The self-assembly in two dimensions of spherical magnets is addressed theoretically. Minimal energy structures are obtained by optimization procedures as well as Monte Carlo computer simulations. For a small number of constitutive magnets N <= 17, ring-like structures are found to be stable. In the regime of larger N >= 18, the magnets form touching concentric rings that are reminiscent of the onion-like structures. At sufficiently large N, the (edgy) shells are hexagonal where dipole moments tend to align to the edge direction. All these relevant predicted shapes are experimentally reproduced by manipulating millimetric magnets.