  We introduce a 2D network built of $\mathcal{PT}$-symmetric dimers with
on-site cubic nonlinearity, the gain and loss elements of the dimers being
linked by parallel square-shaped lattices. The system may be realized as a set
of $\mathcal{PT}$-symmetric dual-core waveguides embedded into a photonic
crystal. The system supports $\mathcal{PT}$-symmetric and antisymmetric
fundamental solitons (FSs) and on-site-centered solitary vortices (OnVs).
Stability of these discrete solitons is the central topic of the consideration.
Their stability regions in the underlying parameter space are identified
through the computation of stability eigenvalues, and verified by direct
simulations. Symmetric FSs represent the system's ground state, being stable at
lowest values of the power, while anti-symmetric FSs and OnVs are stable at
higher powers. Symmetric OnVs, which are also stable at lower powers, are
remarkably robust modes: on the contrary to other PT-symmetric states, unstable
OnVs do not blow up, but spontaneously rebuild themselves into stable FSs.
