The cubic phase formed between the microemulsion and hexagonal phases of the ternary pentaethylene glycol dodecyl ether (C12E5)-decane-water system and that doped with small amounts of sodium dodecylsulfate (SDS) have been investigated. The presence of discrete oil-swollen micelles in the cubic phase, both with and without SDS, was established by NMR self-diffusion. In addition H-2 NMR relaxation experiments have demonstrated that the micelles in the cubic phase are non-spherical, having grown and changed shape upon formation of the cubic phase from the micellar solution. Small angle scattering experiments indicate that the lattice parameter for the cubic phase is inconsistent with a simple packing of micelles. Whilst insufficient reflections were observed to establish the space group of the cubic phase uniquely, those that were are consistent with two commonly observed space groups associated with the micellar cubic phase, Pm3n and Fd3m. The micellar volumes calculated for these space groups are similar and are consistent with a change in micellar geometry from spherical to prolate.