The effects of cosolvents such as glycerol, propylene glycol, ethanol, or glucose (referred here as "glycols") on the phase behavior of a representative poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) (PEO-PPO-PEO) triblock copolymer (PluronicP105, (EO)(37)(PO)(58)(EO)(37))are presented. Regions of lamellar, bicontinuous cubic, hexagonal, and micellar cubic lyotropic liquid crystalline structures (established from small-angle X-ray scattering measurements) have been delineated in the four ternary isothermal (25 OC) PEO-PPO-PEO-water-glycol phase diagrams. Pronounced effects on the concentration range of stability of the different phases we're found when the glycol was varied from ethanol (the least polar glycol examined here) to glucose (the most polar). For example, glycerol and glucose swell the hexagonal phase to lower copolymer content, while propylene glycol and ethanol do not show this effect. Our experimental observations are discussed in terms of modification of the system "interfacial curvature" affected through the ability of different glycols to swell the PEO-PPO-PEO macromolecule to different, extents. A hypothesis is proposed, based on a correlation between the PEO-PPO-PEO-water-glycol phase behavior and the glycol polarity, to account for and predict the effect of glycols on the ternary phase behavior of PEO-PPO-PEO block copolymers.