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In the first part of this monograph the concepts of symmetry operations, symmetry elements and symmetry groups based on the metric tensor invariance are introduced.

In the second part the crystallographic point groups are derived: first the enantiomorphic groups using all possible combinations of the rotation axes; secondly, the centrosymmetric groups; and, finally, the non-enantiomorphic, non-centrosymmetric groups.

This scheme is directed to students who already have a basic knowledge of vector and matrix calculus, and of group theory (i.e. students of the III course in Chemistry).

I hope this presentation will be helpful to teachers in relating some aspects of crystallography to other topics in the field of physical chemistry.

In a crystallography course this subject should be preceded by an introduction
to direct lattice and to reciprocal lattice (distances and angles,
transformations) and followed by a discussion of space groups, i.e. of the
combinations of the possible symmetry operations of the type
{*A* /*t* }.

- Metric tensor
- Symmetry operations
- Symmetry elements and their orientation
- Rotations compatible with a lattice base system
- Symmetry groups

**Copyright © 1980, 1998 International Union of
Crystallography**