Intermediate tutorial take II

Let’s focus on symmetries for a moment. Can you crease the entire bird base in 5 folds? It is possible, and makes use of the symmetry in the base. Heres how you do it:

We made all the creases in 5 steps. Looking at the amount of layers we creased through is instructive as to how many creases we made at once. In step 1 we only creased through 1 layer, in step 2 we creased through 2 layers, thus using a symmetry of 2. In step 3 we creased through 4 layers, thus using a symmetry of 4. In step 4 we creased through 8 layers, thus using a symmetry of 8. And finally in step 5 we creased through 8 layers still using 8 fold symmetry. We can look further at exactly what creases we made when by looking at the following color coded crease patterns for each step. The red is what crease we are actively making, the black is what creases are made as a result of the red crease, and the green are creases made in previous steps:

With the last image being the creases that we actually made:

If you are attentive, you can see all the symmetries of the bird base. Here is the image of the 8 fold symmetric module of the bird base:

You may now be wondering, why am I talking about this symmetry? It is a very important thing to pay attention to for a few reasons:

1) When making all the creases in the model, using the advantages of the symmetry can reduce the time involved and error in the crease locations, case in point, bird base went from 16 creases to 5.

2) When collapsing the model, location A that is symmetric to location B is done the same way as location B.

As you saw, We made all the creases by eventually creasing through 8 layers. I prefer to only crease through 2 layers maximum, as 8 layers becomes too inaccurate due to papercreep. The folding sequence for this is as follows is a common petal fold with the paper folded in half twice:

Now, I am going into so much detail about the bird base because it is a building block for many models. I will now show you how to fold an inscribed bird base. The method is useful for many models because it involves using the symmetries I taught, and also identifying the order of collapse. First, here is the crease pattern:

*Click on the image to see the directions of the creases.

As you see, the solution abides by the rule of alternating crease directions around each vertex. Now, How shall we crease all these creases cleanly? We learned earlier how to crease the bird base using only 2 layers at once. Let’s apply that same formula here. But first we should crease these creases so that we know how big our bird base is:

*Aside: How do we do this in 3 creases? Using the 4 fold symmetry of the model and the technique we learned for the bird base. For the solution, click on the image.

Now, we want to fill in the creases for the bird base. We can use our previous creases as guidelines to determine the size of our bird base, as seen here:

The red lines are the creases we made previously, and in the final result, the green triangle marks the boundaries of our bird base which we have yet to crease. With the green triangle, we now squash it and petal fold it just as we had to crease the bird base previously. Also you can crease the other two gray creases in the final image, to finally have creased the entire crease pattern in only 9 folds, and only through 2 layers at once for the bird base and 4 layers at once for many of the other creases.

Now that we have everything creased, we must determine what creases are most important so we can collapse the model sequentially. Once again, the longer creases are more important, and also the creases that don’t change direction when crossing another crease come first. Looking again at our cp, we see some main creases. Namely the following:

Now, the red creases are the ones at 22.5 degree angles, while the black ones are at 45 degrees. The actual first step is collapsed as follows:

Here the red creases are secondary creases added to help flatten the model, while the green lines mark symmetry. So, what happened to the long creases from the previous crease pattern that were 22.5 degrees? This introduces a 3^rd criterion for determining importance and order. The more important creases tend to be at higher angles. In this case, the 22.5 degree creases simply narrow the vertices, and are not a part of main structure. The main structure is determined by long 45 degree angle creases. This is usually the case. As you see, we added extra creases to be able to flatten the model entirely. If the red creases are not pressed you have the center area still being flat, with the top left and bottom right corners 3D. This is a perfectly manageable state, and if you are able to, do not make the red creases, and continue to the next step of flattening while 3D. Here is what the flattened model looks like now:

Now we want to reverse fold our internal square along the black creases of the following cp:

Giving us the following step:

And finally we can open and squash the remaining 2 symmetric sections of the bird base into place, giving us the full bird base cp:

With the resulting model looking like this:

And finally, narrowing the bottom vertices, and putting in the remaining creases results in a finished base that looks like:

Now, what do we do with this base? I continued narrowing the squares in front and back, and did some reverse folds to a morphed crane with long wing. (This was not designed to be anything but instructive, as this type of cp is seen in many designs). Here is a cp with some more of the detail for my morphed crane:

I did not fill in the crease directions for the added creases. I believe that you should be able to do this using the knowledge gained from previous tutorials.

*Hint: the 4 diamond shapes near the top right and bottom left corners are sinks which come last, while the creases near the top left and bottom right make 4 petal folds.

Finally, here are some photos of the finished bird with two heads, two tails, and really long wings.

Challenge 1: Make something more interesting from the base

Challenge 2: Make the inscribed bird base a different size, or make it off center and make a base from that.

Next time will be a tutorial where we use all four points of the bird base instead of just two.

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