We provide a study of the assembly of single-component nanocrystals (NCs) (nanoparticles) capped with polystyrene by solvent evaporation. We investigate regimes from the colloidal R-G/R-c << 1, with R-c (core radius) and R-G (ligand gyration radius), to polymer limit R-G/R-c >> 1. We show that for increasing chain length, there is the emergence of a "cascade effect," that is, an abrupt drop in internal energy with the resulting potential of mean force dominated by configurations wherein the chains bend over the core in order to maximize contacts with the other NC, which accounts for the large magnitude of the many-body effects in the superlattice free energy. Interestingly, the orbifold topological model, that successfully characterizes the NC interaction in the colloidal limit, quantitatively describes the polymer limit as well. Our results establish that bcc is the equilibrium phase. Implications for recent and future experiments are discussed.