The surfactant-cyclohexane-water ternary phase behaviour and reversed micelle and water-in-oil (w/o) micro-emulsion structure of the cobalt (II) derivative of the anionic amphiphile Aerosol-OT (AOT) [Co(water)6](AOT)2 have been studied by polarising microscopy, small-angle neutron and X-ray scattering (SANS, SAXS). The surfactant forms an H2 reversed hexagonal phase on swelling with up to 25 wt.% cyclohexane. At higher concentrations of oil the fluid L2 reversed micellar phase is present, and a w/o phase forms up to w = 25.0 (w = [water]/[AOT-]). For w > 25.0 at 25-degrees-C a Winsor II system separates cleanly i.e. a w/o droplet system at the 'natural' radius of the monolayer, co-existing with an essentially surfactant-free water phase. The SAXS I(Q) profiles show that major changes in aggregate shape occur as a function of w at constant surfactant concentration. At low surfactant concentrations, [AOT-] = 0.075 mol dm-3, the w = 0 reversed micelles, formed from diluting the H2 phase, are small near-spherical aggregates. The scattering is consistent with cylindrical micelles at low w, 5-10, and spherical w/o droplets at the Winsor II boundary w = 25.0. The results are explained in terms of the influence of parent H2 and co-existing water phases on the aggregate shapes in the L2 phase. We have used the SANS contrast variation method to investigate the internal cross-section structure of the cylindrical, w = 5.0, reversed micelles. The results show that the radius of the polar core, r, is only slightly larger than the hydrated radius of the [Co(water)6]2+ counterion and that the surfactant shell thickness, delta, is essentially equal to the length of the AOT hydrocarbon chains. This suggests an open staggered 'string of beads' structure for the micelles, rather than a polar core that can be significantly swollen with water. This model gives us some insight into structure of the lyotropic H2 phase