In this work, we first synthesized a Zn-Dy complex, [Zn6Dy2(L)6(tea)2(CH3OH)2]·6CH3OH·8H2O (H2L = N-3-methoxysalicylidene-2-amino-3-hydroxypyridine, teaH3 = triethanolamine, 1), by employing H2L, anhydrous ZnCl2, and Dy(NO3)3·5H2O reacting with auxiliary ligand teaH3 in the mixture of CH3OH and DMF. When teaH3 and the solvent CH3OH in the reaction system of 1 were replaced by the auxiliary ligand 2,6-pyridinedimethanol (pdmH2) and the solvent MeCN, another Zn-Dy complex, [Zn4Dy4(L)6(pdm)2(pdmH)4]·10CH3CN·5H2O (2), was obtained. For 1, its crystal structure can be viewed as a dimer of two Zn3DyIII units. However, for 2, four DyIII form a zigzag arrangement, and each of its terminals linked two ZnII ions. Interestingly, although the structural topologies of 1 and 2 are different, the coordination geometries of DyIII in 1 and 2 are all triangular dodecahedron (TDD-8). The difference is that the continuous shape measure (CShM) values of DyIII in 1 are larger than the corresponding values in 2. Magnetic investigation revealed that the diluted sample 1@Y exhibits two magnetic relaxation processes, while 2 only exhibits a single relaxation process. Ab initio calculations indicated that, in the crystal lattice of 1, two complexes exhibiting slightly different CShM values of DyIII result in the double relaxation behavior of 1@Y. However, for 2, one of two DyIII fragments possesses a fast quantum tunneling of magnetization (QTM), resulting in its magnetic process presented at T < 1.8 K, so 2 exhibits single relaxation behavior. More importantly, the theoretical calculations also clearly indicated that the weak ligation at equatorial sites of DyIII in 1 and 2 ensure 1@Y and 2 possess SMM behavior, although the coordination geometry of DyIII (TDD-8) in 1 and 2 severely deviates from the ideal polyhedron and its axial symmetry is low.