Metal-organic polyhedra and frameworks (MOPS and MOFs) were prepared by linking square units M-2(CO2)(4) (M = Cu and Zn) with a variety of organic linkers designed to control the dimensionality (periodicity) and topology of the resulting structures. We describe the preparation, characterization, and crystal structures of 5 new MOPS and 11 new MOFs (termed MOP-14, -15, -17, -23, -24 and MOF-114, -115, -116, -117, -118, -119, -222, -601, -602, -603, -604) and show how their structures are related to the shape and functionality of the building blocks. The gas uptake behaviors of MOP-23 and MOF-601 to -603 are also presented as evidence that these structures have permanent porosity and rigid architectures.