We report a size-dependent change in the morphology of superlattices self-assembled from monodisperse colloidal PbS nanocrystals. Superlattices of large (>7 nm) PbS nanocrystals showed a strong tendency to form multiply twinned face-centered cubic superlattices with decahedral and icosahedral symmetry, exhibiting crystallographically forbidden five-fold symmetry elements. On the other hand, superlattices of small (<4 nm) PbS nanocrystals exhibited no twinning. To explain such a dramatic difference in the twinning probability, we showed that twinning energy in a nanocrystal superlattice is strongly size-dependent. In addition, the interparticle potentials acting during the self-assembly process are "softer" in the case of larger PbS nanocrystals, thus favoring the formation of multiply twinned superlattices. Our work introduces a new class of materials exhibiting multiple twinning, while offering flexibility in designing interparticle potentials.