**4.** *HAC***5***C***6***C***7[***p***,** *q***] Nanotube**

The *HAC*5*C*6*C*7[*p*, *q*] Nanotube is a *C*5*C*6*C*7 net and constructed by using *C*5*s*, *C*6*<sup>s</sup>* and *C*7*<sup>s</sup>* alternately with the trivalent decorations as demonstrated in Figure 3. These tessellations of *C*5*s*, *C*6*<sup>s</sup>* and *C*7*<sup>s</sup>* are usually decorated in a cylindrical or a torodial manner. The 2-dimensional lattice of *HAC*5*C*6*C*7[*p*, *q*] is obtained by repeating pentagons for *q* rows and *p* columns. The construction of this Nanotube can be found in [29]. As an example, a Nanotube with three rows is shown in Figure 4.

**Figure 3.** *HAC*5*C*6*C*7[*p*, *q*] Nanotube with *p* = 4 and *q* = 2.

**Figure 4.** The *m*th period of *HAC*5*C*6*C*7[*p*, *q*] Nanotube.
