## Algorithm for Conversion Between Geometric Algebra Versor Notation and Conventional Crystallographic Symmetry-Operation Symbols

**Authors:** Eckhard Hitzer, Christian Perwass

This paper establishes an algorithm for the conversion of conformal geometric algebra
(GA) [3, 4] versor symbols of space group symmetry-operations [6–8, 10] to standard
symmetry-operation symbols of crystallography [5]. The algorithm is written in the
mathematical language of geometric algebra [2–4], but it takes up basic algorithmic
ideas from [1]. The geometric algebra treatment simplifies the algorithm, due to the
seamless use of the geometric product for operations like intersection, projection, rejection;
and the compact conformal versor notation for all symmetry operations and for
geometric elements like lines and planes.
The transformations between the set of three geometric symmetry vectors *a,b,c*,
used for generating multivector versors, and the set of three conventional crystal cell
vectors **a,b,c** of [5] have already been fully specified in [8] complete with origin shift
vectors. In order to apply the algorithm described in the present work, all locations,
axis vectors and trace vectors must be computed and oriented with respect to the conventional
crystall cell, i.e. its origin and its three cell vectors.

**Comments:** 14 Pages. 6 tables. Preprint (2009).

**Download:** **PDF**

### Submission history

[v1] 2013-06-19 03:58:59

**Unique-IP document downloads:** 98 times

Vixra.org 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.
Vixra.org 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.*

*
*