Points on the graphene lattice can be described by vectors of the form , where , are integers () and , are nonorthogonal unit vectors that can be taken as and , respectively. The chiral indices determine the alignment of carbon hexagons around the circumference of the cylinder. Three different geometrical classifications or "flavors" of nanotubes can be distinguished. "Armchair" configurations are characterized by indices while "zigzag" configurations are described by . Chiral nanotubes have indices with (and ) and can occur in two mirror-image forms. Armchair nanotubes show metallic electric conductivity, while the other flavors are semiconductors with varying characteristics.

In this Demonstration, you can view a nanotube structure with indices or its conceptual graphene precursor. Pink cylinders are drawn as visual aids.