Potential of two points how are they same?

[nishantve1]

Homework Statement

I am confused here .
Each wire is of resistance R
How in this image

E G and D are at the same potential

and in this image

How A and F and Dand G are equivalent?

Homework Equations

I don't think any equations will be used in solving this but I guess V =IR might be

The Attempt at a Solution

In the first image what I figured out is since the points E G and D are at one resistor drop from H so they are at the same potential but I am not able to figure out in the second situation

I am taking help of this website
http://physicstasks.eu/uloha.php?uloha=285
but its quiet confusing
I JUST WANTED TO KNOW WHATS THE METHOD BEHIND FINDING POINTS WITH EQUAL POTENTIAL IN SUCH CASES ?

 

[ehild]

Symmetrically equivalent points are at equal potential. Those points are equivalent which transform into each other during a symmetry operation.
Have you got a cube? Turning it around the body diagonal HB by 120° would not change anything: It looks the same as before. If you connect the battery to the points H and B, on the same axes, nothing happens again as the battery transforms into itself.
In the other case, the battery is in the mirror plane EHCB. The point A is mirror image of F, and D, G are also mirror images to each other, so they are equivalent.

ehild

 

[nishantve1]

Thank you ! So much respect .

 

[nishantve1]

Just a little more help . Please explain what's up with this one

Where is the symmetry here if the Cell is connected btw A and B ?
Also in the second figure why doesn't current flow through FG and AD ?

 

[ehild]

It is a mirror plane again...

ehild