A large deployable reflector for an antenna suitable for being installed on board a satellite and provided with a support structure, a parabolic mirror carried by the support structure and a connection arm for mounting the support structure on the satellite; the support structure being a jointed reticulate structure that is able to assume a compact inoperative stowed configuration and an operative deployed configuration and is composed of ‘n’ elements articulated to form tetrahedrons having respective triangular bases, which are connected to each other at the axial ends of respective first sides and have respective external vertices, which are opposite to said respective first sides and, when the reflector is arranged in the deployed configuration, ideally lie on a cone tangent to the parabolic mirror.