# 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.

• Mean distance between 2 points within a sphere math.stackexchange.com/questions/167932/… might help Sep 5, 2012 at 4:17
• I seem to recall hearing that the problem of maximizing the minimum is unsolved. But maximizing the sum is another matter. Sep 5, 2012 at 4:24
• A bunch of previous questions are closely related. None is an exact duplicate of this one, but you may find the answers and references there of interest.
– user856
Sep 5, 2012 at 4:56
• "Straight line"? Through the sphere or on the surface? Sep 5, 2012 at 6:37
• Straight line through the sphere. Sep 6, 2012 at 16:43