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Different variants of the initial mutual orientation of C60 particles were considered, namely the particles were brought in contact in such a manner that either their pentagonal or hexagonal faces were the closest to each other, or a bond (chiefly that common for two hexagons) in one particle was located over a pentagonal or hexagonal face of the other, or some edges of the two faceted polygons were nearly parallel (though at a distance that prevented the formation of covalent bridges). According to the results of nonempirical modeling, there is a number of isomers of (C60)2 dimer, the differences in the distance between the centers of mass of the particles in different isomers being chiefly no larger than 0.1 A, though in certain cases the difference reaches nearly 0.2 A. The total electronic energies of the low-lying isomers also fall in a relatively narrow interval of 0.8 kcal/mol, some of the isomers having energy 1.2–3.5 kcal/mol higher than that of the global minimum. Dissociation energies of isomers are about 7.5–9 kcal/mol, and the energy barriers that separate the corresponding minima on the potential energy surface vary depending on the character of isomers they interrelate, most of them being no smaller than 5 kcal/mol, which means that the corresponding rotation can by no means be free, but rather noticeably hindered. Combined analysis of the relative stabilities of isomers and their geometric characteristics enabled us to suggest an explanation of the sequence of solid-state changes that take place in fullerite with temperature.