As colloidal self-assembly increasingly approaches the complexity of natural systems, an ongoing challenge is to generate non-centrosymmetric structures. For example, patchy, Janus or living crystallization particles have significantly advanced the area of polymer assembly. It has remained difficult, however, to devise polymer particles that associate in a directional manner, with controlled valency and recognition motifs. Here, we present a method to transfer DNA patterns from a DNA cage to a polymeric nanoparticle encapsulated inside the cage in three dimensions. The resulting DNA-imprinted particles (DIPs), which are 'moulded' on the inside of the DNA cage, consist of a monodisperse crosslinked polymer core with a predetermined pattern of different DNA strands covalently 'printed' on their exterior, and further assemble with programmability and directionality. The number, orientation and sequence of DNA strands grafted onto the polymeric core can be controlled during the process, and the strands are addressable independently of each other.