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 their 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 printed features as small as 0.3 millimeters in engineering acrylate polymers and printed soft structures with exceptionally smooth surfaces into a gelatin methacrylate hydrogel. Our process enables us to construct components that encase other preexisting solid objects, allowing for multimaterial fabrication. We developed models to describe speed and spatial resolution capabilities and demonstrated printing times of 30 to 120 seconds for diverse centimeter-scale objects.