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Three-Dimensional Point Groups

Part of the Lecture Notes in Mathematics book series (LNM,volume 2113)

Abstract

In this chapter, we give a complete classification of the 32 three-dimensional point groups. Our treatment is self-contained, but the principles of the classification come from [Sc80, Chap. 4]. Our goal is to describe the point groups as explicit groups of matrices.

Keywords

  • Point Group
  • Permutation Matrix
  • Dihedral Group
  • Central Inversion
  • Sign Matrice

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Fig. 2.1
Fig. 2.2

References

  1. R.L.E. Schwarzenberger, N-Dimensional Crystallography. Research Notes in Mathematics, vol. 41 (Pittman Advanced Publishing Program, Boston, Mass.-London 1980)

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© 2014 Springer International Publishing Switzerland

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Farley, D.S., Ortiz, I.J. (2014). Three-Dimensional Point Groups. In: Algebraic K-theory of Crystallographic Groups. Lecture Notes in Mathematics, vol 2113. Springer, Cham. https://doi.org/10.1007/978-3-319-08153-3_2

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