Trends in the aerospace industry are driving payloads to be smaller and less expensive while yet delivering comparatively large antennas. Deployable reflectarray antennas (RA) are the object of much research to meet these demands because they operate in a flat plane and are easier to stow than parabolic reflector antennas. Because they operate in flat plane, deployable RAs are well-suited to thickness-accommodated origami-inspired mechanisms. This work addresses pattern selection and modification, thickness accommodation, actuation, and stabilization of origami-inspired mechanisms intended to be used as RAs. First, a modified Miura-ori pattern termed volume-efficient Miura-ori (VEMO) is introduced, selected for its ability to fold into a rectangular profile and easily adapt to different aspect ratios. An optimization algorithm seeking to maximize surface area subject to the constraints of an allotted cuboid volume and a deployed aspect ratio of one is introduced. Second, a set of five genres of magnetic hinge concepts are presented to serve as actuation and stabilization mechanisms. Particular focus is given to hinges composed of a single pair of cuboid magnets. Two such self-actuating and self-stabilizing hinges are presented and characterized. Third, the behavior of such hinges is explored. We demonstrate the existence of bistability in select configurations and characterize their equilibrium positions. Potential energy, axial force data, angular position of unstable equilibria, and transition values from bistability to monostability are also modeled. Results are verified through experimental torque and stability data for selected configurations. Fourth, the union of magnetic hinges and surrogate folds is explored. The lamina-emergent torsion (LET) array is selected with justification. Novel stress considerations are presented for LET arrays with thin torsion elements and various magnetic hinges demonstrate viability for actuation and stabilization. Finally, current methods for accommodating thickness in flashers are presented and issues associated with those methods are discussed. Two methods for accommodating thickness in flashers such that panels are constant thickness are proposed.