Compute Angle Between Multiple 3d Vectors

[Vexom]

Imagine a point with n vectors (all with equal magnitude) coming out from that point that equally cancel each other out in magnitude. How would you calculate the equal angle between n vectors?

For example: 2 vectors (equal magnitudes) coming from one point that cancel each others magnitude would have 180 degrees between the vectors, 6 vectors (equal magnitudes) would have 90 degrees between all vectors, etc.

Is there an equation for this type of problem?

 

[lewando]

I can see "equal angles" up to the 4 vector case. Beyond that, opposing 180 degree angles begin to creep in.

 

[mfb]

In general, in 3 or more dimensions you cannot have a full symmetry between all vectors. This is only possible if your vectors correspond to the vertices or faces of a Platonic solid. In 3 dimensions, that gives you 4, 6, 8, 12 and 20 as options. They have well-known formulas for all angles.
For all other numbers, you'll need an asymmetric distribution. The Archimedean solids keep some symmetry, but you'll still get different angles with them.