The formation of a "quasicrystal" on a closed surface has been considered for the Thomson problem on the arrangement with the lowest energy of N Coulomb charges on a sphere. The stable and metastable states of the system of charges with the charge number N = 2-100 and the symmetry groups of the corresponding configurations have been determined. The structure and possible structural transitions between the system states are described in terms of the introduced notion of a closed quasi-two-dimensional triangular lattice with topological defects. The graph of lattice defects is defined. A method for classifying the system in terms of the charge and the arrangement of topological defects in the lattice is suggested and extended to the case of an arbitrary lattice. The use of the model is considered on various physical examples, in particular, on a closed hexagonal lattice with disclinations in fullerenes.
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