DNA self-assembly has produced diverse synthetic three-dimensional polyhedra. These structures typically have a molecular weight no greater than 5 megadaltons. We report a simple, general strategy for one-step self-assembly of wireframe DNA polyhedra that are more massive than most previous structures. A stiff three-arm-junction DNA origami tile motif with precisely controlled angles and arm lengths was used for hierarchical assembly of polyhedra. We experimentally constructed a tetrahedron (20 megadaltons), a triangular prism (30 megadaltons), a cube (40 megadaltons), a pentagonal prism (50 megadaltons), and a hexagonal prism (60 megadaltons) with edge widths of 100 nanometers. The structures were visualized by means of transmission electron microscopy and three-dimensional DNA-PAINT super-resolution fluorescent microscopy of single molecules in solution.