The assembly of two-dimensional (2D) graphene into three-dimensional (3D) polyhedral structures while preserving the graphene's excellent inherent properties has been of great interest for the development of novel device applications. Here, fabrication of 3D, microscale, hollow polyhedrons (cubes) consisting of a few layers of 2D graphene or graphene oxide sheets via an origami-like self-folding process is described. This method involves the use of polymer frames and hinges, and aluminum oxide/chromium protection layers that reduce tensile, spatial, and surface tension stresses on the graphene-based membranes when the 2D nets are transformed into 3D cubes. The process offers control of the size and shape of the structures as well as parallel production. In addition, this approach allows the creation of surface modifications by metal patterning on each face of the 3D cubes. Raman spectroscopy studies show the method allows the preservation of the intrinsic properties of the graphene-based membranes, demonstrating the robustness of our method.