## 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

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