Rods, helices and polyhedra

Abstract

Helices can be found in the art and architecture of many periods, but almost always as single elements. They can be combined to make infinite structures that provide a range of possibilities for sculpture that have been little explored. The most symmetrical arrangements of helices in three dimensions can be derived from the known ways of packing rods. Some of these possibilities suggest new forms that have helices that pass through the vertices of polyhedra, and, because of the symmetry, there can be a possibility other than the standard construction of a helix through four points. One of the infinite structures is the basis for a newly described enantiomorphic saddle polyhedron that can fill space with its mirror image. GRAPHICAL ABSTRACT