A dictionary is a data structure that supports insertion, deletion, and retrieval operations. To maintain a database, a dictionary machine accepts an arbitrary sequence of instructions at a constant rate. We designed two new VLSI dictionary machines on general-purpose networks that emulate the binary cube. One machine runs on a shuffle-exchange network. It includes a novel architecture to implement pipelining of dictionary instructions. The other machine runs on a cube-connected-cycles network. The design of this machine relies on the existence of a Hamiltonian path, which we establish explicitly for every cube-connected-cycle network.