Using achiral ligand cyclohex-1-ene-1,2-dicarboxylic acid (H2L), in the presence or absence of N-donor coligands, five metal(II) complexes formulated as Zn(L)(4,4'-bpy)center dot H2O (1), Cu(L)(4,4'-bpy)(0.5) (2), Cd-2(L)(2)(phen)(2)(H2O)(2)center dot 3H(2)O (3), Zn-5(L)(4)(mu(3)-OH)(2)(H2O)(2) (4) and Cd(L)(H2O) (5) have been synthesized and structurally characterized by single-crystal X-ray diffractions. Complex 1 shows a homochiral network based on novel twisted hexanuclear cyclic units, which are fused by sharing metal ions into a 3D framework. Complex 2 exhibits a 2D framework constructed by 1D chain linked by 4,4'-bpy. 4,4'-bpy exhibits twisted and planar conformations in complexes 1 and 2. In complex 3, alternating 1D left-handed and right-handed helical chains are observed. Complexes 4 and 5 display different 2D frameworks based on a Zn5 unit and Cd-O-Cd infinite linkage, respectively. Complex 1 shows a strong CD signal, and complexes 4-5 are achiral. The twisted 4,4-bpy plays an important role in the formation of the chiral complex 1. The five complexes show different absorption and photoluminescence properties as well as different thermal stabilities.