CHEMICAL APPLICATIONS OF TOPOLOGY AND GROUP THEORY .I. COORDINATION POLYHEDRA

Possible polyhedra for coordination numbers four through nine, inclusive, are generated by considering maximum symmetry polyhedra with numbers of vertices (v), edges (e), and faces (f) satisfying the relationships e + 2 = v + f (Euler's relationship), 2e ≥ 3f, 3v ≤ 2e, and 4 ≤ v ≤ 9. The polyhedra corresponding to the various possible sp3dn hybrids are next examined. Polyhedra with minimum flexibilities, maximum symmetries, and maximum numbers of faces are favored in actual complexes. © 1969, American Chemical Society. All rights reserved.