Designed protein cages and related materials provide unique opportunities for applications in biotechnology and medicine, while methods for their creation remain challenging and unpredictable. In the present study, we apply new computational approaches to design a suite of new tetrahedrally symmetric, self-assembling protein cages. For the generation of docked poses, we emphasize a protein fragment-based approach, while forde novointerface design, a comparison of computational protocols highlights the power and increased experimental success achieved using the machine learning program ProteinMPNN. In relating information from docking and design, we observe that agreement between fragment-based sequence preferences and ProteinMPNN sequence inference correlates with experimental success. Additional insights for designing polar interactions are highlighted by experimentally testing larger and more polar interfaces. In all, using X-ray crystallography and cryo-EM, we report five structures for seven protein cages, with atomic resolution in the best case reaching 2.0 Å. We also report structures of two incompletely assembled protein cages, providing unique insights into one type of assembly failure. The new set of designed cages and their structures add substantially to the body of available protein nanoparticles, and to methodologies for their creation.