Linear Algebra and Group Theory for Physicists pp 367-405 | Cite as

# The Crystallographic Point Groups

Chapter

## Abstract

A crystallographic point group is a finite-dimensional group *G* of rotations and reflections each of which is a symmetry operation of a crystal sending it into itself with *one fixed* point through which pass the axes of rotations and planes of reflections. Thus *G* is a finite-dimensional subgroup of the Full Orthogonal Group * O*(3) consisting of 3rd order orthogonal matrices with determinants ±1. We note that the group

*D*

^{3}of symmetries of an equilateral triangle discussed in example 5 of section 1–2 is itself a crystallographic point group consisting only of rotations.

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## References

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