Multi-symmetric close packings of equal spheres on the spherical surface

Abstract

An analysis is presented for the Tammes problem: how must n points be distributed on the surface of a sphere in order that the minimum angular distance between any two of the points be a maximum? With the analogy of the capsid structure of small 'spherical' viruses, locally extremal arrangements are constructed in tetrahedral, octahedral and icosahedral symmetry. Thirty arrangements defined by four packing sequences are investigated. By the applied construction process, novel locally extremal configurations for n = 78, 96, 108, 144, 150, 192, 198, 270, 360, 372, 480, 492 and improvable configurations for n = 114, 282 are obtained. A table is given of the investigated arrangements; most of them are putative solutions of the Tammes problem.