Carbon nanotubes are an interesting but as of yet incompletely understood part of nanotechnology, an area of science that has really grown up in just that last 15 years. From the mathematical perspective nanotubes have an interesting molecular structure based on the hexagonal honeycomb structure of graphite. In this talk I will describe the geometry and symmetries of nanotubes. There is an infinite family of such nanotubes, so describing the structure takes some care. Multivariable calculus should provide plenty of background to make this talk accessible. There will be a brief recap from lecture I of this series to motivate the atom labeling problem - a graph theory problem - for nanotubes.