A reversible transformation between 1D, 2D, and 3D is demonstrated for the first time in coordination polymers comprising Cu^II ions and bidentate terephthalate (BDC²⁻). 1D uniform chains were reversibly transformed into 2D layers with the construction of Cu-paddlewheels by eliminating water molecules. 2D/3D reversible transformation was achieved by removing/rebinding N,N-dimethylformamide coordinated to the paddlewheels. These dimensional transformations significantly changed chemical and physical properties such as gas sorption and magnetism. Although the uptake in open-framework 1D and 2D Cu-BDC was insignificant, pronounced absorption was observed for 3D Cu-BDC. Drastic difference in magnetic behavior is consistent with their coordination structures; uniform 1D chain of Cu^II in 1D Cu-BDC and 2D sheet based on Cu^II-paddlewheel dimers in 2D Cu-BDC. Ferromagnetic behavior observed in air-exposed 3D Cu-BDC is attributed to the 3D structure formed by the connection of 2D sheets.