The phase LaF3 has a composition obeying Lewis's rule of octet completion. The ionic radii r(La3+) = 1.22 Å, r(F1−) = 1.33 Å suggest a coordination near LaF8. The crystal structure will therefore be homeotypic to CaF2. If aH is the threefold primitive hexagonal cell of CaF2 then aLaF3 ≈ aH(√3;1) in abbreviated matrix notation. This commensurability allows the earlier found binding of CaF2 to be inserted into aLaF3. Since there are fewer cations in LaF3 than in CaF2 this binding needs several adjustments. An adjustment in the hexagonal basal plane causes smaller displacements of the atoms in LaF3 than those in Na3As. An adjustment in the a3 direction causes compression of the cell along a3 and a change in the stacking sequence of the fluorine layers parallel to a1, a2, compared with CaF2. The energetic interpretation of LaF3 is compatible with stability observations in the mixture CaF2(YF3)M.