Equivalent resistance between C and D?
I guess this should be a way to redraw the above schematic:



$${{R_4 \cdot R_5} \over {R_4 + R_5} } + { {(R_2 + R_3)\cdot R_1} \over R_1 + R_2 + R_3} = {R^2 \over 2R} + {2R^2 \over 3R} = {7 \over 6} R$$ which goes in parallel with R6, so:

$$({7 \over 6}R^2) / ({13 \over 6}R) = {7 \over 13}R$$ should be the equivalent resistance.