We propose a novel imaging method for near-complete, surround, 3D reconstruction of geometrically complex objects, in a single scan. The key idea is to augment a time-of-flight (ToF) based 3D sensor with a multi-mirror system, called a light-trap. The shape of the trap is chosen so that light rays entering it bounce multiple times inside the trap, thereby visiting every position inside the trap multiple times from various directions. We show via simulations that this enables light rays to reach more than 99.9% of the surface of objects placed inside the trap, even those with strong occlusions, for example, lattice-shaped objects. The ToF sensor provides the path length for each light ray, which, along with the known shape of the trap, is used to reconstruct the complete paths of all the rays. This enables performing dense, surround 3D reconstructions of objects with highly complex 3D shapes, in a single scan. We have developed a proof-of-concept hardware prototype consisting of a pulsed ToF sensor, and a light trap built with planar mirrors. We demonstrate the effectiveness of the light trap based 3D reconstruction method on a variety of objects with a broad range of geometry and reflectance properties.