A quotient space approach to model nanotori and determine their symmetry groups
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.
M. Loyola, M.L.A.N. De Las Penas, E. B. Santoso, and G. Estrada (2014/06). A quotient space approach to model nanotori and determine their symmetry groups. American Institute of Physics (AIP Proceedings), 1602, 620-626.