I’ve folded quite a few pieces in my Diagonal Shift series recently, and this piece is the latest addition to the series. In all of my previous pieces in the series, I’ve either used only one diagonal shift element or used two diagonal shifts in the same plane. In this piece, the two diagonal shifts are rotated 90 degrees from each other, and the painted designs follow the same pattern rotation. Keeping track of the rotation made this piece especially challenging to design, particularly drawing the crease pattern onto the paper.
It’s interesting to see how this piece came out. Since most of the pieces in this series have all their angles in the same plane, there are a few very interesting viewing angles, but the other views don’t add much of anything. But this piece has a more complicated geometry in three dimensions. It’s hard to pick a view to photograph because there isn’t any one angle that shows the full shape (more views below). Seeing the relationships between the shapes from a variety of angles make the piece more interesting to look at in real life.
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.
I’ve previously posted several crease patterns for my diagonal shift designs. Since posting those crease patterns, I designed a diagonal shift variant where the top and bottom halves of the paper form tubes of different widths and folded several models based on that design. Here are some crease patterns for a couple versions of diagonal shift variants. The dimensions on these don’t quite match any of the models I’ve folded, but they at least show the approach I used.
First, the single diagonal shift variant:
Diagonal shift variant
The bottom half of this crease pattern is identical to the crease patterns I posted before. Just above the middle, the diagonal lines only go partway past the middle of each gore, and the top section forms a narrower tube. This crease pattern gives something similar to the central part of this model.
These designs can also be combined in a couple ways. One option is to mirror the diagonal shift element vertically, giving a double diagonal shift pattern like the one in this vase:
Double diagonal shift variant
Another other option is to also shift the top diagonal shift section over by 8 gores (half the width of the paper, excluding the overlap), which gives something like this model:
Double diagonal shift variant 2
The math behind these designs is a good bit more complicated than I enjoy doing by hand, so I’ve set up spreadsheets to automatically do most of the math for me. I haven’t written about that aspect yet, but I might do that at some point when I have time.
I’m very excited to announce that I’ll be participating in two origami shows this summer!
1. FAVA Folding Festival
The FAVA gallery in Oberlin, OH has been hosting the FAVA Folding Festival since 2008, organized by James Peake. The info for this year’s show isn’t online yet, but the show will be open from May 11 until late July. I will have about 6 pieces in the show, including selections from both my Intersections and Diagonal Shift series.
2. Surface to Structure
Surface to Structure: Folded Forms will be exhibited at the Cooper Union in New York City. This was also the site of the first origami exhibit in the United States, in 1959. The show will be open June 19 – July 4 and is curated by Uyen Nguyen with co-advisors Sok Song and Patsy Wang Iverson. I will have one piece from my Diagonal Shift series in the show.
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 backDiagonal 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 backDiagonal 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 backDiagonal 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.
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.
This piece is a return to my diagonal shift series, which I took a short break from. I used the same diagonal shift variant element as in my most recenttwo pieces in the series. This time, instead of using two diagonal shifts to transition from a wide cylinder to a narrow one and then back to a wide one, I only used one diagonal shift. The sizes are aligned so the outer edge on one side is an unbroken curve.
One of the challenges I often run into in designing models is figuring out how my sketch will actually look in three dimensions. Since I have to figure out all the dimensions of the model before I do any folding, it’s very important that my sketch has the proportions I want. But in this piece, the change from a 2D sketch to a 3D folded model changed how the proportions look more than I expected. In the sketch, the top and bottom halves looked more evenly balanced; in the model, the bottom half has a good bit more volume and more visual weight. Even if this piece didn’t look quite like I expected, that makes it more of a learning experience for me than folding something that works exactly how I expected.
After spending a long time folding pieces mostly in neutral colors, I decided I needed a little more color in my work. I decided to experiment not just with color contrast but also with texture. The white near the top is color of the unpainted paper, the black is painted a flat color, and the purple is dripped/blended to add texture. It’s challenging to get smooth blending in the acrylics on paper. The paint dries very quickly, so I had to work very quickly to get the colors to actually blend together.
In this piece, I also varied the texture of the model itself, which I tried several years ago in my pleated and corrugated vase and diamond vases. The corrugated folding style in the lower part of the vase adds more interest and dimensionality to the simple vase shape.
This piece is mainly a test of a couple new ideas for now. I’m starting to explore ideas for my next series. This idea could become a series, but I’ve also still got a couple other ideas I’m considering.
A month or two ago, I ordered greeting cards with photos of my origami from Moo, and I’m finally getting around to posting the photos. Designing the cards was very easy, and I’m happy with the quality. I picked out a few of my favorite models that were correctly proportioned to fit on the card. Of course, my name and website are on the back to make it easy for people to find me.
Cards: front and back
For now, I just bought a small set of cards (25 cards) to see how the process works and so I can use them. Depending on exactly what my upcoming origami plans are, I might buy more soon to sell. Now I just need more reasons to mail cards!
I recently posted photos in progress of a piece I have been working on, and here is the finished piece. This piece is a return to my Intersections series from last year, and the form is adapted from my three-part vase. For more on this piece, see my recent post.
