Remember the key features of carbon allotropes:
Diamond: sp$^3$ hybridized, tetrahedral, 3D network, very hard.
Graphite: sp$^2$ hybridized, planar layers, conductive, soft.
Fullerene: sp$^2$ hybridized (approximately), cage-like structures.
The distance between layers in graphite (~335 pm) is much larger than the bond length within the layers (~142 pm).