Each dancer finds his or her next position by looking forward along the circulate path. If the next spot is directly ahead, that dancer walks directly forward without turning. If the next spot is to the left or right, that dancer will be turning around halfway (180 degrees) in the process of following the path.
Since there are only four spots, doing a Box Circulate four times will bring the dancer back to the original spot.
In a right-handed box, the next position for a dancer facing out will be to the right, so that dancer will be flipping over to the right.
In a left-handed box, the next position for a dancer facing out will be to the left, so that dancer will be flipping over to the left.
The term Box Circulate is most commonly applied to the center box of a larger formation. The caller will identify the four dancers somehow, .e.g, Centers Box Circulate.
In a formation where there are two boxes side by side, if the caller wants the dancers to do a box circulate action in each box, usually the term Split Circulate will be used instead.