Classification of degenerations and Picard lattices of Kählerian K3 surfaces with symplectic automorphism group $D_6$

In [1]–[6] we classified the degenerations and Picard lattices of Kählerian K3 surfaces with finite symplectic automorphism groups of high order. This classification was not considered for the remaining groups of small order ($D_6$, $C_4$, $(C_2)^2$, $C_3$, $C_2$ and $C_1$) because each of these cases requires very long and difficult considerations and calculations.
Here we consider this classification for the dihedral group $D_6$ of order $6$.