The conditions of formation of the Au-induced Si-(6×6) reconstruction, its stability, as well as its atomic structure are studied experimentally using grazing incidence x-ray diffraction techniques. This reconstruction is found to form at 680 K when cooling down eutectic droplets previously obtained by the dewetting of thin gold films deposited at room temperature on a Si(111) substrate. The quality of the reconstruction is found to depend on the annealing temperature. The formation of the (6×6) reconstruction at low temperature after it has been destroyed by ion bombardment, together with the recovery of the Si surface, give evidence of its high stability and highlight the surfactant properties of gold atoms. The determination of the Si(111)-(6 × 6)Au atomic structure is performed using quantitative surface x-ray diffraction with an existing complex model proposed in the literature as a starting structure. The resulting gold structure is found to be 1 ML thick and consists in two domains related by a mirror. They are composed of trimer and pentagonal units with special sites presenting a partial occupancy of 0.5. Our experimental data set does not provide enough accuracy to determine the positions of the Si atoms of the substrate, but ab initio calculations tend to confirm that they are only slightly displaced from the bulk position.