Test Fold

As a follow-up to my recent test fold of diagonal shifts in square tubes, this test fold joins one square tube with one circular (or actually 16-sided) tube.

I’ve played with twists that join tubes of different shapes before, and this design extends that to a shifted twist. As in the previous test fold, the center of the twist relies on the flexibility and stretch in the paper to actually collapse correctly.

I’ve played a bit before with twists in non-round tubes and using them in models. These test folds are my first attempt to combine those with my diagonal shifts, giving two square tubes that are offset from each other. The offsets of the two square tubes are the same in both test models.

In both versions (as in my previous tests), the points on each face of the square tube all fall along a parabola. Because of the offset between the tubes, the vertex of the parabola is aligned with the focus of the twist (the point at which the paper converges).

In the first version, I tried a simpler version of the math that places the focus of the twist at the same height as the vertex of the higher parabolas. In this version, the shortest segments of the twist go through the focus essentially horizontally, giving some vertical separation between the two tubes.

In the second version, the focus is shifted down to eliminate that vertical gap, or at least greatly reduce it. This gives something that looks a lot more like the twists I used in my diagonal shift series.

Somewhat inspired by some of Robert Lang’s recent work, this model has a twist that transitions from a 16-sided ‘circle’ to a square. Interestingly, the bottom edges of the square tube are approximately parabolic segments. The center doesn’t quite collapse cleanly, but it’s close enough for practical purposes. This twist is a bit more challenging to fold than the ones I’m used to. I might try incorporating some multi-shape twists like these into some of my more complex models.

This is a new variation of my recent crimp-bend design from several months ago. In the original design, I had two sine waves that lined up, with the paper between them crimped to create an internal flat plane. For this variation, I’m using one straight line and one sine wave to define the top and bottom of the bend instead of two sine waves. Because the flat and diagonal planes have different lengths, part of the flat crimped plane is visible.

I’ve been working on diagonal shift designs for a couple years, but up to this point all of the fully paper diagonal shifts have been ‘uphill’ shifts. With the basic crease pattern I’ve been using, a specific height of the sine wave naturally gives a matching distance for the uphill shift.

After designing my crimp-bent tubes, I realized I can add one bend immediately above the diagonal shift and one bend directly below. This reorients the shift so it’s angled downhill instead of uphill. Because the shift and the bend use the same sine wave, it’s not obvious unless you look very closely that there are extra layers of paper there.

Most of the origami I’ve done for the past several years has been based on shaping tubes of paper in various ways, whether that’s by adding curves or intersecting the tubes with vertical or diagonal planes. One thing I’ve wanted to figure out for a while is how to create bends and curves in the paper tubes. I’ve explored some simpler approaches to that problem before, but this is the first approach I think I can realistically use as a part of a more complex model.

The concept here was inspired in part by my diagonal shift design. The top and bottom edges of the bend are both sine waves, which get folded such that they touch each other along the bend line. Inside, each gore has a small crimp to create a partial flat plane visible inside the model. The crimps all have slightly different angles, but the mathematical to find those angles is the same that I used for the diagonal shift.

Here’s the inside view for a simple tube of paper:

Things get a bit more complicated when there is already overlap of the paper along the outside of the tube, but the concept is the same. It’s harder to see, but there’s a similar partial plane of paper inside this one, too:

It’s a decent bit of work to measure and score all the appropriate lines for these, especially for the narrower tube, but the folding went more smoothly than I expected. Especially with a bit of wet-folding, all the crimps seem to form fairly easily. I have quite a few ideas of how I’d like to incorporate these into a variety of more complicated designs.

After another long trip, here are some more tessellations. There’s an assortment here of designs folded from instructions, designs reverse-engineered from pictures of the folded models, and my own designs (which may be re-inventions of other people’s models).

… I do something like this:

I like folding tessellations while traveling because they are easy to transport (small and mostly flat) and relatively repetitive to fold because of the repetition in the grid and symmetry of the pattern (and so possible to do when I’m tired). All of these are folded from squares of Elephant Hide paper, some painted with acrylic paint. This paper is great for tessellations because it holds up through a lot of folding and unfolding without getting mushy, which many of the more complicated tessellations require.These models are all folded directly from or adapted from Eric Gjerde’s book Origami Tessellations.

Here are some close-up images of some of the tessellations:

Over the past month, I have been test-folding lots of corrugation patterns in preparation for a new series. Most of these are not original designs; they are folded from crease patterns, reverse-engineered, or experiments vaguely based on images from the Flickr Origami Corrugations group. These are all folded from very cheap origami paper, not anything at all suitable for complex designs. I have previously folded a couple designs incorporating both pleated and corrugated segments, but only with very simple corrugated patterns. I am hoping that with more practice, I will be able to incorporate more complex corrugations and tessellations into my vases.

Here are a couple closer-up images of some of the corrugations:

I recently returned from a long plane trip, and I had a lot of time for origami while in transit. Since my typical folding style isn’t very conducive to folding while traveling, I decided to practice folding tessellations from Eric Gjerde’s book, Origami Tessellations: Awe-Inspiring Geometric Design. It’s a nice introduction, building up from the basic folding techniques to a variety of simple and complex tessellations.

I have folded a couple tessellations before, but this was my first time folding a lot in a short period of time. I learned the proper way to fold grids to minimize errors, but folding the grids still takes a long time (for 32 divisions, close to an hour for a square grid and longer for a hexagonal grid). These tessellations are all folded from cheap 6-inch squares of paper, which isn’t ideal. The paper gets soft too quickly, which limits the complexity of the models I could successfully fold. I would like to eventually incorporate more tessellated/corrugated elements into some of my own 3D designs, but it may still be a while before I build up the skills to do that well.