Four coordination polymers of the bidentate ligand 2,2′-dimethyl-4,4′-bipyridine-N,N′-dioxide (L), [La(L)(NO3)3(H2O)] n (1), {[Gd2(L)3(NO3)6]·6H2O} n (2), {[Sm(L)2(H2O)4]·3ClO4·2L·4H2O} n (3) and {[Nd(L)2(H2O)4]·3ClO4·2L·4H2O} n (4) have been synthesized by the diffusing solvent mixture method. Results of X-ray diffraction analysis reveal that 1, with a Ln/L stoichiometry of 1:1, displays a rare 3-D three-fold interpenetrating diamondoid framework, while 2 has a Ln/L stoichiometry of 1:1.5 and exhibits a polycatenane network with a {82,10} topology and large channels accommodated by water. Complexes 3 and 4, with Ln/L stoichiometry of 1:2, have 3-D two-fold interpenetrating diamondoid structures and large voids. Nonlinear optical property of 2 and luminescence of 3 were also investigated.