I found in this link something I can't understand:
Consider a current flowing out of point a below. The current must split up into three equal portions, since all three branches from point a are connected to the same resistance. Thus, the currents in branches ab, ac, and ad must be equal.
This is the premise needed to remove the resistor bd. But why "same resistance"? Why does it say that the current equally splits between the three branches? I think this is also evidently in contrast with the last simplification step. How could be the current same in the branches if their resistances are 2R,2R,R?
I believe that there's an unneeded assumption. To remove the bd resistor we just can say that the current in ab and in ac (not in ad!) are the same because the shortest journey to d is 2R. Is it wrong?