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The extreme coverings of 4-space by spheres

Published online by Cambridge University Press:  09 April 2009

T. J. Dickson
T. J. Dickson
Affiliation:
University of Western Australia
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The object of this paper is to apply, in the case n = 4, the results of Barnes and Dickson [1] concerning extreme coverings of n-dimensional Euclidean space by equal spheres whose centres form a lattice.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 7 , Issue 4 , November 1967 , pp. 490 - 496
Copyright
Copyright © Australian Mathematical Society 1967

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]Delone, B. N. and Ryskov, S. S., ‘Solution of the problem of the least dense lattice covering of a 4-dimensional space by equal spheres’, Dokl. Akad. Nauk. S.S.S.R. 152 (1963), 523.Google Scholar
[3]Dickson, T. J., ‘An extreme covering of 4-space by spheres’, J. Aust. Math. Soc. 6 (1966), 179–192.CrossRefGoogle Scholar
[4]Voronoï, G., ‘Recherches sur les paralleloédres primitifs (Part. 2)’, J. rein angew. Math. 136 (1909), 67–181.Google Scholar