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Crystallography in spaces of arbitrary dimension

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

The detailed study of n-dimensional crystallography appears to have been initiated by Hermann but unfortunately only a small fragment of his work was ever published(4). Recently, interest in the subject has been revived by the work of Bülow, Neubüser and Wondratschek(2), who not only obtained definitive results on 4-dimensional lattices and space groups but also proposed general definitions and procedures for the n-dimensional case. In particular they introduced the concept of crystal family and so resolved satisfactorily the controversy on whether there are six or seven 3-dimensional crystal systems (see(1)). Their point of view is arithmetic, that is, they use a coordinate system adapted to the particular lattice under consideration and represent elements of its symmetry group by integer matrices.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 76 , Issue 1 , July 1974 , pp. 23 - 32
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

REFERENCES

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