Reciprocal polyhedra and the Euler relationship: cage hydrocarbons, C_nH_n and closo-boranes [B_xH_x]²⁻

• Michael J. McGlinchey and
• Henning Hopf

Beilstein J. Org. Chem. 2011, 7, 222–233, doi:10.3762/bjoc.7.30

• 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

• described. Keywords: cage hydrocarbons; high symmetry; reciprocal polyhedra; Review Platonic polyhedra and the Euler relationship The Platonic solids have long fascinated geometers, artists and chemists alike. Molecular analogues of the tetrahedron (P4, B4Cl4, Si4t-Bu4), octahedron ([B6H6]2−), cube (C8H8