  We construct several examples of (2+1) dimensional N=2 supersymmetric
Chern-Simons theories, whose moduli space is given by non-compact toric
Calabi-Yau four-folds, which are not derivable from any (3+1) dimensional CFT.
One such example is the gauge theory associated with the cone over Q^{111}. For
several examples, we explicitly confirm the matter content, superpotential
interactions and RG flows suggested by crystal models. Our results provide
additional support to the idea that crystal models are relevant for describing
the structure of these CFTs.
