Interpenetration (catenation) has long been considered a major impediment in the achievement of stable and porous crystalline structures. A strategy for the design of highly porous and structurally stable networks makes use of metal-organic building blocks that can be assembled on a triply periodic P-minimal geometric surface to produce structures that are interpenetrating—more accurately considered as interwoven. We used 4,4′,4"-benzene-1,3,5-triyl-tribenzoic acid (H3BTB), copper(II) nitrate, and N,N′-dimethylformamide (DMF) to prepare Cu3(BTB)2(H2O)3·(DMF)9(H2O)2(MOF-14), whose structure reveals a pair of interwoven metal-organic frameworks that are mutually reinforced. The structure contains remarkably large pores, 16.4 angstroms in diameter, in which voluminous amounts of gases and organic solvents can be reversibly sorbed.