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Elias stretch is an origami manoeuvre that is often used while collapsing origami models based on the Box pleating technique. It was named after Neal Elias, who popularized it in the 1970s. The technique is very simple and is used to assemble flaps (polygons) located on the paper edge. Basically, wherever you have a polygon that forms a flap and it is located on the paper edge, you can use Elias stretch manoeuvre to collapse that polygon.
I will show you this on a very simple example. As you can see there is no central polygons, so Elias stretch can be used for every single polygon.
How is Elias stretch manoeuvre used? Well, at the beginning, you should collapse the model in the shape of an accordion. Whether you are collapsing it horizontally or vertically does not matter.
Then we have to select the ridge crease that encloses the part of the paper. It is essential that the ridge crease goes from one edge of the paper to another as shown in figure 3.
Then, you need to determine the point on ridge crease which is farthest from the paper edge. In figure 3 this point is designated as A. Precisely from that point Elias stretch manoeuvre begins. You simply need to stretch the first row next to the observed point as much as possible. The paper will naturally adapt itself to the new situation almost without resistance taking the shape of a box. Precisely because of that stretching, the manoeuvre is called Elias stretch. Now you have to repeat the stretching for each and every successive row until you reach the paper edge. For some unknown reason, people always suggest collapsing from the paper edge toward centre of the paper. Such a procedure put too much stress on the paper and paper resistance is quite high. My suggestion is to always do the collapsing from the centre of the paper toward its edges.
The procedure is identical when the ridge crease is a bit more complex as in figure 5. Here you should also start from the row furthest from the edge of the paper and stretch one row at a time. The paper does not resist too much, clearly forming two flaps. I hope you noticed that ridge crease goes from one part of the paper to another and that all encircled axial creases change their direction.
Now you can apply the Elias stretch on the other side of the so-called accordion. At first glance, an equally complicated ridge crease can be found here. Fortunately, unlike the previous one, it touches the edge of the paper at the point A, and therefore can be divided into two parts. That is exactly what we’re going to do. The selected ridge crease is now quite simple even though it is relatively large and goes deep into the paper, but it is not special in any way. Needless to say, the procedure is identical like in all previous examples. The procedure itself is shown in Figure 6.
In the end, it remains to collapse the last ridge crease, which was left out by splitting previous ridge crease into two parts (Figure 7). With this last step, the model is successfully collapsed using nothing but Elias Stretch manoeuvre.
In the end, I would suggest you collapse the same crease pattern, but this time start by making the accordion created in the first step in the opposite direction. It will be a good exercise and will show you that the procedure is completely universal.
The procedure is literally applicable whenever edge polygons have to be collapsed. Due to its simplicity and universality, it can be applied in almost any situation, regardless of the number and the shape of edge polygons. As such, it is one of the most important tools for collapsing crease patterns based on the box pleating technique.