Abstract from the Italian book: ARCHITETTURA DELLE SUPERFICI PIEGATE - le geometrie che muovono gli origami (http://mcarchitetture.blogspot.it/2014/01/book-architettura-delle-superfici.html) wrote by A. Casale, G. M. Valenti, M. Calvano.
The geometry of the faces influence the mobility of the structure and its spatial configurations. As we said, the quadrilateral piece constrains the direction of motion, if two vertices opposite to the hinge get close, the whole structure is reduced; if the same two vertices move away, the whole structure is relaxed. However, if we divide each face into two triangles and build an additional fold which connects the mountain vertex with the valley vertex, the entire structure will be able to obey to the different needs of movement. The faces can rotate around their common vertex arranging themselves into new configurations. The movement opted for one module is transmitted to the adjacent modules and the new force, generated in a specific place, will decrease more and more away from the epicenter of the motion.
These additional folds, do not have a specific connotation of the verse, they are neutral and can move up and down depending on the thrust of the proposed motion.