Platonic hydrocarbons
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 . It has not yet been synthesized without substituents, but it is predicted to be kinetically stable in spite of its acute bond angle and angle strain. Some stable derivatives, including tetra(tert-butyl)tetrahedrane (a hydrocarbon) and tetra(trimethylsilyl)tetrahedrane, have been produced.
Cubane (C8H8) has been synthesized.
Angle strain prevents formation of an octahedron, and since 4 edges meet at each corner, there would be no hydrogen atoms; 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.
Dodecahedrane (C20H20) has been synthesized.
The tetravalency (4-connectedness) of carbon excludes an icosahedron since 5 edges meet at each vertex; pentacoordinate carbon, such as CH5+, is unlikely, although both icosahedrane and octahedrane have been observed in boron compounds.
...
Wikipedia