The double gyroid network morphology has been the focus of extensive research efforts as one of the most appealing block copolymer structures for practical applications. We performed an extensive study of the phase behavior of the supramolecular complex PS-b-P4VP(PDP)(x) to develop a systematic route to its double gyroid morphology. The morphological characterization of complexes was accomplished by transmission electron microscopy (TEM) and small-angle X-ray scattering (SAXS). Several compositions with the cubic Ia(3)over bard symmetry were found in a narrow region between the lamellar and the cylindrical phase. Experimental TEM images were compared to computer simulations of projections through multiple gyroid planes. Typical gyroid patterns "double wave" and "wagon wheel" were regularly found. The size of the gyroid unit cell was calculated from the SAXS data. The lattice parameter could be varied (from ca. 70 to 125 nm) by altering the molar mass of the block copolymer precursors. A number of complexes were found to exhibit characteristic biphasic morphologies coexisting lamellar and gyroid phase or gyroid and cylindrical phase. Finally, gyroid complexes with different relative PDP ratios were obtained which provides the opportunity to generate nanoporous structures with tunable porosities by dissolving the amphiphiles.