1.Graphite is made up of multiple flat layers of carbon, where the layers are not covalently bonded together. Three covalent bonds hold the atoms in each layer together, forming a repeating hexagonal ring structure. What holds the layers together is the delocalization of one electron per carbon. (This is is similar to the bonding in metals).2.Graphene is made up of a single layer of carbon atoms. It is the same as graphite whereby the layer of carbons arrange themselves into a repeating hexagonal ring structure, with 3 bonds to surrounding carbons. One electron is delocalized . It can be thought of as a single layer of graphite.3.Fullerenes are structures of carbon arranged into shapes. These shapes are hollow, and typically the structure is made from a single layer of carbon atoms. Much like graphene or graphite their structure is made up of repeating structures of polygons. However this is not just hexagons and could be pentagons or heptagons. An example is Buckminsterfullerene which is a 'ball' consisting of 60 carbon atoms. Carbon nanotubes can also be considered as fullerenes. these are hollow spheres with open ends 4.Diamond is an example of a giant covalent network. This is where every carbon is covalently bonded to four neighbouring carbons, which is repeated in all three dimensions.(other allotropes include amorphous carbon - no defined structure and a mix of bonding and shapes and lonsdaleite - similar structure to diamond but in a hexagonal arrangement.