Buckyballs is actually the name given to spherical fullerene molecules, which are hollow molecules made up of carbon atoms that are shaped like a sphere.
More specifically, buckyballs are formed when a total of
Each carbon atom is covalently bonded to three other carbon atoms. You can trace these bonds along the lines of
Now, the most common form the buckyballs contain
Here's a very cool video from periodict Videos featuring Professor Poliakoff