Fig. 1. Three carbon nanotubes represented as a facetted polyhedra with an atom at every vertex.

Fig. 2. Points lying on two helices and forming an equilateral triangle in three-dimensional space.

Fig. 3. Points forming a regular triangular pyramid. (Points A and B lie on the x-axis and C lies on the z-axis, while the equilateral triangle ABC lies in the xz-plane).

Fig. 4. Points forming rotated pyramid projected onto xy-plane. (View looking down axis of carbon nanotube and points a, b, c and d are equidistant from axis point e).

Fig. 5. Difference between exact and conventional radius (r − r₀) for carbon nanotubes of type zigzag: (5, 0)–(13, 0), chiral: (4, 2)–(10, 5), and armchair: (3, 3)–(8, 8).

Fig. 6. Difference between exact and conventional unit length (L − L₀) for carbon nanotubes of type zigzag: (5, 0)–(13, 0), chiral: (4, 2)–(10, 5), and armchair: (3, 3)–(8, 8).

Fig. 7. Bond angle for carbon nanotubes of type zigzag: (5, 0)–(13, 0), chiral: (4, 2)–(10, 5), and armchair: (3, 3)–(8, 8).

Results of the polyhedral model using σ = 1.44 Å

Comparison of radii from conventional model, new model and ab initio calculations of Cabria et al. [11] using σ = 1.44 Å

Comparison of radii from conventional model, new model and ab initio calculations of Machón et al. [1] using σ = 1.425 Å

Comparison of radii from conventional model, new model and ab initio calculations of Popov [2] using σ = 1.42 Å