  We provide a general set of rules for extracting the data defining a quiver
gauge theory from a given toric Calabi-Yau singularity. Our method combines
information from the geometry and topology of Sasaki-Einstein manifolds,
AdS/CFT, dimers, and brane tilings. We explain how the field content, quantum
numbers, and superpotential of a superconformal gauge theory on D3-branes
probing a toric Calabi-Yau singularity can be deduced. The infinite family of
toric singularities with known horizon Sasaki-Einstein manifolds L^{a,b,c} is
used to illustrate these ideas. We construct the corresponding quiver gauge
theories, which may be fully specified by giving a tiling of the plane by
hexagons with certain gluing rules. As checks of this construction, we perform
a-maximisation as well as Z-minimisation to compute the exact R-charges of an
arbitrary such quiver. We also examine a number of examples in detail,
including the infinite subfamily L^{a,b,a}, whose smallest member is the
Suspended Pinch Point.
