A deployable assembly for antennae includes a structure having a reflective surface and n pairs of segments, each pair of segments corresponding to one side of a deployed polygonal shape. N hinge joints are between the two segments of a side. N hinged angular links are between every two adjacent sides. The structure is changeable from a stowed substantially cylindrical shape into a deployed substantially planar polygonal shape with n sides. A deployable boom is between two segments. The boom lays stowed between the two segments before deployment and ends in a feeder electromagnetically feeding the antenna and includes a clamping element for keeping the structure closed when stowed. The feeder acts as structural support element when stowed and electromagnetic feeder for the antenna when deployed. A cable network shapes the reflective surface, with corresponding cables held by tensor elements protruding from the back of the segments.