We have investigated by small-angle neutron scattering (SANS) the ternary system containing water, alkane and the surfactant mixture benzyltetradecyldimethylammonium chloride and tetradecyltrimethylammonium bromide, which we have found to form a cubic liquid crystalline phase. A contrast variation experiment with equal volume fractions of water and oil showed three Bragg reflections varying in agreement with theoretically calculated scattering amplitudes for an infinite periodic minimal surface (IPMS) with cubic symmetry. We have, in addition, studied the “ringing” gel phases of the system water/octane/didodecyldimethylammonium bromide by SANS and electron microscopy.