The complexation of a preorganized thioether-functionalized bis(pyrazoly)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 angstrom 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 Fd $(3) over bar $ with PF6- or BF4- and rhombohedral R $(3) over bar $ with CF3SO3- or NO3-) 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, CO2 and CH4.