Test Fold

I recently folded an initial test model with a diagonal shift. At that point, there were still quite a few problems with my test model, including a combination of mathematical complications and folding difficulties. Since then, I have made several changes that help solve those problems without significantly changing the appearance of the final models:

To make the math easier, I created an Excel spreadsheet that automates most of the calculations based on the distances and angles between each fold. This is the first of my models where I have relied on the computer to help figure out the dimensions. I also made a change to the crease pattern that simplified both the folding process and the math.

In my new folding process, the diagonal shift creates a half-twist in the paper, so the paper on the far left above the diagonal shift ends up on the far right on the bottom half of the model. The amount the top and bottom halves are shifted along the diagonal is related to how steep the diagonal is. When the diagonal is close to horizontal, there is very little shift. As the diagonal gets steeper, the amount of shift increases.

I am planning on incorporating this design element into more complex models and hopefully posting some crease patterns soon.

Why should circles get all the attention?

I’ve experimented a bit with breaking away from circle-based designs previously in models like my seed pod bowl and spiral bowl, but this design is the furthest I’ve deviated from a circle. The oval is made of portions of two sizes of circles, one with a radius of 1 inch and the other with a radius of 4 inches. The two ends are each 3/8 of a circle (135 degrees) with the small radius, and the two flatter sides are each 1/8 of a circle (45 degrees). That means that the four segments add up to 360 degrees, one full rotation.

The flat base on this shape (shown in the image above) doesn’t close nearly as nicely as most of the circular designs I fold. To get the base to stay flat, I had to wet-fold it and weigh it down while it dried. My circular bases usually stay put without any wet-folding. Even though the edges of the paper line up correctly, it’s easy to open a wide gap. Without adding glue, anything I put inside this model would probably just fall through the bottom.

Despite the extra challenges, I think this approach is ready to use on more complicated models. The model fits together exactly how I expected it to based on the math, and the folding process is certainly doable.

This concept is an extension of the ideas I worked on this winter and early spring, particularly my Intersections series and my last test fold. Like those earlier pieces, I’m combining a curved form with a flat plane. The difference here is that instead of the flat plane being perfectly vertical, here the flat plane is along a diagonal. This requires a very different folding strategy.

I have several ideas of where I’d like to go with this folding strategy, but for now I’m still working out the engineering for it. This test piece was folded from a fairly simple-looking crease pattern, but actually folding it was surprisingly difficult. Even using Elephant Hide paper, which is a very tough paper, some of the internal layers started to tear. I want to try various tweaks to the proportions to see if I can find a version that collapses more easily. Also, in my current version the flat plane is essentially a circle, but it should be elongated into an ellipse. If I can find a way to cleanly fold an ellipse, that may remove some of the distortions to the tube.

This model is a practice piece, somewhat building on my Intersections series. It’s the first model with no curves that I’ve folded in quite a while. Since the top diagonal plane is intersecting a simple square box, it’s not too hard to figure out how to tuck the extra paper inside. However, that will change very quickly if I move to more complex shapes.  I like the simplicity and sleekness of this form, which gives a very different aesthetic than my normal folding style. This piece is folded from one uncut rectangle of Elephant Hide paper.