Controlling the spontaneous organization of nanoscale objects remains a fundamental challenge of materials design. Here we present the first characterization of self-assembled superlattices (SLs) comprised of tetrahedral nanocrystal (NCs). We observe self-assembly of CdSe nanotetrahedra into an open structure (estimated space-filling fraction φ ≈ 0.59) which has not been anticipated by many recent theoretical studies and simulations of tetrahedron packings. This finding highlights a gap in the understanding of the hierarchy of energy scales acting on colloidal NCs during self-assembly. We propose a strong dependence of ligand-ligand interaction potential on NC surface curvature. This effect favors spatial proximity of vertices in the dense colloidal crystal and may be considered an emergent "patchiness" acting through chemically identical ligand molecules.