Hello all, apologies if this is obvious, but searching the internet did not provide me with a satisfactory answer. I am trying to design a sphere with 40+ points on it, which are all equidistant. To rephrase, what is the number series of points on spheres that are equidistant to each other? To begin with, the series is 2 (one point at the top, one at the bottom), then 4 (equidistant pyramid), 8 (cube), then ... what follows? What is the closest number to 40 (or whatever) where all are equidistant, and what are the angles? Illustrations welcome. No buckminster fullerenes please or whatever (since they don't fulfill this criterium), what I desire here is that all points on the sphere have an equal distance to the next. Any budding or professional mathematicians who could help me? I imagine Riemann or the likes have worked this out.... it'd be awesome to see the mathematics behind the deduction of this problem. Regardless, I am after the real thing. How can one draw this most efficiently on a physical sphere? Preferably on the inside of a hollow sphere (otherwise I'll have to stick needles through the points drawn on the outside of the sphere)? Any input is appreciated. Thanks.