Platonic hydrocarbon
A Platonic hydrocarbon is a hydrocarbon (molecule) whose structure matches one of the five Platonic solids, with carbon atoms replacing its vertices, carbon–carbon bonds replacing its edges, and hydrogen atoms as needed.
Not all Platonic solids have molecular hydrocarbon counterparts.
Tetrahedrane (C4H4) is a hypothetical compound. It has not yet been synthesized without substituents, but it is predicted to be kinetically stable in spite of its angle strain. Some stable derivatives, including tetra(tert-butyl)tetrahedrane (a hydrocarbon) and tetra(trimethylsilyl)tetrahedrane, have been produced.
Cubane (C8H8) has been synthesized. Although it has high angle strain, cubane is quite kinetically stable, due to a lack of readily available decomposition paths.
Angle strain would make an octahedron highly unstable due to inverted tetrahedral geometry at each vertex. There would also be no hydrogen atoms because four edges meet at each corner; thus, the hypothetical octahedrane molecule would be an allotrope of elemental carbon, C6, and not a hydrocarbon. The existence of octahedrane cannot be ruled out completely, although calculations have shown that it is unlikely.
...
Wikipedia