In R^{d}, I have n > d+1 points. The mean distance between pairs of points is 1. How can I minimize the variance of the distances (equivalently, the mean squared distance)? I'm mainly interested in d ∈ {1,2,3} although I'd be curious if there were any patterns for larger values of d. As for values of n, I'm interested both in specific solutions for small values, and general patterns in larger values.

For $d=1$, it is minimized by arithmetic progression. 

