The atomic structure of the Au 6 x 6 on Si(111) phase has been determined using direct methods and surface X-ray diffraction data. This surface structure is very complicated, with 14 independent gold atoms, relaxations in 24 independent silicon sites and three partially occupied gold sites. In one sense the structure can be described as microdomains of the parent root 3 x root 3 An on Si(111) structure. A better description is in terms of a tilling of incomplete pentagonal and trimer units, essentially a pseudo-pentagonal glass. In terms of these structural units it is possible to explain all the gold structures in the coverage range 0.8-1.5 monolayers as pseudo-glasses with strong short-range order but varying degrees of long-range order. (C) 1998 Elsevier Science B.V. All rights reserved.