Optical microscopy, differential scanning calorimetry, small-angle X-ray diffraction and nuclear magnetic resonance spectroscopy have been used to study the lyotropic phases formed by trioxyethylene glycol monohexadecyl ether with water (²H₂O). The phase diagram exhibits regions corresponding to lamellar (L_α), inverse cubic [V₂(1), V₂(2)], gel (L_β) and isotropic liquid phases (W, L₂, L₃). The two V₂ phases were identified by both optical microscopy and small-angle X-ray measurements. The gel phase exhibits a large melting entropy, and part of the molecule has a much restricted mobility. Low-angle X-ray data indicate that the alkyl chains are ordered, with a thickness equivalent to one hydrocarbon chain length. Taken together these data confirm a monolayer ‘interdigitated’ alkyl chain structure for the gel. In the presence of water the gel is stable (at thermodynamic equilibrium) below 40 °C. Anhydrous C₁₆EO₃ exhibits polymorphic phase behaviour. After melting the crystalline surfactant, a metastable gel structure forms on cooling and the crystalline solid reforms only after lengthy storage at low temperature. The maximum water-layer thickness of the L_α phase is larger than that of L_β despite the expected weaker inter-layer attractions in the latter case. This implies the existence of an additional repulsion in L_α, possibly arising from elastic undulations of liquid bilayers.