Diamond: four, strong covalent bonds for each carbon atom, very hard, very high melting point, does not conduct
Graphite: three covalent bonds for each carbon atom, layers of hexagonal rings, high melting point, layers free to slide as weak intermolecular forces between layers, soft, can be used as a lubricant, conduct thermal and electricity due to one delocalised electron per each carbon atom
Fullerenes: hollow shaped molecules, based on hexagonal rings but may have 5/7-carbon rings, C60 has spherical shape, simple molecular structure, high tensile strength, conductivity
Nanotubes: cylindrical fullerene with high length to diameter ratio, high tensile strength, conductivity
Graphene: a single layer of graphite