Twelve balls on a balance

You have 12 identical-looking balls. Eleven weigh the same; one is either heavier or lighter than the rest, and you do not know which.

You have a balance scale with no weights. You may use it at most 3 times (each time placing some balls on the left pan and some on the right, then comparing heavy/light/balance).

Can you always find the odd ball within 3 weighings and determine whether it is heavy or light?