Consider a cube made up of 12 wires each of resistance 1Ω.The equivalent resistance between point A and B is

In this circuit the vertices E and D (F and C) are equivalent, they are on the same potential. The resistance of the whole cube is not changed by merging these vertices into one. Let us merge the vertices E and D (F and C) into one junction, redraw the circuit into the plane and supplement each cube edge with a resistor. The resistance of each edge isR.

Solving the above circuit we will get the total resistance to be 7/12 R