Self-assembly of isotropically interacting particles into desired crystal structures could allow for creating designed functional materials via simple synthetic means. However, the ability to use isotropic particles to assemble different crystal types remains challenging, especially for generating low-coordinated crystal structures. Here, we demonstrate that isotropic pairwise interparticle interactions can be rationally tuned through the design of DNA shells in a range that allows transition from common, high-coordinated FCC-CuAu and BCC-CsCl lattices, to more exotic symmetries for spherical particles such as the SC-NaCl lattice and to low-coordinated crystal structures (i.e., cubic diamond, open honeycomb). The combination of computational and experimental approaches reveals such a design strategy using DNA-functionalized nanoparticles and successfully demonstrates the realization of BCC-CsCl, SC-NaCl, and a weakly ordered cubic diamond phase. The study reveals the phase behavior of isotropic nanoparticles for DNA–shell tunable interaction, which, due to the ease of synthesis is promising for the practical realization of non-close-packed lattices.