I was googling for new origami tessellation ideas and came across Ben Parker's snowflake design. I was going to attempt that, when a related image caught my eye. I think he called it "Hidden Treasure". It was a little more complex and really piqued my interest. Second only to coming up with my own tesses, one of my favorite past times is trying to figure out how to fold those of others. This one wasn't too difficult to determine. The front shapes were obvious. Some hexagons at the center of the 'snowflakes'. I thought at first, triangles on the back for the negative space. As I began putting it all together it became obvious that it was not triangles. It was that blunted corner triangle that follows the grid. The same shape featured in this tessellation . Those shapes land on the rear of the paper to create the negative space triangles on the front and make everything else synchronize nicely into a flat fold tessellation. It's a beautiful design. Wish I...

A lot of origami tessellations employ equilateral triangles in their design. In some they are the focal point. In others they help to bridge the gap between other shapes. This tessellation uses right triangles instead. It starts off typically with a central small hexagon. Instead of a classic hex twist, it uses an offset twist. This is how the triangles are formed. An offset hex twist is simply folding a small hex twist as you would an open back hexagonal twist. Instead of using the natural axes of the grid, you bisect them. Whichever direction the central hex goes, the next repetition goes opposite. If your grid were big enough to allow for more repetitions I imagine you would need to keep alternating. I used the mountain and valley folds at the ends of the triangles to determine which way the second generation would flow. There are some additional offset folds to make everything play nicely together. But nothing very complicated. All in all, it was not a difficult f...

 This is a classic weave pattern. Open back hexes and small triangle twists are just one pleat apart. This results in the woven pattern on the other side. I think I've tried to do this before. It seems familiar. But I couldn't find any pictures of such a tessellation in my personal archive. I suspect I may have attempted it and failed before. On this occasion, I was able to complete the project. It's a fairly simple pattern, but because everything is so close together it's a little tricky to execute. You can see from the crease pattern pictured further down that the triangles are only one pleat off of the axes of the hexagons. This makes everything fit together rather tightly. There's a lot of overlap. After completing the center, it gets temperamental. You can partially fold sections, but everything is interdependent for the most part. Good preceases are a necessity.

When you google origami tessellation crease patterns something called the waterbomb flagstone tessellation comes up in the top results. It looked pretty simple, but I found it rather fussy. I really need to start working with better paper. Unlike your typical flagstone, which has triangle twists on the rear, this has little rectangles. It's a familiar pattern that still proved quite difficult. The front is offset hexagons and natural triangles. The back side is the rectangles. It feels almost like it's not meant to lay flat. But it also feels like it could flatten with a stronger paper. I didn't bother to flatten it with weights or books. All the time I spent working the folds were enough to create the intended pattern. It seemed like if I tried to make it entirely flat, it would be ruined. You can see the rectangles in the rear view. I've fiddled with rectangles and hexes before. But this was a whole new level.

I saw an image of this tessellation on flickr. The image I saw was of a much higher density. Double the repetitions of my fold. I would love to find out how that folder did it. They must have employed a different technique than I used. I used my knowledge of the fujimoto hydrangea to figure out the crease pattern. I mapped that out, modifying for the desired result. Then I just went ahead and treated it as a crease pattern and collapsed everything in unison. Now, I know, when you normally fold hydrangeas or clovers, you do it in stages. It's not a collapse. It's a series of folds that add up to something. If it's possible to fold this in stages, I didn't find it. I just worked the paper gingerly until it eventually yielded to my persistence. But there's no way I could've done a much higher density that way without some kind of incredibly resilient paper. Any insights would be appreciated.

So, I found the crease pattern for this on google. Whose it is, I'm not certain. I was drawn to it because it seemed pretty straight-forward, but it was actually really difficult to fold. I'm sure my paper didn't make it any easier. It was probably too small and probably not the best density. The first time I folded this, it was good on the front, but terrible on the back. At that point, I felt that I understood it well enough to do a much better version. The second attempt did come out much better, but really wasn't much easier. I really like this pattern. Pointed rectangles on the front. Octagons on the back. It's simple in theory, but complex to execute. Very elegant. All those fiddly little diagonals seem to wreak havoc on my paper. Honestly, I think it just needs bigger paper. That would probably make all the difference. Or a much sturdier paper. But I pressed onward and was able to complete a second attempt with a pretty good result.

I had found a tessellation and crease pattern on flickr that I was curious to fold. I did fold it. Twice. This isn't it. More on that next time. This is the pattern it inspired me to create. It's probably nothing new. It's pretty obvious to the grid. Nevertheless, it was new to me. It's full on winter weather here in the northeast, so my photos are not lit the way I would like, but next  springtime is distant dream. So we persevere. For a change of pace, I've been working with a square grid rather than my favored triangle grid. I find square grid tessellations of any real complexity more difficult to fold. Everything seems to happen in a much smaller space and is nestled so close together. And they always seem to need way more preceases. Even with a clear and perfectly feasible plan, there's quite a lot of struggle to get the paper to do what I want it to do. Maybe that's just my inexperience with square grid tessellations. This one, however, is...

It's about time I added a new origami tessellation. This one was as frustrating as it was satisfying. My paper was not cooperating, but I persevered. I've explored similar designs. This one took it a step further. It uses the smallest rhombuses natural to the grid to connect an array of stars that are formed from offset hexagons and the resulting triangles. When you fold an offset small hex twist small triangles naturally form. This creates the stars. A typical hex twist follows the normal grid lines of a triangle grid. These hex twists fold bisecting the grid lines. However, unlike traditional open-back hexes, they are the smallest hex available on the grid. The hex shape itself does follow the grid. It's only the twist that is offset. I actually have a crease pattern from my planning stage which I haven't yet photographed. That would probably explain it better than words can. I'll hopefully upload it soon. There are also larger triangles on the rever...

This is a slightly more complex variation on a previous tessellation that I did a while back. There are rhombuses, triangles and hexagons all working together. In my version the triangles and rhombuses are mountain folds, while the hexagons are valley folds. When I first began folding the crease pattern, I was just kind of winging it. I wasn't entirely certain where I was going with it. So I wound up with random mountain and valley folds. I later unfolded and refolded following the consistent pattern shown. I thought about folding it differently, where the genders of the folds in individual modules went in alternating directions in some kind of pattern. That would probably be really interesting, but the paper didn't feel strong enough and I didn't feel patient enough. Normally, when I think of triangle twists my mind automatically goes to the classic offset triangles that do not follow the standard lines of an origami triangle grid. But there are many pos...

I found the crease pattern for this tessellation using google. I'm a sucker for rhombus twist based flagstones.I would call this one a rhombus spread tessellation. It reminds me of Eric Gjerde's famous spread hex tess re-imagined to use rhombuses. It begins with your standard small hex based rhombus flower at the center. It then proceeds to repeat the rhombuses in a linear pattern off of the center starting points. I really like it. It was a pretty standard flagstone fold. Patience is definitely required.  If you use a hexagon as your starting shape the edges are difficult. As with other flagstones the fold does not naturally fit that shape. It's a pattern that fits very nicely in a smaller 32 pleat grid. The end result is pretty impressive. Kudos to whomever first conceived of it.

I spent a lot of time at work trying to suss out the pattern for this design. I'm not sure too whom it belongs. Maybe Origami Yonca. Maybe Marjan Smeijsters. I got  close a few times. But too many distractions and interruptions hindered the process. When I was able to really focus, I discovered it was very similar to a design I had already done. It used the same process that I had used to create my ringing bells tessellation . At last the technique came back to me. It's a relatively knew way of folding for me. Rather than twists. It's more of a compression. The overall composition has a lot in common with flagstones, but rather than using rear side triangle twists to reconcile the front, it relies on the geometry of the grid to compactify and nestle the shapes close to each other. Given a little quiet time, I was able to work it all out. It's an unforgiving technique. You need pretty sturdy paper. So even though I was able to map the crease pattern, it took m...

This one came to me after seeing and working on some other people's  similar, but different tessellations. There's this technique of folding toward and under or over a grid shape. It may have a name. If it does, I don't know it. It creates different possibilities from  classic twist folds. That's the method I used here. Small triangles and small rectangles overlap each other to form hexagonal rings. If you have a fairly sturdy paper, it's not too difficult to fold. It takes some time though. It's slow going. A lot of little detail work. The second photo shows the rear of the tessellation. This should give some further insight into the structure should you choose to attempt it. I don't have a crease pattern. I drew it for the first time on the sheet I folded for the result. It's not a complicated structure. It didn't require testing and planning. I started with a small triangle at the center. Then rectangles off of those points. Repeat...