Here's a fun and straightforward origami tessellation that I knocked out fairly easily at work one day. Just a basic hex flower that repeats. On the reverse side it results in a stars pattern. For a simple design it has a really lovely end result. It's not difficult to see that it's just hex twists with teardrop shaped petals attached to it. To create the repetitions I simply added additional hex twists off the center that connected to the central axes. Only caveat is to leave enough space between to fit the petals of the repeaters. To the best of my recollection I left 4 pleats between. I wanted to leave more, but the paper size/grid size didn't allow for it. I actually saw a similar design that left more space between each, which looked really nice. But bigger grids required bigger paper or at the very least more patience. I was actually more struck by the pattern that formed on the back side of the paper. It was an unexpected surprise.  A gorgeous series of ...

I came up with this design and it was definitely legit from a structural perspective. All the folds worked together in perfect synchronicity. It's a very tight design though, so actually folding it was a challenge. At first I had the hexes and the triangles all on the front. While I was able to complete the central module, the paper was practically dust by the time I started trying to collapse the surrounding repetitions. So I decided to try moving the hex twists to the back of the design to make more room for the very closely packed triangle twists on the front. It was still very difficult to fold. But that did do the trick. It's definitely not a tessellation for the faint of heart. But after some maniacal persistence I was able to finally coax the paper into the places I wanted it to go. The funny thing is, it's a very humble looking pattern when you first draw it out. It looks like it will be easy. But because of the way the triangle twists overlap one another...

 This is another tess that I found online. I believe I found it somewhere on flickr. So... someone else's concept. They didn't provide a crease pattern or instructions. At first, I was overcomplicating it. Then I tried drawing out the pattern, including the shadow effects. That's when it became clear to me. Arranging the hexagons as they did in a 3D cube pattern has quite an impressive effect. But, the folding of the design, is actually quite basic. There's really only one technique involved beyond the usual triangle grid. The last image shows a rudimentary crease pattern. It's simply large hexes all connected by triangles. To fold the design you perform a sort of waterbomb fold on each triangle. That enables you to flatten the hexes. The lines in the triangles that surround the central hexagon illustrate how to fold them. You squeeze together the outer edges of the triangles in mountain folds collapsing along those inner vertexes as valleys. If you lay ...

This is a fun design that was inspired by a Lydia Diard design I folded not long ago. It's a similar structure. It begins with an open back hexagon twist at the center. That is then surrounded by more hexagons. The interesting part is how they connect. Single pleat veins are squashed and flattened where each corner of the central hex meets the surrounding hex petals. This creates the appearance of another layer hiding behind the hexes. The hexagons can continue tessellating out from each other infinitely. This design would be really stunning applied to a larger grid. The front and back of the design are shown. The third image is a very crude crease pattern formation. It illustrates pretty clearly how the vertices of the hexes are flattened and connected.

This is a tessellation I attempted to recreate that I had found somewhere on the Internet. You can find lots of them, but many lack crease patterns or instructions on how to fold. That's become a fun new aspect of my origami habit. Trying to figure out how to recreate tesses from their folded pics. I really like how this one looks when I take the photo with back light, but no flash. This technique really brings out the structure of the folds. Giving a 3-D appearance to otherwise flat designs. This is a flagstone of large open back hexagon twists on one side connected by their surrounding triangle twists on the other side.  The second photo shows the reverse side of the same design. The third photo is a very basic crease pattern I created on a smaller piece of paper with a much smaller grid. It's simple, but should be quite helpful to those familiar with this form of origami. That's generally how I suss out the larger designs. Figure it on a smaller scale and...

I saw this tessellation somewhere. I can't remember where now. But I liked it enough to figure out how to fold it. Little did I know when I started that it was a flagstone tessellation. I should've known, but I didn't find that out until I started puzzling out its construction. . They can be a pain. And this one was. There was a lot of pre-folding. That was 90% of the work. After that, it was a matter of slowly coaxing all those pre-folds into their proper places. It was not an easy task. It was however, a very pleasing result. It's a series of hexagon twists on the back of the paper. Then you go to the other side and surround them with rhombuses. Some large triangles allow everything to lay neatly together. The gender of the folds was quite important in achieving the final collapse. Having the right valley and mountain folds was critical. The hexes had to go to the back. The rhombuses had to go to the front. The connective triangles also had to go to th...

 Here's another Peter Keller flagstone. The challenge of folding flagstone is quite appealing. it requires a lot of patience and persistence. Even after you fold the standard grid there are still many more folds to add. It's a whole lot of prep work before you ever begin the actual creation. That's probably true of most origami tessellations. All the work is in the prep. Then you allow that work to pay off in your resulting collapses. With flagstones you also have to work both sides of the paper. The design will have triangles on the back that need collapsing in order for the front structure to work together. I am always grateful when origami artists publish their crease patterns. And Peter has many published on his flickr account. The one for this design can be found at: https://www.flickr.com/photos/syngola/4968245966/in/album-72157624777290209/ To me it's small pointy stars which are surrounded by much larger flower like petals. I mostly work on a 32 iter...

This tessellation consists of hexagon twists surrounded closely by open back triangle twists. The back lit versions are neat, but I actually think the unlit versions are more beautiful in thise case. That's just my preference. You may see it differently. It's interesting how the triangles in the front images form star shapes around the central hexagons.  There are similar designs out there that use a combination of hexagon twists and open back triangle twists.What's different in this case is that  they've been laid out as snugly as is possible. It was a fun fold. Not terribly difficult, but just tricky enough to make it feel like a genuine accomplishment.

I saw this tessellation on Lydia Diard's Flickr page and I really liked the pattern. It's simple, but elegant.  It was pretty easy to reverse engineer. It's based on a 32 division triangle grid, but you need to add additional folds to connect the hexagons. This is most apparent in the second photo. Those connections will not naturally flatten. They need to be spread squashed. After some trial and error with how best to achieve the desired result I arrived at the following method. I first folded all the large hexagaons. Reinforcing the creases and then unfolding. Then I folded the narrow sections that would connect them. At that point it was easiest to pinch the corners of the hexes while spread squashing the connecting veins. Using the grid to help create pointy sqashes at each axis point of each hex. If you're familiar with tessellating and intermediate origami techniques it should not be hard to figure out as you go. The first photo is the front ba...

 This tessellation is the result of repeating as closely as is possible the classic dual hexagon collapse. You have the smallest hexagon and then the next largest concentrically. The small hex is a valley fold and the larger on is a mountain. You collapse the large one on top of the smaller one and flatten. It's a pretty standard origami maneuver. In this case I just repeated it as often as possible on a single sheet of paper. It's very similar to the spread hex tessellation. In the middle I  squashed the flaps that formed from the collapse. You wind up with a lot of overlapping pleats that you can arrange as you see fit. Or you can do some more squashes. They can also be turned into triangle squashes. The other side gives off a nice star effect as seen in the third image. To create the crease pattern simply layout the concentric collapses in offset rows with one pleat between each repetition. All of the folds, except for the squashed on the central star, conform...

 I was trying to reverse engineer a tessellation from Lydia Diard. I'm still not sure how I figured out the steps to recreate it, but somehow I was able to do so. Just folder's instinct I guess. I did a mini one flower version to figure out the basic structure. Then I did a bigger version where I screwed up the tiling. That version led me to discover how to properly tessellate the design. Her flower iterations were a little bit closer together though  Wish I'd done that. Then I could've had whole repetitions around the edge. Funny thing is, although it's a pretty simple set of folds, it was quite difficult to execute. Or it was for me. Once I did the central portion, it was not easy to do the outer iterations. You can't really flatten the paper during the process. So it's not easy to keep previous folds intact while you're working on new ones. Some of the fold are quite small. So prefolding, unfolding and refolding wasn't a successful ...

Peter Keller's flagstone weave tessellation. This one is really tightly packed. Definitely not for the impatient folder. It takes a lot of finessing and coaxing. I folded, unfolded and refolded so many  times before I was able to begin collapsing the design. Including folding the initial 32 pleeat grid, I probably spent 10 hours all together folding this design. It's hard to know exactly, since I was at work and kept getting interrupted. Suffice it to say, it was a lot of hours before I achieved success. They were enjoyable hours well spent though. It was an easy crease pattern to understand, but a challenging one to fold. I was pretty uncertain for a while that I would finish. I used some ordinary colored printer paper that wasn't very forgiving. It seemed like the papper was going to give out and just go limp and useless. Still, after so much folding, I kept at it. I had nothing to lose. To my surprise, eventually the paper began to cooperate and I was a...

This is similar to a design I was trying to conceive. Almost identical, except my hexagons were smaller. It's a typical flagstone that uses triangles on the backside to 'push' the front twists together. Flagstone tesses result in beautiful backlit pictures. They create optical illusions of three dimensions. The front and back also present very different patterns. https://www.flickr.com/photos/syngola/4967646805/in/album-72157624777290209/ What's interesting about flagstone tessellations is that they are pretty different from standard tesses. Even if you're familiar with the spread hex or other like designs, the flagstone genre is a unique variaation that will require you to learn new techniques in order to fold it. Typical tessellations are folded a few pleats at a time and flattened as you go. It's a progressive, linear process. For a flagstone the easiest way is to sure up all the creases and then unfold. Refolding/collapsing in clusters of single...

Lady's Flower tessellation. https://www.flickr.com/photos/praisepratajev/5526816483/in/album-72157627404378271/ Hexagons surrounded by closely grouped triangles. Looking at the crease pattern, I wasn't 100% sure how to fold the all of the triangle twists. Some seemed to be too close together. But once I got a good portion of the tess folded it became more obvious how some of the triangles rotated to fit into the design. A pretty easy fold compared to similar designs.

Here's a single module version of a crease pattern which can be tessellated infinitely. It's a flagstone tessellation designed by Robin Scholz who posted the crease pattern here .  Flagstone tesses are interesting in that you kinda need to precrease and then assemble all at once. Unlike more traditional tessellations where you simply fold a small portion and then continue folding small portions, flagstones don't lay flat in the intermediate stages. Each twist is dependent upon the other twists which emanate outwardly from it. Or at least, that has been my experience. They are a lesson in patience and persistance. On large grids with many twists it can get kinda crazy. Still, the results are worth it. Little girds like this one are great practice and still pretty interesting when complete.