Point groups are the symmetry groups of 3D-Euclidean space, when not taking translation into account. The exist 32 point groups in 3D space.

Software

Download the new visualisation scripts (v2.0) In order to use the point group visualisation scripts, you first need to download and install CLUViz version 6.1.12 or higher. If you have already installed the SpaceGroupVisualizer you do not need to install CLUViz again.

This script was initially developed by C. Perwass and E. Hitzer during a visit of E. Hitzer at the university of Kiel in summer 2004.

The idea behind this script is to visualise the different point groups by drawing representative crystal cells and also visualising the possible symmetry operations for each. Also the basis vectors from which the symmetry operation generators can be constructed in Geometric Algebra are shown. It is hoped that this will help people new to the subject to understand what point groups are all about.

Publications

The following is a list of publications that describe the theoretical background of point groups.

Download an introduction to the description of point groups using Geometric Algebra. This subject was initially treated by David Hestenes as referenced in the paper.