The phase diagram of a vertex model introduced by P. Di Francesco (Nucl. Phys. B 525, 507 1998) representing the configurations of a square lattice which can fold with different bending energies along the main axes and the diagonals has been studied by Cluster Variation Method. A very rich structure with partially and completely folded phases, different disordered phases and a flat phase is found. The crumpling transition between a disordered and the flat phase is first-order. The CVM results

more »

... e confimed by the analysis of the ground states and of the two limits where the model reduces to an Ising model.