On the topology of real Lagrangians in toric symplectic manifolds

We explore the topology of real Lagrangian submanifolds in a toric symplectic manifold which come from involutive symmetries on its moment polytope. establish analog Delzant construction for those Lagrangians, says that their diffeomorphism type is determined by combinatorial data. As an application, we realize all possible types connected Lagrangians del Pezzo surfaces.