A novel class of polycoronands is described with each coronand structure replacing a smaller sized ring on the surface of a fullercnic polyhedron. The coronand structures evidently relieve some curvature strain. Further through the complexation of metal ions in the coronand structures, there arises the possibility of closing and opening these holes, thereby allowing not only the storage of another species in the endohedral cavity, but also the controlling of the circumstances for it to enter or leave. Results and rules for the stabilities of the icosahedral-symmetry species are reported. 1995, Taylor & Francis Group, LLC. All rights reserved.