Fullerenes are a class of carbon molecules, which form sheets, tubes and flat planes. Being single, large molecules, fullerenes are extremely strong and useful.
Carbon nanotubes, or carbonan, are used to make any body armor worth having, and also found in ship hulls. They are extremely difficult to break, and rapidly conduct heat away from its source. As a result, carbonan armor can only be penetrated by extremely powerful projectiles, or by very hot energy weapons such as plasguns Single carbonan filaments are also used in the "Dorothy" melee weapon, which can be thought of as the logical extreme of the cheese-cutter, but with a wire fine/sharp enough to cut steel.
Spherical fullerenes or nanobottles are used to safely store antimatter, by encapsulating a single charged antihelium atom within each sphere; the resulting "fullerened antimatter" contains antimatter at the parts-per-thousand level and is stable under room conditions.
It is unknown whether flat sheets of carbon atoms, or graphene, find utility in the Schlockiverse, although in the 21st century carbonan and graphene are both believed to have computer applications.