Suppose that the voltage V is applied between the points A and B then
V = IR = I0 R0 ,
where R is resistance of whole the grid, l0 the current through the grid and I ,the current through the segment AB. Now from symmetry, I/4 is the part of the current, flowing through all the four wire segments, meeting at the point A and similarly the amount of current flowing through the wires, meeting at B is also I/4. Thus a current I/2 flows through the conductor AS, i.e.
I0 = I/2
Hence, R = R0/2