Martin's problem of the cube with resistors on the edges suggested the following generalization.

Consider a cube in D-dimensions (D>1) with all edges composed of resistors with equal resistance say R.  Find the equivalent resistance between the two diagonally opposite points.

I have not tried solving it yet so I do not know how much harder it is going to be than the D=3 case. One thing is clear though- it would be very hard to draw a picture so perhaps a more algebraic approach is needed? Anyway let's give it a shot and see if we can come up with a general formula for such a configuration....

Happy hunting!