A new flexible Cd2+ metal organic framework (MOF), denoted as UCY-3, which is the second example of a MOF with the ligand H3CIP [H3CIP = 5-(4-carboxybenzylideneamino)isophthalic acid], is reported. It shows a unique (3,3,6)-connected topology and is based on a neutral non-oxo triangular [Cd3(COO)6] secondary building unit that appears for the first time in MOFs chemistry. UCY-3 displays significant structural flexibility, capability for exchange of the guest solvents by various organic molecules in a single-crystal-to-single-crystal fashion as well as breathing capacity allowing the incorporation of relatively large amount of benzene into its pores. Overall this work indicates that MOFs based on semi-rigid polytopic ligands may adopt unprecedented structural types and exhibit unexpectedly high absorption capacities for relatively bulky organic molecules, as a result of their flexibility and breathing capability.