The accepted picture of the structure of a micelle in solution arises from the idea that the surfactant molecules self-assemble into a spherical aggregate, driven by the conflicting affinity of their head and tail groups with the solvent. It is also assumed that the micelle's size and shape can be explained by simple arguments involving volumetric packing parameters and electrostatic interactions. By using wide Q-range neutron diffraction measurements of H/D isotopically substituted solutions of decyltrimethylammonimum bromide (C(10)TAB) surfactants, we are able to determine the complete, atomistic structure of a micelle and its surroundings in solution. The properties of the micelle we extract are in agreement with previous experimental studies. We find that similar to 45 surfactant molecules aggregate to form a spherical micelle with a radius of gyration of 14.2 angstrom and that the larger micelles are more ellipsoidal. The surfactant tail groups are hidden away from the solvent to form a central dry hydrophobic core. This is surrounded by a disordered corona containing the surfactant headgroups, counterions, water, and some alkyl groups from the hydrophobic tails. We find a Stern layer of 0.7 bromide counterion per surfactant molecule, in which the bromide counterions maintain their hydration shells. The atomistic resolution of this technique provides us with unprecedented detail of the physicochemical properties of the micelle in its solvent.