From an examination of the known, fully ordered structures of trioctahedral, kaolin-type silicates, four rules are obtained which govern the way in which the layers forming the structures are stacked together. All the possible structures which may be formed in conformity with these rules are then derived. A consideration of the nature of the rules shows that the polymorphism in these silicates is unlikely to be caused by random slip occurring during the early stages of crystal formation, followed by growth around a screw dislocation.Recent work on cronstedtite by Steadman & Nuttall (1963, 1964 has revealed eight structures of this mineral which differ from each other principally in the way in which the trioctahedral kaolin-type layers are stacked together. Polymorphism of this kind had been known previously in other minerals of this class, such as amesite and chrysotile, but these did not show such an extent of structural variety.The present work was undertaken as an attempt to discover general principles underlying all these ordered structures, in the hope that knowledge of this kind would assist in the discovery of further structures, and, more important, would lead to an understanding of the way in which the minerals are c(,cfl\o 'o o formed. The first purpose has already been fulfilled, and details are given in an appendix. The trioctahedral layerThe ideal structure of this layer is shown in Fig. 1. No attempt has been made to show there the departures from regularity which real layers invariably possess, since these vary from one polymorph to another. This paper will not be concerned with detailed variations of the composition or geometry of the layer, but it may be that such details do influence the structures decisively; Newnham (1961), for example, has shown how the structures of the dioctahedral minerals kaolinite and dickite appear to be determined very largely by the distortion of the layers. The octahedral part of each layer will be referred to as being above the tetrahedral part. Interlayer relationshipsIn all known structures, the layers fit together in such a manner that the oxygen atoms of one layer and the hydroxyl groups of the layer below are related in ways similar to those shown in Fig. 2(a) and (b). These again are ideal positions. The distinction is made there between the structures in which oxygen atoms fall (a) in triangles of hydroxyl groups which have no cation beneath them and (b) in triangles which do have cations beneath them. The relationships of (a) and (b) (Fig. 2) will be referred to as c~ and respectively.In the derivation of the possible structures which may exist, the structures will be regarded as being formed by stacking layers together, each layer suffer-

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Single-crystal X-ray diffraction photographs have revealed eight polymorphs of cronstedtite, and the structures of four of them, with space groups P31m, P63cm, P31 and R3, have been determined.All the structures, assumed to have the idealized composition (Fe2+)3(Fe3+Si)Od(OH)s, are formed from kaolin-type layers, the principal differences being in the manner in which these layers are stacked together. Distortion of the Fe, Si-O, OH tetrahedra is related to the cation-anion attraction either within a layer or between adjacent layers.