14 rods arranged around a ball with rhombic dodecahedral symmetry

I originally thought that this was the optimal arrangement. Now, it depends what you mean by optimal, but in the sense on maximizing the minimum separation it's just sub-optimal.

Compare this model with the previous picture and see that I needed a rod that was 1mm longer (it's that rubber disk) to get the same minimum spacing of two Geomag bars between balls.