# The Basic Theory

The most basic concept in a nanotube structure is the chiral vector C defined by

C=n*a1+m*a2

Where n,m are the chiral vector numbers and a1,a2 are the basis vectors of the graphene sheet. The basis vectors are functions of the bond length of the chemical element constructing the tube

### Carbon Sheet

### Boron Sheet

### Silicon Sheet

There are 3 basic types of nanotube structure

- Zigzag – with m=0 and any n
- Chiral – with n ≠ m
- Armchair – with n=m

In the illustration above a zigzag structure is produced by rolling the tube along OE, a chiral structure is rolling in the OA direction and an armchair is rolling at OD direction. All nanotubes can be classified using the chiral vector system

The polyhedral model (Lee,Cox and Hill) used in this program is abetter description of the structure of the nanotube. The conventional rolled-up model of nanotubes completely ignores any effects due to curvature, this new approach takes into account the curvature and provide a mathematical basis to calculate the geometry of the nanotube with better precision. I will not dive into the mathematics but the general approach to the construction of the nanotube is first calculating the radii of the tube using the polyhedral model and constructing the nanotube atom helix using the radius and some angles that are parameters of the geometry. For more information read this wonderful review paper