I have a practical application which relies upon the generation of evenly distributed points on a sphere. When I first considered this problem, I learned that some number of polyhedrons (Platonic polyhedrons) had each vertex lying evenly spaced from the others within the surface of a sphere. I also found that there was a finite number of these shapes and I needed far more points on my sphere (10's of thousands) Next I learned that there was an accepted methodology to distribute points in a roughly even fashion through a numeric technique whereby each point is treated as having a repulsion to his neighbors and the system of points is adjusted until the net repulsion reaches a minimum. This latter technique seems valid enough given that one knows the critical number of points to introduce to ensure that the distribution is even (i.e. the distances between points is consistent over all cases.) However, how does one go about finding N, such that all points may be evenly spaced?