Abstract
After recalling some in principle known but seldom mentioned facts about variety of concepts/notions of the nuclear shapes, we briefly summarize the results of the recent microscopic calculations predicting the existence of the large-elongation (hyper-deformed) nuclear configurations — as well as another series of calculations predicting that some nuclei should exhibit high-rank symmetries: the tetrahedral and the octahedral ones. The latter are associated with 48- and 96- symmetry elements, respectively, of the nuclear mean-field Hamiltonian. Obviously the physics motivations behind the hyper-deformation and the high-rank symmetry studies are not the observations of the new geometrical forms as such; in our opinion these motivations are much deeper and are given in the text.
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