Self-assembly of rigid building blocks with explicit shape and symmetry is substantially influenced by the geometric factors and remains largely unexplored. We report the selective assembly behaviors of a class of precisely defined, nanosized giant tetrahedra constructed by placing different polyhedral oligomeric silsesquioxane (POSS) molecular nanoparticles at the vertices of a rigid tetrahedral framework. Designed symmetry breaking of these giant tetrahedra introduces precise positional interactions and results in diverse selectively assembled, highly ordered supramolecular lattices including a Frank-Kasper A15 phase, which resembles the essential structural features of certain metal alloys but at a larger length scale. These results demonstrate the power of persistent molecular geometry with balanced enthalpy and entropy in creating thermodynamically stable supramolecular lattices with properties distinct from those of other self-assembling soft materials.