  Connections between different M2-brane theories are established via the Higgs
mechanism, which can be most efficiently studied on brane tilings. This leads
to several M2-brane models, with brane tilings or Chern-Simons levels which
have not been considered so far. The moduli spaces of these models are
identified and examined in detail. The toric diagrams are constructed using
Kasteleyn matrices and the forward algorithm.
