Branes at orbifolded conifold singularities and supersymmetric gauge fieldtheories

We consider D3 branes at orbifolded conifold singularities which are not qu otient singularities. We use toric geometry to study the moduli space of th e gauge theories on the D3 branes. We find that topologically distinct phas es are related by a flop transition. It is also shown how the conifold sing ularity is partially solved to an orbifold singularity in some phases if we give expectation values to some of the chiral fields.