Cocrystals and isomers, two well-known unique concepts in supramolecular chemistry, are rarely put together until now. For the first time, we report three unprecedented and interesting cocrystals of twin isomers of coordination polymers (CPs) in situ formed by typical Keggin anions and Cu(II)-4,4'-bis(hydroxymethyl)-2,2'-bipyridine (Cu(II)-H2L) complex moieties. In cocrystals 1-3, the Cu(II)-H2L complex moieties are quadrisupported on Keggin-type anions through W(Mo)-Ot-Cu-Ot-W(Mo) (Ot is the terminal O atom) links in the crystal to form two twin ionic/neutral CPs with a fixed chemical stoichiometry. Cocrystals 1-2 contain ionic isomers as {[Cu1(H2L)(H2O)2]2[P1W12O40]} n n+/{[Cu2(HL)(H2O)2]2[P2W12O40]} n n- for 1 and {[Cu1(H2L)(H2O)2]2[P1Mo12O40]} n n+/{[Cu2(HL)(H2O)2]2[P2Mo12O40]} n n- for 2. Cocrystal 3 contains neutral isomers as {[Cu1(H2L)(H2O)2]2[Si1W12O40]} n and {[Cu2(H2L)(H2O)2]2[Si2W12O40]} n. Cooperation of conformation and hydrogen bond network isomerism of Cu(II)-H2L fragments and tetracoordinated mode isomerism of Keggin anion is perfectly embodied in twin isomers. Moreover, based on hydrogen-bonding interactions, twin isomers are alternately arranged in a 1:1 stoichiometric ratio to give a cocrystal. Complicated accumulation of three types of hydrogen-bonding assemblies in the same crystal may be the reason that they give conductivity values over 10-4 S·cm-1 at 100 °C under 98% relative humidity.