Note that this is a different network than the original network of Ttokoro.
If the entrance is at the top (as shown) then the exit should be at the crossing of Z7, Z11 and Z12, not on the crossing of Z2, Z3 and Z7!
Infinity 2D mesh. RCD=4/π-1/2. This is Google puzzle.
How about Infinity 3D mesh. R(0,0,0)-(1,1,2)
in the infinity 3D mesh. The answer is
This is well known 1/3.
Diagonal resistance of resistor 3D mesh.
n=1 The resistance of resistor 3D mesh of (0,0,0) to (1,0,0) is 7/12 ohm.
n=2 Do you know the resistance of resistor 3D mesh of (0,0,0) to (2,0,0) ?