5 Cube Expansion

A sequence of polyhedra illustrating the 5 cubic, or cartesian systems inherent in icosahedral symmetry. Here, the cubic systems do not overlap or intersect each other, but rather expand to accomodate each other in composite polyheda. Thus, the single purple cube expands to merge with a similarly expanded orange cube, forming a polar triacontahedron. This is a zonohedron having 6 directions of edges, corresponding to the 2 cartesian systems it incorporates. The next expansion includes a third cubic system, color coded blue. The expansion continues to include fourth and fifth systems, colored red and green respectively. The largets polyhedron can be seen as a composite of the 5 cartesian systems. Although this polyhedron has hexagonal and decagonal faces, these can be paritioned in a manner that reveals it as a zonohedron. This will be illustrated in a separately posted model.