I'm not too sure about the exact terminology since Wikipedia is throwing me all over the place. I'm looking for a formula to find out if for n faces a 'regular polyhedron' can exist. In case that's not the right term, I'll specify as to say a three dimensional shape comprised of vertices that are equidistant from each other and equiangular. I'm sort of looking for the extension of platonic solids.
I'm trying to answer a question that was posted on StackOverFlow here https://stackoverflow.com/questions/14805583/dispersing-n-points-uniformly-on-a-sphere/14807728#14807728
about arranging point on a sphere so that each one will be equidistant form each other. Essentially so that its a perfectly uniform distribution. Well I have an idea for an algorithm to do this, and given the research I've done I just need to find a formula so I can round n faces to the nearest platonic solid extension in order to beable to distribute the points perfectly evenly.
Is there such a formula? Or a formula to find for n faces a shape that would come close? (like a soccer ball).
On, a side note, any better ideas to tackle this?