There was thought to be only two allotropes of carbon orignally:
Nanotubes are derived from a graphene carbon lattice (ie the same as
in graphite) and were discovered in 1991 by the Japanese electron microscopist
Sumio Iijima who was studying the material deposited on the cathode during
the arc-evaporation synthesis of
Nanotubes can be made by directing a laser at graphite causing some of the hexagonal sheets to be displaced from the graphite and react to form nanotubes. They are fullerene-related structures which are made from sheets of graphite effectively rolled up to form cylinders - which are then closed at either end by hemispherical fullerenes:
The fullerene caps contain pentagonal rings in the same way the fullerenes that they are derived from do.