Sphere packing, helices and the polytope {3, 3, 5}

The packing of tetrahedra in face contact is well-known to be relevant to atomic clustering in many complex alloys. We briefly review some of the structures that can arise in this way, and introduce methods of dealing with the geometry of the polytope {3, 3, 5}, which is highly relevant to an understanding of these structures. Finally, we present a method of projection from S₃ to E₃ that enables coordinates for the key vertices of the collagen model of Sadoc and Rivier to be calculated. Received 27 March 2001