Trivalent Polyhedra as Duals of Borane Deltahedra: From Molecular Endohedral Germanium Clusters to the Smallest Fullerenes

The duals of the most spherical closo borane deltahedra having from 6 to 16 vertices form a series of homologous spherical trivalent polyhedra with even numbers of vertices from 8 to 28. This series of homologous polyhedra is found in endohedral clusters of the group 14 atoms such as the endohedral germanium cluster anions [M@Ge(10)](3−) (M = Co, Fe) and [Ru@Ge(12)](3−) The next members of this series have been predicted to be the lowest energy structures of the endohedral silicon clusters Cr@Si(14) and M@Si(16) (M = Zr, Hf). The largest members of this series correspond to the smallest fullerene polyhedra found in the endohedral fullerenes M@C(28) (M = Zr, Hf, Th, U). The duals of the oblate (flattened) ellipsoidal deltahedra found in the dirhenaboranes Cp*(2)Re(2)B(n)(−2)H(n)(−2) (Cp* = η(5)-Me(5)C(5); 8 ≤ n ≤ 12) are prolate (elongated) trivalent polyhedra as exemplified experimentally by the germanium cluster [Co(2)@Ge(16)](4−) containing an endohedral Co(2) unit.