The call Linear Cycle starts in a wave. First, each end and adjacent center hinge, creating a box with the original center as the lead dancer. Then that lead dancer folds behind the adjacent dancer, and the two of them walk past the dancers from the other half of the wave, similar to a Double Pass Thru. Finally, they "peel" in the same direction as the original hinge, to become a couple facing the the dancers from the other half of the wave.
From a left-handed wave the hinge will be by the left, the fold will be to the left, the dancers will pass left shouldlers with the ones from the other half of the original wave, and the peel will be to the left.
In either case, the result will be facing couples.