Using known interatomic distances, it is possible to construct ideal crystal structures of layer silicates using the distance least squares method (DLS). This approach has been applied to the problem of the atomic arrangement of tetrahedral cation disordered micas by constructing models of all possible arrangements of Al and Si in the tetrahedral sites. This paper describes the DLS models for four micas, all one-layer polytypes: muscovite, phlogopite, margarite and xanthophyllite. The unit cell and atomic positional parameters are listed for each.