Molecular self-assembly offers a means of spontaneously forming complex and well-defined structures from simple components. The specific bonding between DNA base pairs has been used in this way to create DNA-based nanostructures and to direct the assembly of material on the subnanometre to micrometre scale. In principle, large-scale clonal production of suitable DNA sequences and the directed evolution of sequence lineages towards optimized behaviour can be realized through exponential DNA amplification by polymerases. But known examples of three-dimensional geometric DNA objects are not amenable to cloning because they contain topologies that prevent copying by polymerases. Here we report the design and synthesis of a 1,669-nucleotide, single-stranded DNA molecule that is readily amplified by polymerases and that, in the presence of five 40-mer synthetic oligodeoxynucleotides, folds into an octahedron structure by a simple denaturation-renaturation procedure. We use cryo-electron microscopy to show that the DNA strands fold successfully, with 12 struts or edges joined at six four-way junctions to form hollow octahedra approximately 22 nanometres in diameter. Because the base-pair sequence of individual struts is not repeated in a given octahedron, each strut is uniquely addressable by the appropriate sequence-specific DNA binder.