Molecular self-assembly offers a 'bottom-up' route to fabrication with subnanometre precision of complex structures from simple components. DNA is an attractive building block for self-assembly in general due to the specific bonding between base pairs and for templated self-assembly in particular due to the enzymatic capability for faithful reproduction of long sequences. Templated self-assembly of DNA into custom two-dimensional shapes on the megadalton scale has been demonstrated previously with a multiple-kilobase ?scaffold strand? that is folded into a flat array of antiparallel helices by interactions with hundreds of oligonucleotide 'staple strands'. Here we extend this DNA-based method to nanoconstruction of custom three-dimensional shapes by staple-directed folding of a scaffold into layers of antiparallel helices constrained to a honeycomb lattice. Scaffold and staples assemble together in a single step after mixing to produce shapes that have precise proportions ranging from 10?100 nm per dimension and profiles resembling structures such as a square nut, a slotted cross, and a railed bridge. Individual objects can be directed to polymerize into higher-order structures such as linear tracks displaying a feature with 36 nm periodicity or wireframe icosahedra with a diameter of 100 nm.