The solution properties of water-soluble amphiphiles in nonaqueous polar solvents are important in the elucidation of the effects of solvent quality on self-assembly and also in practical applications where the use of water as a solvent is undesirable. We studied the self-assembly of a poly(ethylene oxide)-poly(propylene oxide) (PEO-PPO) block copolymer (Pluronic P105 : EO37PO58EO87) in formamide (as selective solvent for the PEO block) and present here results an the binary concentration-temperature phase diagram and on the microstructure. In addition to formamide-rich and polymer-rich solution regions, four "gel" regions with different microstructures, stable over a wide temperature range (fram 20 degrees C to more than 90 degrees C), have been identified and characterized by small-angle X-ray scattering (SAXS). The PEO-PPO block copolymer in formamide exhibits a thermoreversible transition from a micellar solution to a micellar cubic gel (of Pm3n crystallographic structure) at 25-35 wt % polymer concentrations. At higher polymer concentrations, regions with hexagonal (cylindrical), bicontinuous cubic, and lamellar (smectic) lyotropic liquid crystalline microstructures are stable. The formation of the bicontinuous cubic structure (consistent with the Ia3d crystallographic space group and the gyroid minimal surface) in formamide is notable, given the rarity of such structure in PEO-PPO block copolymer-water systems. The change of solvent from water to formamide did not diminish the structural polymorphism of the PEO-PPO block copolymer. However, the stability regions of the different structures (and in particular of the micellar cubic) in the case of formamide are shifted to higher polymer concentrations and temperatures compared to water. These observations can be related to a higher solubility of both PEO and PPO in formamide compared to water, and a higher effective PEO/PPO block ratio of the polymer. The interfacial area-per-polymer values (extracted :from SAXS data) in the lamellar and hexagonal structures are 10% and 20% higher, respectively, in the case of formamide than in water, in corroboration with the phase behavior observations.