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A sufficient condition for an extreme covering of n-space by spheres

Published online by Cambridge University Press:  09 April 2009

T. J. Dickson
T. J. Dickson
Affiliation:
The University of Western Australia
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The problem of finding the most economical coverings of n-dimensional Euclidean space by equal spheres whose centres form a lattice, which is equivalent to a problem concerning the inhomogeneous minima of positive definite quadratic forms, has been discussed recently by Barnes and Dickson [1]. The reader is referred to [1] for a complete background on the problem. Terms and notations used will be as in that paper.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 8 , Issue 1 , February 1968 , pp. 56 - 62
Copyright
Copyright © Australian Mathematical Society 1968

References

[1]Barnes, E. S. and Dickson, T. J.: ‘Extreme coverings of n-space by spheres’, J. Aust. Math. Soc. 7 (1967), 115–127.CrossRefGoogle Scholar
[2]Dickson, T. J.: ‘The extreme coverings of 4-space by spheres’, J. Aust. Math. Soc. 7 (1967), 490–496.CrossRefGoogle Scholar
[3]Voronoï, G.: ‘Recherches sur les paralleloedres primitifs (Part 2) J. reine angew. Math. 136 (1909) 67–181.Google Scholar