So far, we have described how our dialysis setup allowed us to observe formation of numerous large binary single crystals with an array of forms for a system prepared with a fixed ratio of particle size, surface charge, and number ratio. Within our setup, we are also able to observe more complex hierarchical assemblies, in particular crystals formed through heteroepitaxial growth of one structure templated by another (e.g. Fig. structures IV and V, Extended Data Movie 6). Focusing on samples of L 3 S 4 , we frequently observe formation of thin 'flag'-like protrusions from the sides of L 3 S 4 rods (Fig. ). SEM images of these flags show that they have a sharp 80 degree corner, and a surface arrangement of particles that does not belong to the structure we determined for L 3 S 4 . To inspect this behavior in more detail, we seeded MD simulations with the large L 3 S 4 crystal from Fig. in bulk, which allowed the crystal to grow in all directions. Surprisingly, after several rounds of continued addition of particles, we observed not one but two simultaneous instances of heteroepitaxial growth, one of which produced a structure commensurate with the flags observed in SEM, and one of which we identified as CsCl-like (Extended Data Movie 7). Using our full knowledge of particle positions in the MD simulation, we are able to demonstrate that the nucleation of these secondary crystals occurs due to commensurate arrangements of particles within the two different unit cells. This investigation shows that the (210) face of CsCl and (022) face of L 3 S 4 are able to interlock, and that the flag structure seen in simulation can be formed by extending a rhombic subset of particles from the L 3 S 4 unit cell (Extended Data Fig. ). The flag formed in MD simulations has a surface structure that closely matches the one observed in experiments. The compatibility of the CsCl unit cell with L 3 S 4 may also explain why they are often observed in contact within the experiments.