Neil Sloane's web page has tables of packings. http://www.research.att.com/~njas/packings/index.html#I surface of sphere http://www.research.att.com/~njas/packings/dim3/ coordinates The first URL has (among many other things) his best results for the maximum minimum angle for K points on the surface of an ordinary sphere. The second URL points to numerical coordinates of the points. They seem to have been obtained numerically -- 20 digit floating point values, including some numbers that should probably be 0 but instead are small values like 10^-20. I didn't see any formulas, so these coordinates are good candidates for algebraic number recognition. More digits will be needed, but this shouldn't be a big problem. The tables don't mention proofs, although there are lots of references in other parts of the web page. One curiosity: There are two instances where K and K+1 points have the same angle, indicating that removing a point from the K+1 packing doesn't make room to expand the remaining K points. These are 5,6 and 11,12. I didn't see any more cases up to 130 points, the table limit. The higher dmensions had some longer runs, where K...K+5 all had the same minimal angle. Is there a general "packings" web page? I had no idea Neil's tables existed -- they're pretty well hidden under the code phrase "spherical codes". Rich rcs@cs.arizona.edu