  We discuss a class of 3-dimensional N=4 Chern-Simons (CS) quiver gauge models
obtained from M-theory compactifications on singular complex 4-dimensional
hyper-Kahler (HK) manifolds, which are realized explicitly as a cotangent
bundle over two-Fano toric varieties V^2. The corresponding CS gauge models are
encoded in quivers similar to toric diagrams of V^2. Using toric geometry, it
is shown that the constraints on CS levels can be related to toric equations
determining V^2.
