Crystals differ from another states of the matter by Spaces Groups - discrete groups with finite independent regions. But such group have place not only in euclidean space but also in the other spaces with constant curvature: in hyperbolic and in spherical spaces which we can locally not distinguish from the euclidean space. Such model allow to consider quasicrystals and fullerenes as ideal crystals in spaces with non-zero constant curvature. Using this approach allows to solve many problems of fundamental physics (packing Galaxies and Supergalaxies in Universe, structure of the neutron stars, black holes) by methods of crystallography.
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