Unfold Form is an innovative, lightweight, and reusable formwork system that enables the rapid construction of sustainable vaulted floors. Using curved-crease unfolding, bending-active plywood plates with textile hinges deploy into a self-supporting, corrugated formwork, facilitating the in-situ casting of material-efficient shells in unreinforced concrete. Inspired by Gothic vaulting, the system reduces concrete use by 60% and reinforcement steel by 90% compared to conventional slabs by relying on structural geometry rather than excess material. The corrugations enhance stiffness while creating an expressive architectural aesthetic, a direct outcome of its fabrication and structural logic. Prefabricated with low-cost materials, flat-packed for efficient transport, and assembled in just 30 minutes, Unfold Form is scalable across high-tech and low-tech contexts. Successfully demonstrated in Zurich and Cape Town, it offers a pioneering approach to low-carbon construction, proving that structural efficiency and sustainability can also generate captivating design innovation.