Giving professor P. P. Fedorov his due as the leading specialist in fluoride systems and using his theoretical investigations on the topology and geometry of phase diagrams of binary and ternary fluoride systems, as well as experimental results, obtained by colleagues under his leadership, the total geometric description of the systems, forming the LiF-NaF-CaF 2 -LaF 3 system, which has considerable promise for the development of fourth generation fuels for nuclear reactors, has been received. For this purpose, three-dimensional computer models of all four ternary systems have been constructed and the T-x-y-z diagram of this fluoride system has been predicted.