The double cover of the icosahedral symmetry group and quark mass textures

We investigate the idea that the double cover of the rotational icosahedral symmetry group is the family symmetry group in the quark sector. The icosahedral (A5) group was previously proposed as a viable family symmetry group for the leptons. To incorporate the quarks, it is highly advantageous to extend the group to its double cover, as in the case of tetrahedral (A4) symmetry. We provide the basic group theoretical tools for flavor model-building based on the binary icosahedral group I′ and construct a model of the quark masses and mixings that yields many of the successful predictions of the well-known U(2) quark texture models.