Answer:
From Wikipedia:
"Allotropy or allotropism 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 element's atoms are bonded together in a different manner."
Conversion, therefore (logically) would mean that one would be able to reduce the carbon allotrope to atoms and then re-assemble them into a different allotrope.
For example, in order to form a diamond allotrope from a group of carbon atoms requires enormous amounts of pressure and temperature.