  The $\mathcal{N}=1$ superconformal field theories that arise in AdS-CFT from
placing a stack of D3-branes at the singularity of a toric Calabi-Yau threefold
can be described succinctly by dimer models. We present an efficient algorithm
for constructing a dimer model from the geometry of the Calabi-Yau. Since not
all dimers produce consistent field theories, we perform several consistency
checks on the field theories produced by our algorithm: they have the correct
number of gauge groups, their cubic anomalies agree with the Chern-Simons
coefficients in the AdS dual, and all gauge invariant chiral operators satisfy
the unitarity bound. We also give bounds on the ratio of the central charge of
the theory to the area of the toric diagram. To prove these results, we
introduce the concept of a properly ordered dimer.
