Carbon nanotubes (CNTs) can be thought of as a rolled sheet of graphene. The direction on this roll can change, it can either be straight across or on a twist. The diameter of nanotubes is also variable. Therefore, different nanotubes must be labeled in a way that conveys these differences. The convention to do is uses two numbers n and m. These numbers correspond to the number of 
(red)and 
(blue) used to define the unit square, which defines the circumference of the nanotube. This means that 
To visualize this choose n and choose m and then show
and
.
Next, let's see the resulting vector when we add the vectors. So as previously stated, this resulting vector is the circumference and the vertical axis of the tube will be vertical to this vector. To visualize this watch the tube roll and notice what happened to the circumference vector.
Now try with other values of n and m to see how the chirality and diameter of nanotubes can change.
(red)and (blue) used to define the unit square, which defines the circumference of the nanotube. This means that
To visualize this choose n and choose m and then show
and
.
Next, let's see the resulting vector when we add the vectors. So as previously stated, this resulting vector is the circumference and the vertical axis of the tube will be vertical to this vector. To visualize this watch the tube roll and notice what happened to the circumference vector.
Now try with other values of n and m to see how the chirality and diameter of nanotubes can change.