By definition, a fullerene is 'a closed graphitic form of carbon with exactly twelve pentagons
'. Should this seem a little confusing, remember that graphite
(planar sheets of hexagons) cannot form sphere
s. Therefore, pentagon
s are necessary to allow proper curvature - exactly twelve in the case of buckminsterfullerene
Since this was the form found first, other fullerenes are defined by this benchmark - so some carbon tubes are fullerenes (those with the appropriate number (ratio?) of 5 to 6 membered rings, and capped at the ends with hemispheres) while others are rolled up graphite sheets - like a rolled up newspaper.
The smallest fullerene is, therefore, C20+ (this ion has recently been made) - not to be confused with dodecahedrane or C20H20 which has no double bonds and is much more stable. An example of a fullerene larger than a buckyball is C70, which has an extra 'belt' of hexagons round the middle (five times two extra atoms - work it out :).
If you were wondering "what size is a bucky ball?", you should know that it is 7 Ångstrom or 7 ten-billionths of a meter. This is smaller than most proteins, and almost a third the diameter of (B)-DNA. Fullerene tubes can be larger in diameter (large enough even to fit bucky balls inside - or DNA!) and could potentially extend indefinately. Since they are defined to be closed, there should be a cap on the end of tubes, but these could be quite long.