Find the equivalent Resistance between A and B

Explanation

I Method : MIRROOR SYMMETRY
The branches AC and AD are symmetrical
`therefore` current through them will be same.
The circuit is also similar from left side and right side like mirror images with a mirror placed alone CD therefore current distribution while entering through B and an exiting from A will be same .Using all these facts the currents are as shown in the figure. It is clear that current in resistor between C and E is 0 and also in ED is 0 .It's equivalent is shown in figure (b)

`R_(eq)=(2R)/(3)`
II Method : FOLDING SYMMETRY
`therefore` The potential difference in R between (B,C) and between (B,D) is same `V_(C)=V_(D)`
Hence the point C and D are same hence circuit can be simplified as

This called folding.
Now , it is Balance Wheatstone bridge

`R_(eq)=(2RxxR)/(2R+R)=(2R)/(3)`
In II Method it is not necessary to know the currents in CA and DA