Step 1: Recall the structure of graphite.
Graphite consists of layers of hexagonally arranged carbon atoms. Each carbon atom in graphite is bonded to exactly 3 other carbon atoms within the same layer. The bond angles are all 120 degrees. This arrangement is characteristic of \(sp^2\) hybridisation.
Step 2: Determine the hybridisation in graphite.
Since each C in graphite forms 3 sigma bonds (one to each neighbouring C) and has 1 unhybridised p orbital perpendicular to the layer (which contributes to the delocalised pi system giving graphite its electrical conductivity), the hybridisation is \(sp^2\).
Step 3: Recall the structure of fullerene (C60).
Fullerene (Buckminsterfullerene, C60) has a cage-like structure made of 20 hexagons and 12 pentagons (resembling a soccer ball). Each carbon atom is bonded to exactly 3 other carbon atoms (2 bonds in hexagonal rings and 1 bond in a pentagonal ring).
Step 4: Determine the hybridisation in fullerene.
Since each C in fullerene also forms 3 sigma bonds to neighbouring carbons and has a p orbital contributing to the delocalised pi system spread over the cage, the hybridisation is \(sp^2\). The slight curvature of the cage introduces a small \(sp^3\) character, but the dominant hybridisation is \(sp^2\).
Step 5: Compare the two allotropes.
Both graphite and fullerene have each carbon bonded to 3 other carbons in approximately trigonal planar geometry, so both are \(sp^2\) hybridised. This contrasts with diamond, where each C is bonded to 4 carbons tetrahedrally (\(sp^3\) hybridisation).
Step 6: State the final answer.
The hybridisation of carbon in fullerene is \(sp^2\) and in graphite is also \(sp^2\).
\[ \boxed{sp^2 \text{ (fullerene)},\ sp^2 \text{ (graphite)}} \]