A lot of tires are directional these days--they rotate in a direction fixed by the tread pattern. You may find yourself behind the wheel of a large automobile. And you may say to yourself, "Directional tires go on the left or the right, I can't put a left tire on the right or a right tire on the left." And you may say to yourself, "But it doesn't matter if I swap front and back." And you may ask yourself, "Is that an equivalence relation? If it is I can quotient my tire-space and say modulo front-equivalent-to-back, I have two ways to locate directional tires, one of which is the right way, and one of which is the wrong way." And you may say to yourself, "That has to be a Boolean algebra of tire orientations."