Hermite Constants
N.B. A detailed on-line essay by S. Finchwas the starting point for this entry.
The Hermite constant is defined for Dimension 
as the value
(Le Lionnais 1983). In other words, they are given by
where
is the maximum lattice Packing Density for Hypersphere Packing and 
is theContent of the -Hypersphere. The first few values of 
are 1, 4/3, 2, 4, 8, 64/3, 64, 256,.... Values for larger are not known.For sufficiently large ,
See also Hypersphere Packing, Kissing Number, Sphere Packing
References
Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/hermit/hermit.html
Conway, J. H. and Sloane, N. J. A. Sphere Packings, Lattices, and Groups, 2nd ed. New York: Springer-Verlag, p. 20, 1993.
Le Lionnais, F. Les nombres remarquables. Paris: Hermann, p. 38, 1983.
- Icosian Game
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