In a recent paper (Burgoyne, J.; Holmes, M. C.; Tiddy, G. J. T. J. Phys. Chem. 1995, 99, 6054) we showed that binary mixtures of the poly(oxyethylene) surfactant, nonaethylene glycol mono(11-oxa-14,18,22,26-tetramethylheptacosyl)ether (C(30)EO(9)), in (H2O)-H-2 exhibited an extensive intermediate mesh phase between a higher temperature lamellar phase and a lower temperature hexagonal phase. Here, we present small angle neutron scattering results obtained from a sample of the hexagonal phase shear aligned in a couette type flow cell and then gently heated into the intermediate mesh phase. The scattering pattern shows a 6-fold symmetry of the (110) reflection and indicates that the structure of the phase is a six connected rhombohedral mesh with space group R (3) over bar m. The unusual structure is explained by the competition between the need to reduce surface curvature on raising temperature because of decreasing head group hydration and the repulsive interaggregate head group overlap (HGO) interaction.