I was going to say you were wrong lulu until I read more about it. I had thought that only buckyballs were fullerines, but you are right.
A carbon nanotube is a member of the fullerine family. The nanotube is shaped like a cylinder that's open at both ends.
The fullerine family has more than just cylinder shapes. It includes soccer ball shapes and other closed shapes.
The buckyball is another member of the fullerine family, shaped like a soccer ball.
