Spherical distribution of 5 points with maximal distance sum (Q542388)

The paper shows that on a sphere, the sum of distances among 5 points is (uniquely) maximized, if two points are placed at antipodal ``poles'' and the remaining three are placed equidistantly on the ``equator''. The proof is computer assisted and is based on interval analysis. It is worth noting that this configuration is also known as a spherical 1-design [\textit{R. H. Hardin} and \textit{N. J. A. Sloane}, Spherical designs, \url{http://www2.research.att.com/~njas/sphdesigns/}].