Platonic hydrocarbon

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Platonic hydrocarbons are the molecular representation of platonic solid geometries with vertices replaced by carbon atoms and with edges replaced by chemical bonds. Not all platonic solids have a molecular counterpart:

Tetravalent carbon excludes an icosahedron (5 edges meeting at each vertex) as a feasible objective;
Angle strain prohibits an octahedron. Since 4 edges meet at each corner, there would be no hydrogen atoms, and this hypothetical octahedron molecule would be an allotrope C₆ of elemental carbon, not a hydrocarbon.

The following platonic hydrocarbons, on the other hand, have been synthesised:

Tetrahedrane (C₄H₄) but only with proper substituents;
Cubane (C₈H₈);
Dodecahedrane (C₂₀H₂₀).

Note that with increasing number of carbon atoms in the frame, the geometry will eventually approximate a sphere. This is ultimately accomplished in fullerene although not a Platonic hydrocarbon itself (Buckminsterfullerene, C₆₀, has the shape of a truncated icosahedron, an Archimedean solid).