Polyhedra for Coordination Numbers from Four to Nine

Polyhedra for Coordination Numbers from Four to Nine 

The choice of favored coordination polyhedra, or even the assignment of a coordination polyhedron to a given chemical structure, would appear to be very complicated in view of the large number of topologically distinct polyhedra with as few as seven vertices. However, the properties of atomic orbitals coupled with an assumption of maximum symmetry for a given hybrid of atomic orbitals makes this problem both tractable and interesting. 

The coordination polyhedra for coordination numbers 2 and 3 are trivial, namely, linear or bent for coordination number 2 and trigonal planar or pyramidal (minus the apex) for coordination number 3. For coordination number 4 the two possibilities are tetrahedral using sp hybrids and square planar using sp d( - y ) hybrids. Polyhedra for coordination numbers 5 through 8 can be generated by the following processes  

Addition of one or two d orbitals to a four-orbital spherical sp manifold to give five- and six-coordinate polyhedra, respectively 

Subtraction of one or two d orbitals from a nine-orbital spherical sp d manifold to give eight- and seven-coordinate polyhedra, respectively 

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