Condensed Matter


Crystal Cells in Geometric Algebra

Authors: Eckhard Hitzer, Christian Perwass

This paper focuses on the symmetries of space lattice crystal cells. All 32 point groups of three dimensional crystal cells are exclusively described by vectors (three for one particular cell) taken from the physical cell. Geometric multiplication of these vectors completely generates all symmetries, including reflections, rotations, inversions, rotary-reflections and rotary-inversions. The sets of vectors necessary are illustrated in drawings and all symmetry group elements are listed explicitly as geometric vector products. Finally a new free interactive software tool is introduced, that visualizes all symmetry transformations in the way described in the main geometrical part of this paper.

Comments: 6 Pages. 5 figures. Proceedings of the International Symposium on Advanced Mechanical Engineering, between University of Fukui (Japan) - Pukyong National University (Korea), 27 Nov. 2004, pp. 290-295 (2004).

Download: PDF

Submission history

[v1] 2013-06-19 03:49:27

Unique-IP document downloads: 103 times is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus