Given N unit points charges on the surface of a unit conducting sphere,
what configuration of charges minimizes the Coulombic energy ∑i>j=1N1/rij? Due to an exponential rise in good local minima, finding global
minima for this problem, or even approaches to do so has proven extremely
difficult. For \hbox{N=10(h2+hk+k2)+2} recent theoretical work based on
elasticity theory, and subsequent numerical work has shown, that for N∼>500--1000 adding dislocation defects to a symmetric icosadeltahedral lattice
lowers the energy. Here we show that in fact this approach holds for all N,
and we give a complete or near complete catalogue of defect free global minima.Comment: Revisions in Tables and Reference