Buckyballs are spherical molecules made up of carbon atoms arranged in a pattern of hexagons and pentagons like on a soccer ball. There is a whole family of such molecules, ranging from the 60-atom buckminsterfullerene (named after Buckminster Fuller, a pre-space architect who invented the Geodesic Dome) and ranging up to enormous molecules that are big enough to see with the naked eye. Each variety adds more hexagons but always has exactly 12 pentagons in the pattern.
Buckyball cages are used to contain individual uranium molecules in fission reactor fuel, preventing the molecules from getting close enough to each other to achieve critical mass and explode. Buckyball compounds are incredibly tough, as their molecular bonds are even stronger than diamond; and, as they have no liquid state, they cannot melt.
Buckytubes are tube-shaped molecules made
up of carbon atoms in a hexagonal array, similar to buckyballs. The carbon bonds in buckytube molecules are the strongest possible molecular bonds, and thus no other normal material substance can cut through a buckytube. Wires made of buckytube filaments are used to make monomolecular cutting blades in a variety of handheld weapons. Fullerene Mesh armor is made of a mesh of buckytube threads.