Why is central fold opening so popular?

Post is a part of a larger series (Design process):

Analysing various Origami models one can see that oftentimes central vertical crease is missing. Why is it so, and why many authors resort to such a solution is something I will try to explain in this blog post.
But before we start, I would like to show you one real-life examples, just to be sure you know what I am talking about. So, if you look at figures 1 you will clearly see that there is no central vertical crease. The model is simply open along its central vertical fold.

Abrashi Origami central fold
Figure 1: Crease pattern of a model called Carnival in Venice (designed by Arijan Abrashi)

Why is it so, and what is an idea behind this kind of solution?
But, before I try to explain this idea, I have to say a few words about the origin of this problem.
In other words, I will have to say something about the so-called central flaps and their position on a folded base. You see, in most cases, origami authors prefer having a model with free flaps. Meaning, they prefer a model in which all flaps can rotate freely in any direction. Unfortunately, this is almost impossible to achieve if a model has one or more so-called central flaps. This is so, in most cases, because central flaps are almost always hidden/locked inside some other flaps or a river. They are hardly ever free.
If this explanation sounds vague and complex, my suggestion is to read and analyse the blog post “Can central flaps be free?”.
Nevertheless, let me show you problem of central flap on a simple example (figure 2).

Abrashi Origami central fold
Figure 2.

As you can see central flaps D, H and G on a fully folded base are hidden inside flaps B, F and E, and as such, not only that they are not visible, but they could barely move anyway, in any direction. In most cases this is not useful. Origami authors hardly ever need flaps that are buried inside another flap.

Central fold opening (simple version)

Finally, we come to the main topic: opening of a central vertical fold.
By now, you have most likely realised what is a purpose of this action. First, you will get wider model (if this suits you), but what is real reason is the fact that by doing so we will free central flaps. It is important to stress that only central flaps that are positioned along the opened central fold will be free.

Abrashi Origami central fold
Figure 3.

As you can see from figure 3, in our simple example, by opening central fold, model stays more or less the same. Number and length of all flaps is unaltered. Such favourable development comes from the fact that the central fold was an axial crease along its whole length (look at the crease pattern on figure 3). Remember this, opening a central fold without altering a whole model is possible only if a central fold is an axial crease along its whole length.
But there is something you should be aware of. You see, by opening a central fold only one of central flaps was freed. One in the middle. This is so, since only central polygon in the middle is located on the central fold.

Central fold opening (more advance version)

Things become more complex if a central fold is not an axial crease along its whole length. If it is partially a hinge crease then by opening a central fold, model will be altered significantly. To make this problem clear let me show you one nice example. Look on figure 4.

Abrashi Origami central fold
Figure 4.

Compared to the previous example this crease pattern is even simpler. In the lower part of the crease pattern one of the polygons as well as a river are missing. At the same time, left and right polygon become bigger.
So, let’s open its central fold to see what is going to happen.

Abrashi Origami central fold
Figure 5.

As you can see, opening itself is relatively easy to perform, but what interests us is the final result. Again, central flap in the middle is wider and free as expected. A flap on the top also become wider. So, upper part of the model is literally the same as in the previous example. Nevertheless, difference is apparent if you look at these two flaps at the bottom.
So, what has really happened?
First, both large flaps were shortened by one unit. Additionally, you got a river in-between these two large polygons and the rest of the model (river is marked in green). Also, four additional polygons appear in-between these large ones.
If you look a folded model (figure 5), can you see these small newly formed polygons (N, M, L and K)?
Not really.
Well, that is because they are literally buried deeply inside the newly formed river. Believe me. They are there for sure. You can even pull them out, but be aware that you will have to use a lot of force and you will have to dismantle sizable portion of the model to do so, since paper will resist a lot (figure 6). Also, there is no real purpose for doing so, therefore most authors tend to leave these small flaps buried inside.

Abrashi Origami central fold
Figure 6.

Now, let’s look once again the newly formed crease patter on figure 5. As you can see, not only central crease disappeared, but consequently the complete model configuration has been changed. Remember this. There is a substantial difference if we open central fold that is an axial crease along its whole length and if it is not.

Real-life example

Before I end this post, I would like to show you a real-life example with such a feature. On figure 7 you can see the crease pattern of modal called the Cerambycid Beetle taken from the Robert Lang’s book “Origami Design Secrets”.

Abrashi Origami central fold
Figure 7.: The Cerambycid Beetle crease pattern

You can immediately see that central vertical fold is missing, meaning the model is opened there. Also, it is evident that between upper two polygons/flaps there are seven smaller ones. These polygons are here as consequence of central vertical fold opening. But not only because of that. These new polygons are result of a fact that central vertical fold was partially a hinge crease before it was opened. It was hinge crease of two twelve-unit long polygons on the paper upper edge.
So, whenever you see this kind of a pattern (raw of small polygons on a central non-existent fold) you can be pretty sure they have its origin in above explained procedure.

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