An allotrope is a variant form of an element with the same chemical composition but different molecular structure and properties. The document discusses several common allotropes including carbon (diamond, graphite), phosphorus (white, red), oxygen (O2, O3), sulfur (rhombic, monoclinic), boron (amorphous, crystalline), and silicon (amorphous, crystalline). Allotropes have substantial differences in their physical properties due to variations in atomic bonding arrangements.