$c_{12}$         1          -1       -$\nicefrac {1}{2}$   $\nicefrac {1}{2}$       -1           1          -1           1
    Symmetry     $S_x S_y$   $S_x A_y$      $S_{x} S_{y}$           $S_x A_y$        $A_x S_y$   $A_x A_y$   $S_x S_y$   $S_x A_y$
   Point of BZ   $\Gamma$      $M-0$           $K_{1}$               $K_{2}$          $K_{1}$     $K_{2}$      $M+0$        $D$

\[table3\]

From Fig.\[Fig6\] it is easy to see, that in cases \[Fig6a\] and \[Fig6b\] the wave functions are plane waves with $\lambda = \frac{3}{2} a$, where $a$ is the length of the vector connecting the nearest neighbors of atoms A and B. The fronts of these waves are parallel to axis $x$, which means that the wave vector ***k*** is directed along the axis $y$.

The length of the wave vector of these waves $k = \frac{2\pi}{\lambda} = \frac{4\pi}{3a}$ coincides with the length of ***k*** in Brillouin zone point $K_1$ (Fig.\[Fig3\]) - thus, Figures \[Fig6a\] and \[Fig6b\] show the wave functions at point $K_1$. In cases \[Fig6c\] and \[Fig6d\] one can easily see, that the fronts of the wave of each sublattice are at an $120^\circ$ angle to the $x$ axis. Therefore, the waves vectors are directed at a $30^\circ$ angle to the $x$ axis, that is the point $K_2$ in Fig.\[Fig3\]. The length of these waves is also $\frac{3}{2} a$. 