I recall that the puzzle says "one ball is heavier than the others" not "one ball is a different weight". That being the case, here is the solution:
1. Split the 12 balls into 2 groups. Place the groups on the scale. The heavier group has the heavy ball.
2. Split the 6 balls from the heavy group into 2 groups. Place the groups on the scale. The heavier group has the heavy ball.
3. Take 2 of the remaining 3 balls, place them on the scale. If the scales are even, the heavy ball was left off the scale. If one side of the scale is heavier, that's the heavy ball.
1. Split the 12 balls into 2 groups. Place the groups on the scale. The heavier group has the heavy ball.
2. Split the 6 balls from the heavy group into 2 groups. Place the groups on the scale. The heavier group has the heavy ball.
3. Take 2 of the remaining 3 balls, place them on the scale. If the scales are even, the heavy ball was left off the scale. If one side of the scale is heavier, that's the heavy ball.