Natural proteins can be versatile building blocks for multimeric, self-assembling structures. Yet, creating protein-based assemblies with specific geometries and chemical properties remains challenging. Highly porous materials represent particularly interesting targets for designed assembly. Here, we utilize a strategy of fusing two natural protein oligomers using a continuous alpha-helical linker to design a novel protein that self assembles into a 750 kDa, 225 Å diameter, cube-shaped cage with large openings into a 130 Å diameter inner cavity. A crystal structure of the cage showed atomic-level agreement with the designed model, while electron microscopy, native mass spectrometry and small angle X-ray scattering revealed alternative assembly forms in solution. These studies show that accurate design of large porous assemblies with specific shapes is feasible, while further specificity improvements will probably require limiting flexibility to select against alternative forms. These results provide a foundation for the design of advanced materials with applications in bionanotechnology, nanomedicine and material sciences.