It is possible to design DNA molecules that can form unusual structures and topologies. Stable DNA-branched junctions have been used to construct polyhedral catenated molecules with the connectivities of a cube and of a truncated octahedron. The truncated octahedron has been constructed following a solid-support-based methodology. Branched-DNA molecules are flexible, suggesting that triangular and deltahedral DNA objects should be favored as the components of two- and three-dimensional nucleic acid arrays. DNA polyhedra are complex catenanes. The engineering of single-stranded DNA knots and catenanes exploits the fact that a node can be equated with a half-turn of DNA.