In order to visualize how nanotubes are built up, we start with graphite, which is the most stable form of crystalline carbon.
Graphite consists of layers of carbon atoms. Within the layers the atoms are arranged at the corners of hexagons which fill the whole plane. The carbon atoms are strongly (covalently) bound to each other (carbon-carbon distance ∼ 0.14 nm ). The layers themselves are rather weakly bound to each other (weak longrange Van der Waals type interaction, interlayer distance of ∼ 0.34 nm). The weak interlayer coupling gives graphite the property of a seemingly very soft material. The property us to use allows to use graphite in a pencil.
Carbon Nanotubes are considered to be a curved graphene sheet. Graphene sheets are seamless cylinders derived from a honeycomb lattice, representing a single atomic layer of crystalline graphite.
The structure of a Single-Wall Carbon Nanotube (SWCT) is expressed in terms of one-dimensional unit cell, defined by the vector
Rolling up the sheet along one of the symmetry axis gives either a zig-zag (m=0) tube or an armchair (n=m) tube. It is also possible to roll up the sheet in a direction that differs from a symmetry axis to obtain a chiral nanotube. As a well as the chiral angle, the circumference of the cylinder can also be varied.
Here is an example of a carbon nanotube (8,8), an armchair nanotube of a radius 5.42Å and length of 24.6Å, consists of 320 carbon atoms, generated by the visualization program - AViz2,
Here some links to interesting sites I found on carbon nanotubes:
1. A carbon nanotube page.
2. The nanotube site.
3. Physical properties of Carbon Nanotubes.
 Adler, A. Hashibon, N. Schreiber, A. Sorkin, S. Sorkin, G. Wagner (2002). Visualization of MD and MC Simulation for Atomistic Modeling. Computer Physics Communication, 147, 665-9