Ten rhombic triacontahedra (RT) can be connected face-to-face to form a ring. Also connected face-to-face, twelve such rings are set parallel to the twelve faces of an imaginary dodecahedron. As the distance of the rings from the center varies, at specific distances certain RTs coincide to form clusters of 60 RTs positioned at the vertices of a small rhombicosidodecahedron, or 30 RTs positioned at the vertices of an icosidodecahedron.