Description: Permanently shadowed regions (PSRs) on the poles of the Moon receive no direct sunlight. Frozen ices may collect there, and this motivates future exploration using landed science assets. However, getting power to these future science assets remains a challenge. The proposed work will advance lightweight, highly compactible, low-cost-of-production modular solar reflectors to address this challenge. These solar reflectors could be positioned on high ground adjacent to the PSRs (e.g., crater rims, mountains) that remain sunlit, and concentrate and redirect sunlight towards a landed asset. For particular architectures, we predict 100 W to 1 kW (electric) power could be delivered from a sunlit reflector to an asset with a photovoltaic (PV) array 10 km away. Each parabolic reflector consists of a highly reflective front surface, supported by an ultrathin carbon fiber composite shell. A curved-crease origami fold pattern allows the composite shell to be wrapped compactly for stowage. The key innovation is the rational, mechanics-based algorithmic design of fold patterns on doubly curved surfaces that allows for compact and reversible stowage of paraboloidal shell structures without cuts or slits. This provides elastic stowage and recovery of as-built shape. We will (1) develop system-level numerical models using ray tracing to evaluate power delivery performance and tune the overall architecture, (2) develop origami design algorithms to address specific needs, e.g., folding off-axis paraboloids, and (3) fabricate sub-scale reflector prototypes using carbon composites to demonstrate stowage and shape recovery after stowage.