Reciprocal polyhedra and the Euler relationship: cage hydrocarbons, C(n)H(n) and closo-boranes [B(x)H(x)](2−)

The closo-boranes B(x)H(x)(+2), or their corresponding anions [B(x)H(x)](2−) (where x = 5 through 12) and polycycloalkanes C(n)H(n) (where n represents even numbers from 6 through 20) exhibit a complementary relationship whereby the structures of the corresponding molecules, e.g., [B(6)H(6)](2−) and C(8)H(8) (cubane), are based on reciprocal polyhedra. The vertices in the closo-boranes correspond to faces in its polycyclic hydrocarbon counterpart and vice versa. The different bonding patterns in the two series are described. Several of these hydrocarbons (cubane, pentagonal dodecahedrane and the trigonal and pentagonal prismanes) are known while others still remain elusive. Synthetic routes to the currently known C(n)H(n) highly symmetrical polyhedral species are briefly summarized and potential routes to those currently unknown are discussed. Finally, the syntheses of the heavier element analogues of cubane and the prismanes are described.