Understanding the Symmetry of the Resistor Cube Problem

[black_hole]

Homework Statement

I am looking at the classic resistor cube problem-the one in which there is a cube with resistors all of the same value on each side. Particularily I am having trouble understanding the symmetry argument for the case in which the current enters and exits across the diagonal of a face. I realize that two of the sides "by symmetry" are going to be at the same potential. I don't undertand what is meant by "by symmetry." it would be extremely helpful if someone could explain that to me. Thanks.

Homework Equations

The Attempt at a Solution

 

[jbsteele]

The symmetry argument for the resistor cube problem is based on the idea that if two sides of the cube are equivalent, then the current must flow in the same way through both sides. In other words, if one side has a certain amount of current flowing into it, then by symmetry, the other side must have the same amount of current flowing into it. This is because the resistance of the cube is the same on both sides. Therefore, the current entering and exiting across the diagonal of a face must be equal, since the two sides of the cube are symmetrical.