We report on a ternary isothermal system consisting of a poly(ethylene oxide)/poly(propylene oxide) (PEO/PPO) amphiphilic block copolymer, "water", and "oil" (where "water" and "oil" are selective solvents for the different blocks), which exhibits the richest structural polymorphism ever observed (in equilibrium) in mixtures containing amphiphiles (such as block copolymers, surfactants, or lipids). The microstructure resulting from the self-assembly of the PEO/PPO block copolymer can vary from normal (oil-in-water) micelles in solution, through all types of normal and reverse (water-in-oil) lyotropic liquid crystals (normal micellar cubic, normal hexagonal, normal bicontinuous cubic, lamellar, reverse bicontinuous cubic, reverse hexagonal, reverse micellar cubic), to reverse micelles, as the relative volume fraction of the apolar ("oil"-like) components increases over that of the polar ("water"-like) components. The structure in the liquid crystalline phases has been established with small-angle X-ray scattering; both the normal and the reverse bicontinuous cubic structures are consistent with the Ia3d crystallographic space group (and the Gyroid minimal surface), while the normal and reverse micellar cubic structures are consistent with the Im3m and FdSm space groups, respectively. The self-assembly of amphiphilic block copolymer in selective solvents described here provides a link between the self-assembly of surfactants in water (and oil/cosurfactant) and the self-assembly of block copolymers in the absence of any solvent. Furthermore, the ability of the PEO/PPO amphiphilic block copolymers to attain diverse microstructures is of great importance to numerous practical applications, especially since such copolymers are commercially available (as poloxamers, Pluronics, or Synperonics).