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New views of crystal symmetry guided by profound admiration of the extraordinary works of Grassmann and Clifford

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.

preprint2013arXivOpen access
Eckhard Hitzer
math.RTGraphicscond-mat.mtrl-scimath.RA
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Open access1 author4 topics
Imported metadata coverageMissing code, dataset, citation and institution fields are tracked without dominating the paper.Details
Citations: 0Reviews: 0Saves: 0Code: not linkedDataset: not linkedInstitutions: 0

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Eckhard Hitzer

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