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

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 biological consideration of helix building molecules, but the final purpose is to have a geometrical tool to study geometrical relationship occurring between different helices or strands. This can occur for instance in protein folding studies.