Platonic particles are promising materials with nanoscale light-matter interactions in plasmonics and biosensing, due to their unique structure caused by vertices, edges and facets. The position and orientation of Platonic particles play a crucial role in determining the resultant assembled structures at a liquid/liquid interface. Therefore, it is desirable to develop a reliable theory that can predict the interfacial configuration of an isolated Platonic nanoparticle from nanoparticle-solvent interactions and solvent-solvent interactions. Here, we numerically explored all possible orientations of a Platonic nanoparticle, including three specific orientations: vertex up, edge up, and facet up orientations. We found that a specific orientation is more preferred than random orientations. We also demonstrated that the free energy change theory could quantitatively predict the position and orientation of an isolated Platonic nanoparticles at a liquid/liquid interface, where the surface wettability of the nanoparticle determined the most stable position and the preferred orientation. Molecular dynamics simulations were used to test our theory where the surface wettability of a Platonic solid was adjusted from extremely hydrophobic to extremely hydrophilic by changing the charge amount on the Ag surface. The molecular dynamics simulation results were in excellent agreement with our theoretical prediction for an isolated Ag Platonic nanoparticle at a hexane/water interface. Our proposed theory bridges molecular-level simulations and assembly structure of Platonic nanoparticles in experiments, in which the insights from nanoparticle wettability in solvents can be used to predict macroscopic superlattice structure in experiments. This work advances our ability to precisely predict the final structures of the Platonic nanoparticle assemblies at a liquid/liquid interface.