Define and explain allotropy forms of carbon. allotopic forms of carbon

"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.