# Distributing $N$ points on the sphere so that the sum of their mutual distances is maximized?

Generaliation the result in our paper for sum and similarly my previous question for product. I have a question:

My question: Distributing $N$ points on the sphere so that the sum of their mutual distances is maximized?

• why not just put $N/2$ points on the North pole and $N/2$ points on the South pole? – Carlo Beenakker Jul 11 '18 at 9:47
• Nice question !!!! – zeraoulia rafik Jul 11 '18 at 12:58
• @Carlo Beenakker For n=4 the tetrahedron is better. – LeechLattice Jul 11 '18 at 13:18