C70, C80, C90 and carbon nanotubes by breaking of the icosahedral symmetry of C60.

  title={C70, C80, C90 and carbon nanotubes by breaking of the icosahedral symmetry of C60.},
  author={M. Bodner and J. Patera and M. Szajewska},
  journal={Acta crystallographica. Section A, Foundations of crystallography},
  volume={69 Pt 6},
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. The branching rule for the H3 orbit of the fullerene C60 to the subgroup H2 yields a union of eight orbits of H2: four of them are regular pentagons and four are regular decagons. By inserting into the branching rule one, two, three or n additional decagonal orbits of H2, one builds the polytopes C70, C80, C90 and… Expand
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