Concentric Clusters

Abstract

Symmetrical clusters may be constructed by placing regular polyhedra in contact with each other either across faces, along edges or at vertices. These clusters are either compact or ((loose)). The latter type leave voids which themselves have an interesting symmetrical ((sponge)) structure. The search for more compact clusters of polyhedra with S-fold symmetry has led to the discovery of concentric clusters and their exponential developments called explosions. The contacts are sometimes across faces, sometimes along edges. This method of construction cannot be carried out indefinitely; the process becomes blocked after several steps. Envelopes of these completed clusters will have the form of a polyhedron in the family icosi-dodeca, thus certain new composite entities called hyperpolyhedra.