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

The *HAC*5*C*7[*p*, *q*] Nanotube can be studied as a *C*5*C*7 net and it consists of *C*5<sup>s</sup> and *C*7<sup>s</sup> with the trivalent decorations. An example is presented in Figure 1, which can be decorated in a cylindrical or toroidal manner. The 2-dimensional lattice of *HAC*5*C*7[*p*, *q*] were ever been discussed in [28], in which *p* and *q* are the cardinalites of heptagons in one row and periods in whole lattice, respectively. As an example, such a Nanotube with three rows is presented in Figure 2.

**Figure 1.** *HAC*5*C*7[*p*, *q*] Nanotube with *p* = 4 and *q* = 2.

**Figure 2.** The *m*th period of *HAC*5*C*7[*p*, *q*] Nanotube.
