THE OPTIMAL PACKING OF CIRCLES ON A SPHERE

The closest packing of x circles on the surface of a sphere is calculated in the same way that the stereochemical arrangement of atoms around a central atom is determined. A number of improved packings have been discovered for x = 19 to 80. A notable feature is that the structures are generally of low symmetry. The packing density p, defined as the fraction of the spherical surface that is enclosed by the circles, increases only very slowly as the number of circles increases and the values remain substantially below that for a close packed plane, or for an octahedron or icosahedron.