the lattice requires the following rules regarding the construction of a closed cluster with approximation of the nearest neighbors.

-   ***Rule 1.*** Each atom of sublattice A is bonded with three atoms of sublattice B and vice versa.

-   ***Rule 2.*** All real and closing bonds have the same energy levels.

-   ***Rule 3.*** The number of atoms in a cluster N must be divisible by six.

The last rule is explained in detail in section\[sec:Wave functions\].

All three rules in fact are satisfied within the construction in Fig.\[Fig1b\], although the second rule seems to be broken at first sight: for example, the closing bond between atoms 1 and 4 looks different from that between 1-2 or 1-6, since atom 4 is further away from 1. However, it must be kept in mind that the bond 1-4 is not a real bond. In distinction from Fig.\[Fig1c\], the closed cluster 1(b) must be understood as a diagram or graph, which makes it easier to obtain the Hamiltonian matrix. Furthermore, if these Hamiltonian matrix elements corresponding to the closing bonds are chosen the same as for existing bonds, then the “interaction” between atoms like 1 and 4 in 1(b) in fact describes 