  We study a new duality which pairs 4d N=1 supersymmetric quiver gauge
theories. They are represented by brane tilings and are worldvolume theories of
D3 branes at Calabi-Yau 3-fold singularities. The new duality identifies
theories which have the same combined mesonic and baryonic moduli space,
otherwise called the master space. We obtain the associated Hilbert series
which encodes both the generators and defining relations of the moduli space.
We illustrate our findings with a set of brane tilings that have reflexive
toric diagrams.
