Solution:Allotropes - The different forms of the same element. Allotropes of carbon are diamond, graphite, graphene, carbon nanotubes, fullerenes, and carbon nanobuds. Carbon - It is nonmetallic and tetravalent (its atom making four electrons available to form covalent chemical bonds), discovered by Antoine Lavoisier in 1789. Fullerenes (C-60 Buckminsterfullerene) was discovered by Richard Smalley in 1985.