A doubly curved reflector for compact storage in a folded state includes a plurality of gores, each gore having on either long side a gore side curve. At least one hinge is mechanically coupled between each adjacent gore, the at least one hinge including a fold roll hinge or a living hinge. In a stowed doubly curved reflector state each gore folds about the at least one hinge when folded closed such that a face surface of each gore folds against an adjacent face surface of another gore into a substantially cylindrical structure. In a deployed doubly curved reflector state, each hinge. A doubly curved reflector for compact storage in a folded state and a locked open state, a method of manufacture, and a method for designing a substantially wrinkle free doubly curved foldable reflector having gores of a composite material are also described.