  We introduce four basic two-dimensional (2D) plaquette configurations with
onsite cubic nonlinearities, which may be used as building blocks for 2D PT
-symmetric lattices. For each configuration, we develop a dynamical model and
examine its PT symmetry. The corresponding nonlinear modes are analyzed
starting from the Hamiltonian limit, with zero value of the gain-loss
coefficient. Once the relevant waveforms have been identified (chiefly, in an
analytical form), their stability is examined by means of linearization in the
vicinity of stationary points. This reveals diverse and, occasionally, fairly
complex bifurcations. The evolution of unstable modes is explored by means of
direct simulations. In particular, stable localized modes are found in these
systems, although the majority of identified solutions is unstable.
