Structures as assemblies of coordination polyhedra

In this chapter we shall describe the more important structures that may be built 156 

Angles A-X-A for (a) tetrahedra AX4 or (b) octahedra AX5 sharing a face (F), an edge (E), or a vertex (V). (c) Restriction on distance between X atoms of different polyhedra (see text). The values given for certain of these angles are approximate. More precise values of those which are not directly derivable from the geometry of the polyhedra arc E = 65°58 (cos 11/27), Fjetr. = 102°16 [cos (-17/81)), and Foct. = 131°48 (2 sin vS/6). 

The distance (A—A) between centres of regular AX4 or AX6 groups sharing X atoms 

It should be emphasized that the validity of conclusion (iii) rests on our assumptions (a) that the distance of closest approach of X atoms of different vertex-sharing octahedra (x in Fig. 5.3(c)) may not be less than the distance X-X within an octahedron, and (b) that the octahedra are regular. Structures in which three octahedra share a common vertex but no edges or faces contravene (a) and/or (b). 

---