How to Find Conveniently Spaced Unit Vectors in N-Dimensions?

[Gerenuk]

What is the most convenient way to get a set of unit vectors in N dimensions, such that the angle between two neighboring vectors is about a fixed value?

To be more precise I'd like to find a small number of vectors so that all possible other unit vectors are at most at a certain angle from a vector of this set.

It doesn't have to be precise, which probably would work for platonic solids like cubes only. Some rough method is to take all points on a N-dimensional cube and normalize the vectors. A whacky idea would be to do the same with a cross-polytope, but I don't know how to parametrize that.
But maybe one can do better?

 

[Tinyboss]

Sounds like a sphere-packing problem, where you're packing (N-2)-spheres into an (N-1)-sphere. What I mean is, in 3 dimensions, your normalized vectors live on S^2, and their angular neighborhoods are 1-spheres (circles).

 

[Gerenuk]

Yes, it is. However a full sphere packing problem is highly non-trivial, but I would be satisfied with a more approximate solution. The requirement is to find a reasonable solution which covers all the "surface area".