In this paper, we proposed a number rule for 3d-4f and 4f cyclic coordination cages (CCCs); that is, CCCs consisting of vertex-sharing M-4(mu(3)-OH)(4) (M = 3d transition metal or 4f lanthanide ions) units should have 3 x n metal centers (abbreviated M-3n), where n represents the number of the M-4(mu(3)-OH)(4) subunits. Under this number rule we reasoned that some species of CCCs, for example, the pentadecanuclear 3d-4f wheel and the pure 4f wheels with 9 or 18 centers, should practically have existed. However, there are no such complexes reported in the literature. To realize such CCCs we employed a mixed-ligand approach, that is, to simultaneously use the primary and the ancillary ligands for syntheses. This approach successfully leads to the isolation of two families of CCCs, namely, the Ni(10)Ln(5) (Ln = Gd and Y) mixed-metal wheels and the Er-3n (n = 4, 5, and 6) pure 4f metal wheels. These two families of CCCs unambiguously fill the missing links of the M-3n prototype CCCs. Moreover, dominated ferromagnetic interaction indicates high ground-spin state for the Gd5Ni10 wheel. The ferromagnetic interactions between the nickel centers are verified using the diamagnetic Y(III) analogue, which reveals an averaged coupling constant (J = 2.7 cm(-1)), while accompanied by a large negative zero-field splitting parameter (D = -6.1 cm(-1)) for single Ni(II) ions. Interestingly, the Y(III)-diluted Er-12 wheel shows slow magnetic relaxation behavior, presumably indicating the magnetically anisotropic nature of the erbium(III) ions.