Stucture    

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Stucture

In the ideal case, a carbon nanotube consists of either one cylindrical graphene sheet (single-wall nanotube, SWNT) or of several nested cylinders with an interlayer spacing of 0.34 – 0.36 nm that is close to the typical spacing of turbostratic graphite (multiwall nanotube, MWNT). 

There are many possibilities to form a cylinder with a graphene sheet: the most simple way of visualizing this is to use a "de Heer abacus":

A "de Heer" abacus: to realize a (n,m) tube, move n times a1 and m times a2 from the origin to get to point (n,m) and roll-up the sheet so that the two points coincide...

Basically, one can roll up the sheet along one of the symmetry axis: this gives either a zig-zag tube or an armchair tube. It is also possible to roll up the sheet in a direction that differs from a symmetry axis: one obtains a chiral nanotube, in which the equivalent atoms of each unit cell are aligned on a spiral. Besides the chiral angle, the circumference of the cylinder can also be varied. In general, the whole family of nanotubes is classified as zigzag, armchair, and chiral tubes of different diameters:

Models of different singlewall nanotubes (generated with Mathematica on the left, and taken from Saito et al., APL 60, 2204 (1992) on the right).

You can also generate your own nanotube models with the software Mathematica 4.0 using a notebook by Brandbyge that allows one to draw the structure as well as to compute the energy bands of SWNTs (get it here).

This diversity of possible configurations is indeed found in practice, and no particular type is preferentially formed. The lengths of SWNTs and MWNTs are usually well over 1 µm and diameters range from ~1 nm (for SWNTs) to ~50 nm (for MWNTs). Pristine SWNTs are usually closed at both ends by fullerene-like halfspheres that contain both pentagons and hexagons . As shown in the electron microscopy images below, a SWNT has a well-defined spherical tip, whereas the shape of a MWNT cap is more polyhedral than spherical. An open MWNT, as the name implies, doesn't have a cap and the ends of the graphene layers and the internal cavity of the tube are exposed.  

Transmission electron microsopy (TEM) pictures of the ends 
of different nanotubes. Each black line corresponds to one 
graphene sheet viewed edge-on.

Defects in the hexagonal lattice are usually present in the form of pentagons and heptagons. Pentagons produce a positive curvature of the graphene layer and are mostly found at the cap. Heptagons give raise to a negative curvature of the tube wall. Defects consisting of several pentagons and/or heptagons have also been observed. A simple model indicates that the diameter and/or chirality of the tube is changed from one side of the defect to the other. Such an arrangement forms therefore a link between two different tubes and is accordingly called a junction.

Junction between two SWNTs. Reproduced from Chico et al., PRL 76, 971 (1996).