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 realizat...
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| Main Authors: | , , , |
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| Format: | text |
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Archīum Ateneo
2014
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| Subjects: | |
| Online Access: | https://archium.ateneo.edu/mathematics-faculty-pubs/41 https://aip.scitation.org/doi/10.1063/1.4882549 |
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| Institution: | Ateneo De Manila University |
| Summary: | 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. |
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