Lower-dimensional photopolymerization based additive manufacturing techniques have several drawbacks that currently limit the applicability and scope of 3D printing, including: topological constraints, the requirement for numerous complex support structures that later need to be removed, long print times for complex geometries, relative motion between the liquid resin and printed part, as well as debilitating mechanical weakness and anisotropy resulting from the inherently layered structure of the parts. We propose and demonstrate a novel volumetric 3D printing technique based on one of the most ubiquitous computational imaging methods in the field: computed axial tomography. Computed axial lithography (CAL) is a vat photopolymerization technique that exposes the entire resin volume by projecting images from a multiplicity of angles. The technique is a physical implementation of the filtered back projection algorithm for tomographic reconstruction. We use constrained non-convex optimization in order to generate images that are projected into the resin in order to sculpt a 3-dimensional energy dose that cures the desired arbitrary geometry. This eliminates the requirement for supports and enables complex and nested structures that were previously challenging or impossible to print. Further, the process is layer-less and does not involve any relative motion between the resin and the printed part, which has positive implications for mechanically isotropic part strength. We demonstrate support-less printing of complex geometries containing 10^8-10^9 voxels in 2-4 minutes, orders of magnitude faster than comparable techniques.