Assume a situation where there are n balls tied to a point individually using strings of equal lengths.
Each ball repels the other ball.
Now,
For n=2, the balls would form a line - 180˚,
n=3, the balls would form a triangle - 120˚,
n=4, the balls would form a tetrahedron - 108˚30'28", and so on.
n=6 - octahedron - 90˚
n=8 - cube - 54.74˚
My question is, what would the shape be for n=5 and n=7?
Is there a name for that shape? What would the angle formed be?
Here's a paper that answers that question for $n = 5$, I believe (at least if you assume that all the strings have the same length):
https://www.math.brown.edu/reschwar/Papers/electron.pdf
The shape is apparently called "the triangular bi-pyramid" and consists (after a suitable rotation) of the north and south poles, and three points lying on an equilateral triangle on the equator.
My guess is that there's no known-and-proved answer for $n = 7$, and given the difficulty of the $n = 5$ case (and Schwartz's remark about a "sense of diminishing returns"), I wouldn't guess that there's anyone seriously working on it, but I could easily be wrong.