Assume there are $n$ points $\{x_i\}_{i=1}^n$ on the sphere of a $d$-dimensional unit ball. Let $\theta_{ij}$ denote the angle between $x_i$ and $x_j$. How to choose those $n$ points to maximize $\min_{i,j} \theta_{ij}$?
When $d = 2$, I think we can simply consider the regular polygon with $n$ vertices and $\max \min_{i,j}\theta_{ij} = \frac{2\pi}{n}$. But for $d \geq 3$, it is hard to imagine.