We introduce a metamaterial-based self-deployable system with a rotational periodicity. As a demonstration, we propose an autonomous solar panel array that is programmed to self-deploy in response to changes in the surrounding temperature. We achieve shape reconfiguration and structural stability by exploiting the physical properties in the constituting material and the architecture of the wedge-shaped unit cell. The unit cell consists of one arm of the elastic "flasher" origami and a pair of scissor mechanisms. First, kinematic analysis shows the difference between the theoretical behavior and behavior considering the physical dimensions. This is used to optimize the expansion ratio. Second, the deployment mechanics are enabled through the shape-memory effect inherent in the underlying polymer. A viscoelastic constitutive model is constructed to accurately predict the self-expanding behavior. Lastly, the collapsing and deployment dynamics are discussed. Bifurcation is observed during folding, leading to two different end states, a disk or a cone. By investigating the energy landscape of the system, an apparatus is introduced to enable the disk-shaped folding. A two-stage expansion is observed during deployment. The system first rotates and then expands radially. The resulting system is three-dimensionally (3D) printed, achieves an expansion ratio of 1000% in under 40 s, and shows excellent agreement with simulation prediction both in the collapsed and expanded configurations.