The rhombic dodecahedron is an example of a Catalan solid: it is an isohedral (i.e., all faces are the same) yet a non-isogonal (at least two types of vertices) polyhedron, whose faces are not regular polygons. As noted above, RDs form over a relatively broad range of NP size ratios, but up to a certain limit. When the size ratio of the oppositely charged NPs was increased further, they coassembled into colloidal crystals having the shape of another Catalan solid, namely, the triakis tetrahedron (TT) (Fig. ). Well-defined TTs were obtained from more than 40 combinations of differently sized Au•MUAs and Au•TMAs, indicated by the orange triangles in Fig. . TTs found on the opposite sides of the diagonal line in the phase diagram were from one another. SAXS analysis showed (Fig. ) that TTs have a cubic symmetry with space group I4 ! 3d, i.e., they are isostructural with Th3P4. The Th3P4 unit cell is highly complex and contains 35 atoms/particles, resulting in the unit cell having a large size; e.g., for TTs coassembled from 5.63 nm Au•TMA and 3.73 nm Au•MUA, we found (by SAXS) a unit cell edge length of 20.53 nm. Similar to RDs, TTs were bound by a single type of crystal facet, with the Miller index (211). High-resolution SEM imaging revealed a complex pattern of NPs on the faces of TTs (Fig. , e and Supplementary Fig. ) -another manifestation of the complexity of the unit cell. Interestingly, whereas Th3P4-like packing in NP superlattices has been reported, their morphology (crystal habit) has remained unknown. Notably, the previously reported Th3P4-type superlattices were all coassembled from NPs decorated with hydrogen-bond donors and acceptors, which extends the analogy between highly specific noncovalent interactions and the short-range electrostatic interactions operating in our system.