  In this paper, we mainly consider the problem of spherical distribution of 5
points, that is, how to configure 5 points on a sphere such that the mutual
distance sum attains the maximum. It is conjectured that the sum of distances
is maximal if 5 points form a bipyramid configuration in which case two points
are positioned at two poles of the sphere and the other three are positioned
uniformly on the equator. We study this problem using interval methods and
related technics, and give a proof for the conjecture through computers in
finite time.
