Allotropes are different physical forms of the same element in the same physical state.

(physical state meaning solid/liquid/gas)

For example, diamond, graphite and graphene are allotropes of each other because they are all solid carbon.

4

(the carbon atoms at the edge haven't had all their bonds drawn - look at the atoms in the middle to see the 4 bonds)

Giant covalent lattice structure.

Each carbon is covalently bonded to 4 other carbon atoms, forming a repeating lattice.

Diamond can't conduct electricity.

Diamond doesn’t have any charged particles (electrons or ions) that can move freely throughout the structure.

3

Giant covalent lattice structure.

Each carbon is covalently bonded to 3 other carbon atoms, forming a sheet of hexagonal rings. The separate sheets are held together by intermolecular forces. It also has delocalised electrons that can flow throughout the structure. 

Graphite can conduct electricity. It has delocalised electrons that can flow and carry charge.

1. High melting and boiling points.
2. Soft & brittle.
3. Good conductor of heat & electricity.

1. Carbon atoms are arranged in layers.

1. The forces between layers are weak intermolecular forces.

1. This means they don't need much energy to break, so layers slide over each other easily.

Diamond has the higher melting point as it forms a continuous lattice where all atoms are held together by strong covalent bonds.

In contrast, graphite includes weak intermolecular forces, which require much less energy to break.