The complexation of a preorganized thioether-functionalized bis(pyrazolyl)methane ligand (L) with silver precursors produces supramolecular structures organized at two hierarchical levels: [AgL](6)(X)(6) metal-organic cyclic hexamers and their organization in 3D architectures. The cyclic toroidal hexamers of 22-26 Å external diameter are found to be stable already in solution before self-assembly into the crystalline state. In the 3D lattice, the hexameric building block are arranged in different highly symmetric space groups as a function of a variety of anions (cubic Fd3 with PF(6)(-) or BF(4)(-) and rhombohedral R3 with CF(3)SO(3)(-) or NO(3)(-)) and form cavities with the geometrical shapes of Platonic solids (tetrahedron and octahedron) that can be occupied by a variety of solvent molecules. Upon evacuation, cubic crystals can produce stable frameworks with permanent porosity, which can absorb reversibly several vapors, CO(2) and CH(4).