1. The problem statement, all variables and given/known data Find the resistance across AB. Use symmetry to determine currents. 2. Relevant equations Please see diagram. 3. The attempt at a solution I really don't seem to understand symmetry in circuits. What is the link between the geometrical symmetry of the situation and the way in which the current divides at a junction? Is it the case that if a current can follow two possible paths, and the paths have the same resistances in the same order, that the current along each path is equal?? In the diagram below for example, why is I6 supposed to be zero? How do I know that points D and A are at the same potential??? I've tried expanding everything using Kirchoff's laws, but it just becomes very messy.... Thanks!