On symmetrical $4$-extensions of the grid $\Lambda^2$

The finiteness of the set of all $Aut_0(\Lambda^2)$-symmetrical $4$-extensions of the $2$-dimensional grid $\Lambda^2$ is proved with the help of the finiteness criterion for the set of symmetrical $q$-extensions of the grid $\Lambda^2$, which was obtained by the authors earlier. In addition, the list of all $Aut_0(\Lambda^2)$-symmetrical $4$-extensions of the grid $\Lambda^2$ is presented.