Symmetry of single-walled carbon nanotubes is analyzed using the parent phase approach. Transfer of the planar hexagonal order of graphene sheet onto surfaces of chiral and achiral nanotubes is divided into two steps. At the first step the rotational symmetry of graphene is reduced. In addition, the reflection symmetry is vanished for chiral nanotubes. At the second step the resulting subgroup symmetry is mapped in homomorphical way onto the symmetry group of the single-walled nanotube.

Keywords: crystalline symmetry, group theory, parent phase, single-walled carbon nanotubes, graphene