Phase formation in the NaF-KF-AlF3 system, in the vicinity of the K2NaAl3F12 composition, has been studied. The samples have been prepared by melting the starting components at 650 degrees C. A new phase has been revealed, which appeared to be a low-temperature form of the wellknown K2NaAl3F12 ternary fluoride obtained by the hydrothermal synthesis method. The high-temperature form melts at 598 degrees C and is stable in a narrow temperature region of about 15 deg below the melting point. Thermal analysis, high temperature X-ray diffraction, IR-spectroscopy, Xray fluorescence, and X-ray powder diffraction crystal structure analysis have been applied to study the composition, crystal structure, and thermal properties of the low-temperature phase. The crystal structure consists of trigonal hexagonal two-dimensional (2D) grids built from the [AlF6] octahedra connected via vertices. The 2D grids have a specific wave-like conformation with a wavelength of 11.88 angstrom and an amplitude of 0.46 angstrom. There is a shift of the adjacent grids relative to each other. Because of this shift, the space between the grids changes. The shift leads to the formation of pores adapted to potassium and sodium ions. The reasons for the wave-like structure of layers are discussed. It is shown that the two polymorphic forms differ in the order of cation occupations.