Dear

    I am sorry to say that I could not get what excatly you meant when you said 6* 6 square but if its cube or any geometrical shape which has symmetry bettwen two connecting wire like in case of cube if two wires are connected diagonaly you can slit the cube exactly in two parts each part iwill be exact replica of the other in such cases all the common points will attain same potential which considerbly reduces your circut

 

 

or you can understand this in a different way also i.e if one part of the circuit connected to wire is the mirror image of the other part then if you had to creat the complete picture with half of the circuit and mirorr the all the points which will touch mirorr to give complete picture of the half circuit will be at same potential so wecan take the resistors which hassame potential at two ends

 

 

ITS QUITE DIFFICULT TO EXPLAINF USING SYMMETRY BY WRITTING ONLY HOPE YOU GOT UNDERSTANDING HOW TO USE SYMETRY