"At two corners diaginaly opposite each other are marked A and B, (so you have to pass through three resistors to get from A to B)" Maybe I am reading more into this than needed. If each side has 3 resistors you would have 12 installed in the cube. You would go thru 6 resistors to get from A to B. Are you requiring the circuit to be constructed so that you must go thru 3 resistors from A to B?
