In the figure shown resistance between any two corners connected by short wires is half of the resistance of the wires connected by long wires. Terminals A, B and C are connected to the corners by resistanceless wires. If the equivalent resistance between A and C is $$R$$, find the equivalent resistance between A and B.
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PLACEHOLDER ANSWER - the answer is an expression in $$R$$. Let each side have resistance $$r$$ and each diagonal $$2r$$. Between A and C the network is symmetric, the two corners opposite each other across the diagonal are at the mid potential, and the remaining corner potentials follow from Kirchhoff's current law, giving $$R_{AC} = \frac{3r}{4} = R$$. Solving the same network with the current entering at A and leaving at B gives $$R_{AB} = \frac{11r}{16}$$. Hence $$R_{AB} = \frac{11}{16} \times \frac{4R}{3} = \frac{11R}{12}$$.