Maximum total distance between points on a sphere

What is the configuration (set of locations) of $n$ points on the surface of a sphere such that the sum of distances is maximum for $n=1,2,3,...$?

The sum of distances is measured by summing the lengths of every straight line (through the sphere) connecting every possible combination of $2$ points. All the points are on a single sphere of radius $R$.

Here's a visualization:

Acknowledgements: Based on this Physics S.E. question. Image from StackOverflow.

Solution 1:

As far as I know the answer to the general question is unknown. For the computer approach you can look at this article by Berman and Hanes. Here it is shown that the result for 5 points on the sphere can be found in finite time by computer. Also you can find some interesting references in the introduction part.

Hope, this will help