Two Dy-4 complexes, namely, [Dy-4 (L-1)(4) (NO3)(2)(mu(3)-OH)(2)]center dot 2C(2)H(3)OH center dot 3H(2)O (1) and [Dy-4(L-2)(4)(NO3)(2)(mu(3)-OH)(2)]center dot 3C(2)H(2)OH center dot 8H(2)O (2), were successfully designed and synthesized under solvothermal conditions. X-ray diffraction results show that both of them display unique {Dy4O8} cores, and the four central Dy(III) ions are arranged in a regular rhombic frame coplane. Surprisingly, 1 and 2 with a similar structure show the same metal ion coordination environment, but the topological stacking mode has changed drastically due to the introduction of -CH3 into the ligand of 2. Complex 1 shows a fcu network topology with 10 connections, while 2 displays a bcu topology with 8 connections. In addition, magnetic studies revealed that both of them are single-molecular magnets with effective energy barriers of 79.22 and 67.61 K, respectively. Interestingly, complex 2 has undergone a transition from single relaxation of the zero field to two-step relaxation process of the optimal field. The discussion of the magnetic structure relationship in this work provides a good example for exploring the factors affecting magnetic relaxation dynamics.