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 is R.
Let us consider each loop consisting of two resistors R in parallel connection as a single resistor whose resistance R1 is:
Let us simplify the sketch of the circuit:
The expression for the resistance R2 between the junctions (ED) and (CF) reads:
The expression for resistance of the whole cube reads:
Inserting , we obtain RAB
Thus the total resistance of the cube between the vertices A and B is