Grassmann's work, Hermann
Grassmann was influenced in his mathematical thinking by crystallography. 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.
