An organic subcomponent was designed with 2-formyl-8-aminoquinoline and triazole-pyridine ends. The relative orientations and geometries of these two ends enabled this subcomponent to assemble together with ZnII and LaIII cations to generate a heterobimetallic tetrahedral capsule. The LaIII cations each template three imine bonds that hold together a 3-fold-symmetric metallo-ligand, defining the center of each tetrahedron face. The ZnII cations occupy the other ends of these C3 axes, defining the vertices of the tetrahedron. This is the first example where subcomponent self-assembly brought into being the faces of a polyhedron, as opposed to the vertices. Host-guest studies show positively cooperative binding toward ReO4-, the encapsulation of which also resulted in the quenching of capsule fluorescence.