Deployable reflector system includes a support structure and a reflector surface secured to the support structure. The support structure transition from a compact stowed configuration to a larger deployed configuration to deploy the reflector surface. The reflector surface is comprised of a carbon nanotube (CNT) sheet. The sheet is intricately folded in accordance with a predetermined folding pattern to define a compact folded state. This predetermined folding pattern is configured to permit automatic extension of the CNT sheet from a compact folded state to a fully unfolded state. The unfolding operation occurs when a tension force is applied to at least a portion of the peripheral edge of the CNT sheet. In some scenarios, the support structure can comprise a circumferential hoop.