Six lyotropic liquid crystalline and two solution (equilibrium) phases can be formed (at 25 degrees C) by an amphiphilic diblock copolymer composed of poly(ethylene oxide) and poly(butylene oxide) in the presence of water (selective solvent for PEG) and "oil" (p-xylene, a selective solvent for PBO). Oil-in-water ("normal") micellar solution (L(1)), micellar cubic liquid crystals (I-1), hexagonal liquid crystals (H-1), and a lamellar structure (L(alpha)) are formed with an increase of the copolymer concentration along the oil-lean side of the ternary phase diagram. A micellar solution (L(2)), micellar cubic liquid crystals (I-2), hexagonal liquid crystals (H-2), and bicontinuous cubic liquid crystals (V-2), all of the water-in-oil ("reverse") morphology, are formed in the water-lean part of the phase diagram with increasing copolymer concentration and in the presence of some water. The oil-in-water [water-in-oil] structures can accommodate up to 0.33 [0.40] g of oil [water]/g of copolymer. The formation of a reverse micellar cubic phase (I-2), indexed to the crystallographic space group Fd3m (face-centered), is an important feature of this phase diagram as it is one of the first times that such a structure has been identified. The normal micellar cubic structure (I-1) is body-centered (Im3m). The microstructure in the bicontinuous cubic region (V-2) can be described in terms of a multiply-connected amphiphile bilayer consistent with the Gyroid minimal surface (Ia3d). The absence of a "preferred curvature" in the self-assembly of this macromolecular amphiphile distinguishes it from typical low-molecular weight surfactants and bestows this remarkable structural polymorphism.