We use double emulstions drops to experimentally realize a system to investigate the defect structure in spherical shells of nematic liquid crystal. The ground state of this system is predicted to exhibit a tetrahedral arrangement of four surface defects in a structure reminiscent of a baseball. Instead, we find a much richer set of coexisting defect structures dictated by the inevitable thikness of even the thinnest shells, and the resultant variation of the shell thickness around the sphere. These structures are characterized by a varying number of disclination lines and pairs of surface point defects, one each on the inner and outer surfaces of the nematic shell. The inevitable thikness variation of the shell determines the separation of the defects, and the ultimate configuration. In the limit of thick shells, the structure merges with that of a bulk nematic liquid crystal drop.