1. Abstract

Direct visualization of crystallographic and magnetic point group symmetry by means of computer graphics substantially simplifies the teaching of point group symmetry at the undergraduate and graduate levels. A method is proposed for the creation of still images and animated movies for all 32 crystallographic point groups, and for the 122 magnetic point groups. For each point group, the action of the symmetry operators on scalar and pseudo-scalar objects, as well as polar and axial vectors, is represented as a three-dimensional rendered (ray-traced) image.

• Preface

  • List of symbols

  
  Part I. Points, vectors, and matrices
  
   

• Points and vectors

Introduction

We all know by everyday experience that matter has many different states of aggregation. Chemists also know that matter is made of atoms, ions and molecules, and that the macroscopic properties of any object depend on the size, shape and energies of these microscopic constituents.