Progress in nanocrystal synthesis and self-assembly enables the formation of highly ordered superlattices. Recent studies focused on spherical particles with tunable attraction and polyhedral particles with anisotropic shape, and excluded volume repulsion, but the effects of shape on particle interaction are only starting to be exploited. Here we present a joint experimental-computational multiscale investigation of a class of highly faceted planar lanthanide fluoride nanocrystals (nanoplates, nanoplatelets). The nanoplates self-assemble into long-range ordered tilings at the liquid-air interface formed by a hexane wetting layer. Using Monte Carlo simulation, we demonstrate that their assembly can be understood from maximization of packing density only in a first approximation. Explaining the full phase behaviour requires an understanding of nanoplate-edge interactions, which originate from the atomic structure, as confirmed by density functional theory calculations. Despite the apparent simplicity in particle geometry, the combination of shape-induced entropic and edge-specific energetic effects directs the formation and stabilization of unconventional long-range ordered assemblies not attainable otherwise.