What are allotropy and allotropic modifications? examples

Allotropes are elements that exist in two or more different forms in the same physical state. Allotropes usually differ in physical properties and can also differ in chemical activity.

Diamond, graphite and fullerene are three allotropes of elemental carbon. Graphite is a soft, black, slippery substance; diamond is one of the hardest substances. The various properties of allotropes arise from their chemical structures. Diamonds usually crystallize into a cubic crystal system and are made up of carbon atoms linked by tetrahedrons. Graphite crystallizes in a hexagonal system. In fullerenes, carbon atoms take the form of a hollow sphere, ellipsoid, or tube.