Explain fullerenes.

(N/A) Fullerenes are prepared by heating graphite in an electric arc in the presence of inert gases such as helium or argon.
The sooty material formed by the condensation of vaporized $C_{n}$ small molecules consists mainly of $C_{60}$ with smaller quantities of $C_{70}$ and traces of fullerenes consisting of an even number of carbon atoms up to $350$ or above.
Fullerenes are considered the only pure form of carbon because they have a smooth structure without any 'dangling' bonds.
Fullerenes are cage-like molecules. The $C_{60}$ molecule has a shape like a soccer ball and is called Buckminsterfullerene.
It contains $20$ six-membered rings and $12$ five-membered rings.
$A$ six-membered ring can be fused with six- or five-membered rings,but a five-membered ring can only be fused with six-membered rings.
All the carbon atoms are equivalent and undergo $sp^{2}$ hybridization.
Each carbon atom forms three sigma bonds with three other carbon atoms. The remaining electron at each carbon is delocalized in molecular orbitals,which gives aromatic character to the molecule.
This ball-shaped molecule has $60$ vertices,each occupied by one carbon atom. It contains both single and double bonds with $C-C$ distances of $143.5 \text{ pm}$ and $138.3 \text{ pm}$ respectively. Spherical fullerenes are also called buckyballs.