&  &\\
      &  &  &  &  & 1 & \varepsilon & 1 &  &  &  &1\\
      &  &  &  & 1 &  & 1 & \varepsilon & 1 &  &  &\\
      &  &  & 1 &  &  &  & 1 & \varepsilon & 1&  &\\
      &  & 1 &  &  &  &  &  & 1 & \varepsilon& 1&\\
      & 1 &  &  &  &  &  &  &  & 1 & \varepsilon& 1 \\
      1&  &  &  &  &  & 1 &  &  &  & 1 &\varepsilon \\
 
     \end{array}\right|
=0.$$

\
The solution of equation is given by following values of energy $\varepsilon$: $\pm 3, \pm 2, \pm 2, \pm 1, 0, 0, 0, 0$.

The determinant of cluster N=24 has a form which is analogous to $D_{12}$. The obtained energy values are shown in Table\[Table1\].

   [N]{}                                                                                                                                                                                                                   
  -------- ------------- ------------------------ ------------------------ ------------- ------------- ------------- ------------- ------------- ------------------------ ------------------------ ------- ------- ------- -------
   [6]{}    [$\pm$ 3]{}                                                                                                                                                                             [0]{}   [0]{}   [0]{}   [0]{}
   [12]{}   [$\pm$ 3]{}                                                     [$\pm$ 2]{}   [$\pm$ 2]{}                 [$\pm$ 1]{}                                                                   [0]{}   [0]{}   [0]{}   [0]{}
   [24]{}   [$\pm$]{} 3   [$\pm (\sqrt{3}$+1)]{}   [$\pm (\sqrt{3}$+1)]{}   [$\pm$ 2]{}   [$\pm$ 2]{}   [$\pm$ 1]{}   [$\pm$ 1]{}   [$\pm$ 1]{}   [$\pm (\sqrt{3}$-1)]{}   [$\pm (\sqrt{3}$-1)]{}   [0]{}   [0]{}   [0]{}   [0]{}

\[Table1\]

The main conclusion 