Allotropy is a property by which an element can exist in more than one form that is physically different and chemically similar.
The different forms of that element are called its allotropes.
The main reason for the existence of allotropes of an element is its method of formation or preparation.
Carbon exists in different allotropic forms and based on its physical nature they are classified as below.
Crystalline forms of Carbon
Diamond:
In diamond, each carbon atom shares its four valence electrons with four other carbon atoms forming four covalent bonds.
Here the atoms are arranged in a repeated tetrahedral fashion which leads to a three-dimensional structure accounting for its hardness and rigidity.
Graphite:
In graphite, each carbon atom is bonded to three other carbon atoms through covalent bonds in the same plane.
This arrangement forms hexagonal layers which are held together one over the other by weak Vander Waals forces.
Since the layers are held by weak forces, graphite is softer than diamond.
Fullerene:
The third crystalline allotrope of carbon is fullerene.
The best-known fullerene is Buckminster fullerene, which consists of 60 carbon atoms joined together in a series of 5 and 6-membered to form spherical molecule resembling a soccer ball. So its formula is C60
This allotrope was named as Buckminster fullerene after the American architect
Buckminster fuller. Because its structure reminded the framework of dome shaped halls designed by Fuller for large international exhibitions, it is called by the pet name Bucky Ball.
A large family of fullerenes exists, starting at C20, and reaching up to C 540
