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Five Dimensional Non-Lattice Sphere Packings

Published online by Cambridge University Press:  20 November 2018

John Leech
John Leech*
Affiliation:
Computing Department, The University, Glasgow
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The densest lattice packings of spheres in Euclidean spaces En of n dimensions are known for n ≤ 8 (for full n — references see [6]). However, it i s not known for any n ≥ 3 whether there can be any non-lattice sphere packing with density exceeding that of the corresponding densest lattice packing.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 3 , August 1967 , pp. 387 - 393
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Barlow, W., Probable nature of the internal symmetry of crystals. Nature 29 (1888), 186-188.Google Scholar
2. M, H. S.. Coxeter, Regular Polytopes. New York, 1963.Google Scholar
3. M, H. S.. Coxeter, An upper bound for the number of equal spheres that can touch another of the same size. Proc. Symposia Pure Math. 7 (Providence, 1963), 53-71.Google Scholar
4. Leech, J., Some sphere packings in higher space. Can. J. Math. 16 (1966), 657-682.Google Scholar
5. Melmore, S., Densest packing of equal spheres. Nature 159 (1944), 817.Google Scholar
6. Rogers, C. A., Packing and Covering. Cambridge, 1964.Google Scholar