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![[Figure 4]](oc5035fig4mag.jpg)
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Figure 4
LG symmetry of a chiral single-wall CNT (6,3): L(6,3) = T42/23 D3. The group generators: (i) 24π/21 rotation (around the nanotube axis) followed by a fractional translation f = 0.80 Å (along the nanotube axis), highlighted in blue; (ii) pure rotation (around the nanotube axis) for 2π/3, highlighted in red; (iii) π rotation around the (twofold) horizontal axis (perpendicular to the nanotube axis), highlighted in green. By successively applying the generators to an arbitrarily chosen carbon atom, the orbit representative C0, with cylindrical coordinates (3.11 Å, π/7, 0.23 Å), the entire nanotube is constructed (i.e. the symmcell consists of a single atom). On a different note, the (6,3) CNT is commensurate, with translational period a = 11.28 Å, and its unit cell comprises 84 atoms, while the monomer from which the nanotube can be constructed by the action of generalized translations Z = T42/23 (helical group) consists of six atoms. As L(6,3) is a nonsymmorphic group, the isogonal point group PI = D42 is not its subgroup and differs from the point factor P = D3. |
![[Figure 4]](oc5035fig4.jpg)
 | JOURNAL OF APPLIED CRYSTALLOGRAPHY |
ISSN: 1600-5767
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