How to divide a $3$ D-sphere into “equivalent” parts?

My goal is to put $n$ points on a sphere in $\mathbb{R}^3$ to divide it in $n$ parts, so that their disposition would be as “equivalent” as possible. I don’t exactly know what “equivalent” mathematically means, perhaps that the min distance between two points is maximal.

Anyway in $2$ dimensions it is simple to divide a circle in $n$ parts. In $3$ dimensions I can figure out some good re-partitions for particular values of $n$ but I lack a more general approach.

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A nontrivial problem, I think. You might find some links into the research literature on Ed Saff’s homepage.

You can try the physical method: treat each point as an electron constrained in a sphere, and randomly distribute these point particles in the sphere, then you can solve the equations of motion to reach a stable (minimum energy) state, where each particle maximally separated from its closest neighbours (electric repulsive forces). Here is how to apply this method on a sphere surface.