When used as an accessory to a suit, a handkerchief is known as a pocket square. There are a wide variety of ways to fold a pocket square, ranging from the austere to the flamboyant:

*The Presidential, perhaps the simplest, is folded at right angles to fit in the pocket.
*The TV Fold looks similar but is folded diagonally with the point inside the pocket.
*The One-point Fold is folded diagonally with the point showing.
*The Two-point Fold is folded off-center so the two points don’t completely overlap.
*The Three-point Fold is first folded into a triangle, then the corners are folded up and across to make three points.
*The Four-point Fold is an off-center version of the Three-point Fold.
*The Cagney is basically a backwards version of the Four-point Fold.
*The Puff or the Cooper is simply shaped into a round puff.
*The Reverse Puff is like the Puff, except with the puff inside and the points out, like petals.
*The Astaire is a puff with a point on either side.
*The Straight Shell is pleated and then folded over to give the appearance of nested shells.
*The Diagonal Shell is pleated diagonally and then folded.