A quotient space approach to model nanotori and determine their symmetry groups

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Conference Proceeding

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This paper discusses a geometric model of a nanotorus based on the concept of quotient spaces. The derivation of the symmetry group of the embedded toroidal quotient space in the 4-dimensional flat torus is accomplished using fundamental results from algebra and the theory of manifolds. The realization of these 4-dimensional symmetries as either axial point group symmetries or as non-rigid motions of 3-dimensional round torus will be explored. As a particular example, we discuss the derivation of the symmetry groups of carbon nanotori.