Additive manufacturing promises enormous geometrical freedom and the potential to combine materials for complex functions. The speed, geometry, and surface quality limitations of additive processes are linked to the reliance on material layering. We demonstrated concurrent printing of all points within a three-dimensional object by illuminating a rotating volume of photosensitive material with a dynamically evolving light pattern. We print features as small as 0.3 mm in engineering acrylate polymers, as well as printing soft structures with exceptionally smooth surfaces into a gelatin methacrylate hydrogel. Our process enables us to construct components that encase other pre-existing solid objects, allowing for multi-material fabrication. We developed models to describe speed and spatial resolution capabilities. We also demonstrated printing times of 30–120 s for diverse centimeter-scale objects.