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Classification of crystal lattices

Published online by Cambridge University Press:  24 October 2008

R. L. E. Schwarzenberger
R. L. E. Schwarzenberger
Affiliation:
University of Warwick
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Extract

There are two natural ways in which to attempt a classification of the lattices which occur in crystallography or, more generally, of n-dimensional lattices. The first method is algebraic and proceeds by classifying the symmetry groups of the lattices. Thus an n-dimensional lattice is a discrete subgroup

of Rn and determines a symmetry group

which is a subgroup of the orthogonal group On. Two lattices T1 and T2 are said to determine the same crystal system if the symmetry groups G(T1) and G(T2) are conjugate: that is there exists a linear isomorphism ø: Rn → Rn such that

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 72 , Issue 3 , November 1972 , pp. 325 - 349
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

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