The concentration interval of 48-62 wt % hexaethylene glycol n-hexadecyl ether (C16EO6) in deuterium oxide ((H2O)-H-2) has been investigated using optical microscopy, H-2 nuclear magnetic resonance, and small angle X-ray scattering and the detailed phase behavior established. On cooling from the lamellar phase (L-alpha), the phase sequence defected lamellar (L-alpha(H)), mesh intermediate (Int.), la 3d cubic (V-1), and hexagonal (H-1) or hexagonal plus gel biphase (H-1 + L-beta) was observed. On heating from the hexagonal or two-phase region, the region of intermediate and cubic phases formed on cooling is replaced by an Ia3d cubic phase. The mesh intermediate phase, formed on cooling, is demonstrated to have a rhombohedral structure, assigned the space group R(3) over barm$. It represents a phase in which the water-filled defects of the higher temperature L-alpha(H) phase become correlated between layers. The formation of the phase is driven by the need to introduce more curvature into the interface as the temperature is decreased because of increased ethylene oxide head group (EO) hydration. The interlayer correlation arises from the strong, repulsive head group overlap interaction in this system.