I bought a couple of bar magnets at the local hardware store. They were acting so strangely. I couldn't figure out where the poles were. Finally I realized each magnet had four poles! They weren't quadropolar, rather half of each bar was magnetized one way and the other half the other way. The field is oriented towards the thnnest dimension of the bar, not the longest like in all of the diagrams. Pretty clever setup. I suppose that a permanent magnet could have any number of poles greater than 1.