"Allotropy is a behavior exhibited by some chemical elements. These elements can exist in two or more different forms, known as allotropes of that element."
In each allotrope the atoms are bonded together differently. The end result is different structural modification of an element. Allotropy refers only to different forms of an element within the same phase or state of matter. "The changes of state between solid, liquid and gas in themselves are not considered allotropy."
The following are some Carbon Allotropes:
Diamonds form when the carbon atoms are bonded together in a tetrahedral lattice arrangement.
Graphite forms when the carbon atoms are bonded together in sheets of a hexagonal lattice.
Fullerenes forms when the carbon atoms are bonded together in spherical, tubular, or ellipsoidal formations.