Binary mixtures of the poly(oxyethylene) surfactant, nonaethylene glycol mono(11-oxa-14,18,22,26-tetramethylheptacosyl) ether, in (H2O)-H-2 have been investigated. The phase diagram has been mapped using optical microscopy and deuterium nuclear magnetic resonance. Three lyotropic liquid crystalline phases are formed within the concentration range from ca. 24% to 60% by weight of surfactant; a hexagonal phase, an "intermediate" phase, and a lamellar phase. The intermediate phase is extensive ranging from 32% to 60% by weight and is about 5 degrees C wide. Small angle X-ray and neutron scattering from the intermediate phase shows that it has a mesh structure, probably rhombohedral in symmetry, but that the correlation between layers relaxes as the surfactant concentration decreases. The phase diagram can be simply understood by a dominant "head-group overlap" interaction between the EO chains of neighboring aggregates and between adjacent EO chains on the same aggregate. The length of the alkyl chains is shown to be the most important factor in stabilizing intermediate phases over the more conventional bicontinuous cubic phases normally found between hexagonal and lamellar phases in shorter chain homologues.