Self-assembly provides an information-economical route to the fabrication of objects at virtually all scales. However, there is no known algorithm to program self-assembly in macro-scale, solid, complex 3D objects. Here such an algorithm is described, which is inspired by the molecular assembly of DNA, and based on bricks designed by tetrahedral meshing of arbitrary objects. Assembly rules are encoded by topographic cues imprinted on brick faces while attraction between bricks is provided by embedded magnets. The bricks can then be mixed in a container and agitated, leading to properly assembled objects at high yields and zero errors. The system and its assembly dynamics were characterized by video and audio analysis, enabling the precise time- and space-resolved characterization of its performance and accuracy. Improved designs inspired by our system could lead to successful implementation of self-assembly at the macro-scale, allowing rapid, on-demand fabrication of objects without the need for assembly lines.