Helices and helix packings derived from the {3, 3, 5} polytope

@article{Sadoc2001HelicesAH,
  title={Helices and helix packings derived from the \{3, 3, 5\} polytope},
  author={Jean-François Sadoc},
  journal={The European Physical Journal E},
  year={2001},
  volume={5},
  pages={575-582}
}
  • J. Sadoc
  • Published 1 August 2001
  • Mathematics
  • The European Physical Journal E
Abstract:The {3, 3, 5}-polytope is described and used as template for dense structures. Then larger structures are derived from this polytope, using disclinations. That needs a study of symmetries in this polytope. A discretised version of the Hopf fibration is presented and used in order to generate a family of new polytopes. It is possible to gathered vertices of these structures on several helices and then to consider geometrical relation between these helices. This study is govern by… 

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References

SHOWING 1-2 OF 2 REFERENCES

Regular Complex Polytopes

Frontispiece Preface to the second edition Preface to the first edition 1. Regular polygons 2. Regular polyhedra 3. Polyhedral kaleidoscopes 4. Real four-space and the unitary plane 5. Frieze