# Category Archives: Test Fold

## Test fold: Square/circle twist

Square/circle twist

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.

## Test fold: Bend variation

Bend variation

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.

## Test Fold: Downhill Diagonal Shift

Downhill diagonal shift

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.

## Test folds: Crimp-bent tubes

Wide and narrow crimp bends

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:

Inside view of the wide crimp bend

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:

Inside view of the narrow crimp bend

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.

## New Work: More Airplane Tessellations

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).

Tessellations (1)

Tessellations (2)

Tessellations (3)

## When I spend 40 hours on airplanes…

… I do something like this:

Collection of tessellations

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:

Negative Space Stars, designed by Eric Gjerde

Star Puff Tessellation, designed by Ralf Konrad

Aztec Twist, designed by Eric Gjerde

3.4.6.4, designed by Eric Gjerde

Layered squares, adapted from Christine Edison’s Modern Blue

## Test Folds: Assorted Corrugations

The full box of corrugations

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:

Close-up of a few corrugations

Close-up of a few corrugations

Close-up of a few corrugations

## Test Folds: Assorted Tessellations

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.

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.

Tessellations 1

Tessellations 2

Tessellations 3

Tessellations 4

Tessellations 5

## Test models: Diagonal Intersections

Bisected diagonal shift

This test model is a combination of my two recent series: Diagonal Shifts and Intersections. Even though this piece worked decently as a test model, it doesn’t work quite well enough yet for me to use this in a real model. Hopefully if I do another test fold, I’ll be able to fix some of those problems.

I’ve done a lot of engineering to figure out how to fold my recent series, but I haven’t shown much of the process. This time I took some photos of my first couple test folds to share. I started with some of the measurements I’ve previously used for the diagonal shift models. Creating the flat plane of the model is basically just folding down a rhombus to a single line. My first attempt was to fold the central rhombus into a waterbomb base:

Diagonal intersection draft 1 back

Diagonal intersection draft 1 front

This design looks great from the front, but the back won’t work for the full model. The large triangle sticking up in the back will get in the way of the curved portion of the model. A good start, but not quite useable.

Then I started trying to figure out how to get rid of that extra triangle. I started by inverting the waterbomb base so the triangle was sticking out the front of the model instead of out the back. Then I squash-folded the triangle to flatten it against the front of the model:

Diagonal intersection draft 2 back

Diagonal intersection draft 2 front

This design is much better from the back – there’s no extra paper between the two flaps along the central diagonal. That means I should be able to use it for more complex models. The problem is that the front is very messy-looking: the extra paper from the central rhombus is visible and not especially nice to see there.

In my third test fold, I combined the best parts of my two first test folds. I squash-folded the central rhombus, but I also hid the extra paper on the back side of the model:

Diagonal intersection draft 3 back

Diagonal intersection draft 3 front

This final design is what I used in the full test model (photo at the beginning of this post). I combined it with the diagonal shift approach I’ve already written about. Combining the flat part and the curved part is still a challenge, but it’s one I’m working on. I’m hoping to fold at least one or two full models based on this design, but it may be too complicated to turn into a full series.

## Test model: Organic bowl

Organic bowl

It’s probably fairly obvious that this model is a departure from my normal folding style. Almost all of the folding I’ve done recently has been highly mathematically, precise, and planned. I have folded more organic pieces before, but it’s been a long time. Even those pieces were fairly structured and mathematically based.

This is probably first piece I’ve ever folded without making any actual measurements, and it was completely an experiment. I started by tearing a vaguely round-ish piece of paper from a large scrap I had sitting around. I used a compass to estimate some sizes and divisions and a ruler as a straightedge, but the rest was all free-folded. The flat base is in the center of the paper. I knew there would be a lot of extra paper around the edges, but I didn’t know what the outer sections would look like until I was mostly done folding. I did several rounds of wet-folding and taping the paper into various shapes until I got the paper into a shape I liked.

Organic bowl (view 2)

I had a lot of fun folding something completely free-form, and hopefully I’ll try it again sometime. I’ve been wanting to do some more organic designs for a while. Eventually I’d like to develop a folding approach somewhere between the purely mathematical and the purely free-form, but that’s something I’m still figuring out how to approach.

Organic bowl (view 3)