Hi,
Fullerene is an allotrope of carbon which consists large spheroidal molecules of composition C2n and n> 30.
Structure of fullerene : Most stable fullerene is C60 which is known as bucky ball because it look like soccer ball.
It contain both five membered and six memebered rings.
Number of rings :
Five membered ring : 12
Six membered ring : 20
Six membered ring is fused to both six and five membered ring. But five membered rings fused with only six membered rings. Carbon atoms are equal and under spā2 hybridisation and forms 3 sigma bond with other 3 carbon atoms. Due to delocalisation of remaining one electron gives aromatic character to it. This bucky ball shaped fullerene has 60 vertices with carbon atom present at each vertices. Fullerene contain both double and single bond.
Regards