Equivalent resistance across a circuit made of 12 resistors

[opencircuit]

hey can anybody please tell me how to solve this circuit??

I tried this sum out but I can't understand which points are symmetrical and have same potential..or how the current is distributed

 

[Stonebridge]

The symmetry means that potential at C=D=E=F = 0.5 the pd between A and H
This means there is no current through the arms CD and FG. So you can ignore the 2 resistors there.
This allows you to simplify the circuit using series and parallel resistors.

 

[opencircuit]

ok, I solved the combinations and I got 3/4 R.
but what if the circuit is not symmetrical..that is if we have to find the equivalent resistance between A and B?

 

[Stonebridge]

I also get 3/4 R.
If the circuit is not balanced, I can't see much use for it! Usually, these "bridge" type circuits are only useful when balanced. [eg Wheatstone bridge]

To attempt to answer the question, though, one possibility would be to set up a system of Kirchhoff's Law equations for the various closed loops (where ΣIR = 0) as well as the main circuit supplying the pd that provides the main current.
You would get 6 equations with 6 unknowns and a relationship between the main current and the applied pd. This would give the equivalent R.