I want to put $n$ points on a sphere such that they are as far apart as possible. I know how to do this for certain particular values of $n$. For example, $n=2$ would just be 2 points on opposite sides of the sphere. $n=4$ would be the vertices of a tetrahedron. But what about $n=11$, etc.? And does the corresponding convex hull of that shape have any significance?
Feel free to describe "points as far apart as possible" in any reasonable mathematical way you want. I'd especially like some answer for $n=7$., or any other irregular number not related to a platonic solid.
For huge bonus points, also give answers for higher dimensions $d>3$.
