An algorithm for generating the sphere coordinates in a three-dimensional osculatory packing

David W. Boyd
1973 Mathematics of Computation  
This paper develops an efficient algorithm which generates the pentaspherical coordinates of the spheres in an osculatory packing of the three-dimensional unit sphere. The algorithm has a tree-like structure and is easily modified so that, given a prescribed bound, it counts the number of spheres in the packing whose curvatures are less than this bound. The algorithm has been used to produce heuristic estimates of the exponent M of the packing, and these indicate that M is approximately 2.42.
doi:10.1090/s0025-5718-1973-0338937-6 fatcat:dacw6tutyraoloh4bjjqletcie