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Genesis of spectra of elementary excitations of crystals comprising sublattices belonging to the cubic system is investigated. Using the methods of group theory, the Brillouin sublattice zones are transformed into the Brillouin crystal zones, and degeneration is established caused by the convolution of branches of the spectrum. The degeneration is removed with allowance for hybridization of sublattice states. The special features of the band spectra of some crystals belonging to the cubic system are discussed. Many complex crystal structures are formed by the Bravais interpenetrating translation-compatible sublattices belonging to identical or different systems. The simplest classical examples are crystals with NaCl-like structure comprising two face-centered cubic sublattices ( f c Γ ), CsCl-like structure comprising two primitive cubic sublattices ( c Γ ), diamondand sphalerite-like crystals comprizing two f c Γ sublattices, etc. Of greater interest are cases in which the complex crystal lattice comprises different Bravais sublattices. Examples are provided by fluorite and antifluorite crystals comprising f c Γ and c Γ sublattices; Pt 3 O 4 crystals comprising three body-centered ( v c Γ ) platinum sublattices and one c Γ oxygen sublattice; CrFe 4 Ni 3 (hypothetical) crystals comprising one v c Γ chromium sublattice, three v c Γ nickel sublattices, and one c Γ iron sublattice; As 3 Co crystals comprising twelve v c Γ arsenic sublattices and one c Γ cobalt sublattice, etc. We restrict ourselves to an examination of crystals with the cubic Bravais system. More examples of crystals comprising sublattices belonging to different systems can be given [1].It is clear that the spatial crystal symmetry group will correspond to the sublattice having the least symmetry. If any sublattices have higher translation, point, or simultaneously translation and point symmetry, this additional "latent" symmetry will be manifested through the physical and physicochemical properties of the complex crystal. Additional symmetry can also be approximate. This occurs when any sublattice can be transformed into a more symmetric sublattice by means of small displacements of atoms.Geometrical and crystallographic aspects of forming complex crystals from the Bravais sublattices were examined in [2]. We use this method for crystals belonging to the primitive cubic (PC) system. The translational compatibility between the elementary translation vectors a( L Γ ) (i = 1, 2, 3) of the crystal lattice L Γ and b( S Γ ) (j = 1, 2, 3) of the sublattice corresponding to the Bravais lattice S

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The data on the approximated high-symmetry Bravais sublattices in crystals with the In 4 Te 3 structure are reported. The compatibility matrices are given for the derived combinations of crystal lattice and sublattices. The compatible Brillouin zones of the crystal and the sublattices are constructed. The effect of a "hidden" symmetry inherent in the crystals with the In 4 Te 3 structure on the phonon spectra is described.