Variations on the supersymmetric Q6 model of flavor

We observe that a recently proposed supersymmetric model with Q(6) flavor symmetry admits a new CP violating ground state. A new sum rule for the quark mixing parameters emerges, which is found to be consistent with data. Simple extensions of the model to the neutrino sector suggest an inverted hierarchical mass spectrum with nearly maximal CP violation (vertical bar delta(MNS)vertical bar similar or equal to pi/2). Besides reducing the number of parameters in the fermion sector, these models also provide solutions to the supersymmetric flavor problem and the supersymmetry CP problem. We construct a renormalizable scalar potential that leads to the spontaneous breaking of CP symmetry and the family symmetry.