central part pc and angular sectors s i n the truncated angular sectors s i being arranged around the central part pc in a variant of the invention the layer can comprise a center c additionally the layer c n comprises three concentric areas a first central area zc corresponding to the active surface of the reflector a second peripheral area zp and a third intermediate area zi the third intermediate area zi forming a rim the intermediate area zi is of concave shape with a small radius of curvature typically 5 mm so as to limit the effects of parasitic reflections of the electromagnetic waves towards the source of the antenna this radius cannot be further reduced due to the poor ability of the carbon fabrics to follow curves of small radius without breaking the axis of orientation of the peripheral area zp forms an angle u03b3 with a vertical axis passing through the centers of the central parts pc of the layers forming a stiffener that is directly incorporated into the structure of the reflector allowing the stiffness targets set for high frequency telecommunication applications to be attained fig3 describes the arrangement and the orientation of the fibrous material m constituting the angular sectors s i n of a layer c n the geometrical stability of the reflector in hot or cold temperatures is obtained partly by the use of a single composite material m for all of the component elements of the reflector r preferably the reflector design proposed is compatible with.