The diffraction features of Si(111) 7 × 7 are analyzed and related to various structural models of the Si(111) 7 × 7 surface as one part of a multivariate analysis of this system. The limitations in early sample preparation and measurements produce some uncertainty in previously proposed structures. More recent data is considered here. In addition, models used early on to evaluate the structure of 7 × 7 have been over simplified, idealized models. More complex models are considered within the projection rod method as used for surface crystallography. The origin of numerous diffraction features can be determinedviatheir Fourier components for a wide range of 2-D layers, which provides new insight into the structure as well as the limitations of prior projection analyses. Structures which produce the key elements of the 7 × 7 diffraction are presented and various distortions are considered consistent with other experimental results. In general it is found that the presence of a strong set of 3/7th order beams and near extinction of neighbouring fractional order beams are features which are found experimentally and distinguish an important class of structures. This class has a particular type of 3-fold mirror symmetry, which is not apparent in the widely accepted dimer-adatom-stacking fault, DAS, model. Higher order diffraction features, of which many are weak, are also considered and provide important new structural information. Several new polymorphs of the 7 × 7 are identified which may also satisfy the diffraction derived features and possess some degree of pi-bonding so as to enable magnetic surface states not possible in a pure covalently bonded system such as DAS. The Patterson map of the 7 × 7 surface provide insight into the lost phase information encoded in diffraction and reveal why the DAS structure was experimentally favored. An unusual non-primitive 7 × 7 unit cell is also derived from the Patterson map that possesses unusual symmetry properties, a non-standard surface Brillouin zone with potentially unusual electronic properties.