How can n points be distributed on a unit sphere such that they maximize the minimum distance between any pair of points? This maximum distance is called the covering radius, and the configuration is called a spherical code (or spherical packing). In 1943, Fejes Tóth proved that for n points, there always exist two points whose distance d is d<=sqrt(4 - csc^2[(π n)/(6(n - 2))]), and that the limit is exact for n = 3, 4, 6, and 12. The problem of spherical packing is therefore sometimes known as the Fejes Tóth's problem. The general problem has not been solved.
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