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How can carbon nanotubes be represented using graphene sheets?

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graphene: atomic force microscopy — graphene Atomic force microscopy image of water structures that were trapped beneath a sheet of graphene one atom thick.

Carbon nanotubes can be represented as graphene sheets that have been rolled into seamless cylinders.12

A single-walled carbon nanotube (SWNT) is formed by wrapping a single sheet of graphene into a cylinder with a diameter of approximately one nanometer. The specific structure and properties of the resulting nanotube—such as whether it acts as a metal or a semiconductor—depend on the direction in which the graphene sheet is rolled, which is defined by a chiral vector with integer indices $(n, m)$ . Based on this rolling orientation, nanotubes are categorized as:2

Armchair ( $n = m$ )
Zigzag ( $m = 0$ )
Chiral (other combinations)

Multi-walled carbon nanotubes (MWNTs) are represented as assemblies of these cylinders nested concentrically, with a spacing of about 0.34 nanometers between adjacent layers, similar to the spacing found in graphite. While the sidewalls consist of hexagonal carbon rings, the ends of these tubes are typically capped by fullerene-like domes that incorporate pentagonal rings to allow for closure.12