As a consequence, Fig\[Fig6c\] and Fig.\[Fig6d\] show the wave functions at point $K_2$.

The fact that all four wave functions shown in Fig.\[Fig6\] correspond to the energy $\varepsilon = 0$ can be directly deduced from the form of these functions. Namely, the total energy of the interactions of the atoms with their respective nearest neighbors is equal to zero, taking into consideration the values and signs of $c_n$ from Fig.\[Fig6\].

In Fig.\[Fig6\] it is also apparent, that those structure elements, which are periodically repeated within the wave functions at $\varepsilon = 0$ are triplets of atoms: $1,-1,0$ (Fig.\[Fig6b\]), $1, -\frac{1}{2}, -\frac{1}{2}$ (Fig.\[Fig6a\]) etc. Consequently, the energy value $\varepsilon = 0$ is only possible in clusters, in which the number of atoms $N$ is divisible by three. Since $N$ also has to be even, due to the equal number of atoms in sublattice A and B, the number $N$ finally has to be divisible by six. This is the base for rule 3 of cluster building from section\[sec:essence\].

It is easy to see that in clusters $N=8,10$ and other $N$ not divisible to six, energy values $\varepsilon = 0$ are absent. Therefore, only clusters with by six divisible $N$ must be 