Some less-regular polyhedra

Other equations may be derived from Euler s relation which are relevant to polyhedra with, for example, a specified number of vertices or faces. The former are required in discussions of the coordination polyhedra possible for a particular number of neighbours the latter are of interest in space-filling by polyhedra. For 8-coordination we need polyhedra with eight vertices. These must satisfy the equation S( - 2)f = 12, that is. 

7-cootdination poly-hedia (a) monocapped octahedron, Ho( ( CC)CHCO0)3. H2O, (b) monocapped trigonal prism, Yb(acac)3. HjO. The broken lines show the edges spanned by the chelate ligands the shaded circles represent H2O molecules. 

The triangulated dodecahedron (Fig. 3.7(a)) is the third dodecahedron we have encountered, the others being the pentagonal and rhombic dodecahedra (with 5-gon and 4-gon faces respectively). 

On the other hand we may be interested in polyhedra with eight faces (8-hedra or octahedra), which must satisfy the equation 

Because of the outstanding importance of tetrahedral and octahedral coordination we devote the whole of Chapter 5 to systems buOt from these two polyhedra. The relatively few examples of 5-coordination are described in appropriate places. 

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