The ESCRT-III-like protein Vipp1 couples filament polymerization with membrane remodeling. It assembles planar sheets as well as 3D rings and helical polymers, all implicated in mitigating plastid-associated membrane stress. The architecture of Vipp1 planar sheets and helical polymers remains unknown, as do the geometric changes required to transition between polymeric forms. Here we show how cyanobacterial Vipp1 assembles into morphologically-related sheets and spirals on membranes in vitro. The spirals converge to form a central ring similar to those described in membrane budding. Cryo-EM structures of helical filaments reveal a close geometric relationship between Vipp1 helical and planar lattices. Moreover, the helical structures reveal how filaments twist—a process required for Vipp1, and likely other ESCRT-III filaments, to transition between planar and 3D architectures. Overall, our results provide a molecular model for Vipp1 ring biogenesis and a mechanism for Vipp1 membrane stabilization and repair, with implications for other ESCRT-III systems.