Icosahedral symmetry breaking: C(60) to C(84), C(108) and to related nanotubes.

@article{Bodner2015IcosahedralSB,
  title={Icosahedral symmetry breaking: C(60) to C(84), C(108) and to related nanotubes.},
  author={M. Bodner and E. Bourret and J. Patera and M. Szajewska},
  journal={Acta crystallographica. Section A, Foundations and advances},
  year={2015},
  volume={71 Pt 3},
  pages={
          297-300
        }
}
This paper completes the series of three independent articles [Bodner et al. (2013). Acta Cryst. A69, 583-591, (2014), PLOS ONE, 10.1371/journal.pone.0084079] describing the breaking of icosahedral symmetry to subgroups generated by reflections in three-dimensional Euclidean space {\bb R}^3 as a mechanism of generating higher fullerenes from C60. The icosahedral symmetry of C60 can be seen as the junction of 17 orbits of a symmetric subgroup of order 4 of the icosahedral group of order 120… Expand
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References

SHOWING 1-10 OF 11 REFERENCES
C70, C80, C90 and carbon nanotubes by breaking of the icosahedral symmetry of C60.
TLDR
The icosahedral symmetry group H3 of order 120 and its dihedral subgroup H2 of order 10 are used for exact geometric construction of polytopes that are known to exist in nature and there is an uncountable number of different twisted fullerenes, all with precise icosahed symmetry. Expand
Breaking of Icosahedral Symmetry: C 60 to C 70
TLDR
This symmetry breaking process can be readily applied, and could account for and describe other larger cage cluster fullerene molecules, as well as more complex higher structures such as nanotubes. Expand
Theoretical Study on Molecular Electrostatic Potential of C78
Abstract Density functional theory (DFT) was applied at the B3LYP/6-31G * level to investigate the relative stability of the five fullerene isomers as well as the anions of C 78 . Full geometryExpand
Faces of Platonic solids in all dimensions.
  • M. Szajewska
  • Mathematics, Medicine
  • Acta crystallographica. Section A, Foundations and advances
  • 2014
TLDR
This paper considers Platonic solids/polytopes in the real Euclidean space R(n) of dimension 3 ≤ n < ∞ and recursively decorating the appropriate Coxeter-Dynkin diagram provides the essential information about faces of a specific dimension. Expand
Comparison studies of fullerenes C72, C74, C76 and C78 by tight-binding Monte Carlo and quantum chemical methods
Abstract From C 72 to C 78 , the top 20 low-energy isomers screened out from all isomers of each fullerene are optimized and computed by tight-binding Monte Carlo (TBMC), semi-empirical PM3, and abExpand
Magic numbers and stable structures for fullerenes, fullerides and fullerenium ions
MACROSCOPIC amounts of the two fullerenes C60 and C70 have been available for a year1, and have already had an enormous impact on research in chemistry and physics. Experimentalists are now turningExpand
Capping C72 through C6: studying the relative stability of the five C78 fullerene isomers
Abstract The penultimate step of the circumscribe algorithm proposed on Graph Theoretical footings is analyzed by an involved quantum–chemical AM1 method. The five C 72 isomers generated through theExpand
The geometry of large fullerene cages: C72 to C102
Combining an efficient simulated annealing scheme for generating closed, hollow, spheroidal cage structures with a tight‐binding molecular‐dynamics method for energy optimization, the ground‐stateExpand
Program Fullerene: A software package for constructing and analyzing structures of regular fullerenes
Fullerene (Version 4.4) is a general purpose open‐source program that can generate any fullerene isomer, perform topological and graph theoretical analysis, as well as calculate a number of physicalExpand
Topological characterization of five C78 fullerene isomers
Abstract The characteristic polynomials of five preferable fullerene cages with isolated pentagons are computed and compared. It is shown that one needs at least the twelfth coefficient in theExpand
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