Wireframe DNA origami offers the ability to program nearly arbitrary 2D and 3D nanoscale geometries, with six-helix bundle (6HB) edge designs providing both geometric versatility and fidelity with respect to the target origami shape. Because individual DNA origami objects are limited in size by the length of the DNA scaffold, here, we introduce a hierarchical self-assembly strategy to overcome this limitation by programming supramolecular assemblies and periodic arrays using wireframe DNA origami objects as building blocks. Parallel half-crossovers are used together with lateral cohesive interactions between staples and the scaffold to introduce symmetry into supramolecular assemblies constructed from single DNA origami units that cannot be self-assembled directly using base-stacking or conventional antiparallel crossover designs. This hierarchical design approach can be applied readily to 2D wireframe DNA origami designed using the top-down sequence design strategy METIS without any prerequisites on scaffold and staple routing. We demonstrate the utility of our strategy by fabricating dimers and self-limiting hexameric superstructures using both triangular and hexagonal wireframe origami building blocks. We generalize our self-assembly approach to fabricate close-packed and non-close-packed periodic 2D arrays. Visualization using atomic force microscopy and transmission electron microscopy demonstrates that superstructures exhibit similar structural integrity to that of the individual origami building blocks designed using METIS. Our results offer a general platform for the design and fabrication of 2D materials for a variety of applications.