Carbon exists in several allotropic forms — each a radically different arrangement of the same atoms. Diamond, the hardest natural material, locks carbon into a rigid tetrahedral lattice where every atom bonds to four neighbors. Graphite, soft enough to mark paper, stacks carbon into hexagonal sheets held together by weak van der Waals forces. The same element, the same electrons, the same nucleus — utterly different materials.
Fullerenes emerged in 1985 — hollow carbon cages shaped like soccer balls (C₆₀) or elongated tubes. Buckminsterfullerene, named after the geodesic dome architect, demonstrated that carbon's bonding versatility extends to closed three-dimensional structures. Carbon nanotubes, essentially rolled graphene sheets, exhibit tensile strength exceeding steel by orders of magnitude.
Graphene — a single atomic layer of graphite — was isolated in 2004 by peeling layers with adhesive tape. This two-dimensional material conducts electricity better than copper, is stronger than steel, and is nearly transparent. Amorphous carbon, lacking long-range order, appears as soot, charcoal, and activated carbon — disordered but functionally indispensable.