TETRAHEDRAL MINI- AND MIDI-FULLERENES

We have considered possible ways of forming the simplest tetrahedral fullerenes, namely elementary tetrahedron C-4, truncated tetrahedron C-12, half-truncated cube C-16, fullerenes C-28 and C-36. By analogy with ionic crystals, we introduced "mathematical" compounds, which form a topological cube of two tetrahedra inserted into each other, and construct graphs for them. Combined with the graph analysis, this approach allows obtain a clear knowledge of the tetrahedral fullerene structure. We extended our model to other tetrahedral fullerenes, in particular, tetrahedral fullerenes C-64 and C-76.