The packing of three-dimensional spheres on the surface of a four-dimensional hypersphere

Abstract

Results are given for computer searches for those configurations of N points on the surface of a four-dimensional hypersphere which have maximum values of the least angular distance between pairs of points. The generalised inverse was used to solve the equations giving the corrections to the hyperspherical coordinates in terms of the overlaps of the domains of neighbouring spheres. It is concluded that the use of this curved space offers an alternative to cyclic boundary values for simulations involving the packing of points in three dimensions.