  Given $N$ unit points charges on the surface of a unit conducting sphere,
what configuration of charges minimizes the Coulombic energy $\sum_{i>j=1}^N
1/r_{ij}$? 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{$N = 10(h^2+hk+k^2)+ 2$} recent theoretical work based on
elasticity theory, and subsequent numerical work has shown, that for $N \sim
>500$--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.
