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Abstract The idea of structural ensembles is introduced in the framework of the crystal-chemical model of atomic interactions (CCMAI). The atomic ensemble is treated as a minimal portion of atoms, which predetermines the crystal structure. Inorganic crystal structures such as graphite, white tin, PbO are considered. It is supposed that both atoms and localized electron pairs form these structures. On the basis of CCMAI the hypothetical structure of icosahedral quasicrystals is worked out. In accordance with this hypothesis the initial cluster (or simply cluster) of the quasicrystal has a double-shell structure and each shell has an icosahedral form; the thickness of a shell is equal to the diameter of one atom; the number of atoms in one shell is 10n2 + 2, where n is the number of the shell. The quasicrystal has two subsystems of atoms. One of them consists of the central atoms of clusters and the atoms included in the first shells of clusters. The 13-atom icosahedral bodies form a crystal lattice with space group Fd3. All icosahedra of this atomic subsystem have a perfect form and all of them are perfectly oriented with respective to each other. The first atomic subsystem is responsible for the diffraction of electrons and X-rays. The second atomic subsystem includes atoms of the second shells of clusters. This subsystem has no translational symmetry, but it is partially ordered.
