This is an idea I had. It's pretty simple, but yields a complex result. What I like best about it is that it's versatile. You can create several different tessellations from this one crease pattern. It's open back hexes connected by triangles. The triangles actually follow the folds of the classic grid. I have a sketch that I need to upload. (Update: crease pattern image added below) The hexes alternate directions. Some are exclusively on the back. Some totally on the front. Others go both ways. The triangles are all 2 mountain and 1 valley. What's most interesting about this tessellation is that it offers the folder choices. You can arrange the hexes in in many variations from front to back. I haven't explored it in great detail, but I did play around with the arrangements a little bit. It's pretty versatile. Different patterns emerge depending on how to decide your valleys and mountains. There's a flow to the mountains and valleys of ...

I found the crease pattern for this tessellation on flickr. It was a while ago. So I don't remember where exactly.  It may have been a Joel Cooper design. I'm not certain. Upon further investigation, I found it on my hard drive and it's filed it under Robin Scholz. So I guess he's likely the designer. I did change it. There were originally larger gaps between the triangle twist hex formations. I shrunk the gaps a bit. Made it fit in a smaller grid much nicer. This was an incredibly difficult fold. Super tricky. Diabolical really. At first glance it looked so simple and innocent, but it was anything but. The end result is pretty amazing. It gets exponentially more amazing the bigger the grid you use. Even though I folded it myself. And I spent several hours doing so. Looking at the end result, I still have a hard time believing that's just one square of paper. But it is. It truly is.

This is a pretty straightforward design, but I really like the results. It's no doubt been done before, but I conceived of it without having seen anyone else's prior. I attempted a 64 pleat grid at first, but found everything to be entirely to small to work. So I switched it to a 48 pleat. It was still pretty small, but just big enough for me to successfully fold. I printed a hexagon on printer paper. As large as would fit. Then divided it into thirds on one side. Anything smaller really doesn't do the tessellation justice, as there are insufficient repetitions. Small hexes are flanked by pointy rectangle shapes. The rectangles are 3 pleats from each axis of the central hexagon. Then just repeat. I found it easiest to fold by first reinforcing all the hexes. That made it much less frustrating to move outward from the center iteration. I was then able to fold at will any of the pointed rectangles and the hexes were quite willing to fall into place. The photos ...

 Here's an interesting tessellation. It's open back hex twists with regular triangle twists emanating from it. There are some strange shapes in-between to make the repetitions work together. I just kinda worked it out as I went. I'd love to offer a visual cease pattern. Unfortunately the only accurate one I have was what got folded into the final product. I'm not currently willing to unfold it, since it was such a tedious affair. Update: I recently (Aug 2022) solved this anew and created a crease pattern. The vortexes 2.0 tessellation has all the details.  The interesting part is when you fold over the flaps created by the triangle twists. It creates a completely different design. It was rather difficult to fold. Everything was quite closely packed together. I wasn't really sure it was going to work. But the final result was pretty pleasing.

 This is a flagstone variation. It uses a collapsed hexagon as the base and triangle twists to connect them. An interesting thing happens when you then fold over the available flaps created by those two twists. I have a basic crease pattern below. The inner hexes are valleys. They outer hexes are mountains. Rhombuses shoot off from that. They are mountains. Triangle twists create the transitions between. They are valleys. After you accomplish all that, you can then fold over the flaps created on the front to get the design shown. All the images are of the same tessellation. Respectively... front then back with back light and flash on the camera. Then back and front with back light and no flash.  It's a fairly simple fold that yields a very nice final result. A crease pattern is available in a future post where I recreated this tessellation. See <a href="https://www.solvingorigamitessellations.com/2022/08/spiraling-origami-tessellaton.html">Spiraling Tessellatio...

 This is a variation on a simple tessellation found in Eric Gjerde's popular book. The original tess consists of hexes and triangle twists. In this version I simply fold over the flaps that are created by the triangle twists. I experimtented with also turning them inside out. Similar to a Cooper tess, but I opted to keep it simple instead. It backlights very nicely.

 I saw this tess on flickr. I thought it would be fun and easy to fold and yield a nice result. I wasn't wrong. It was a little tricky to get done. The paper tended to curl up on itself a lot. But it wasn't anything aggressively difficult to do. It's small hex twists on one side. Open back triangle twists on the other. I found it most productive to move back and forth between the front and the back. When you begin to get those hex twists working it creates the veins around the triangles. Rather than just focusing on flattening the triangles, I used the veins to help ease everything into place. It actually looks somewhat different to the human eye than the camera is able to capture. The photos are similar to what you'll see. But it's prettier, in my opinion, in real life.

A Peter Keller flagstone. Dude knows his rhombuses. I got the crease pattern from his flickr. It wound up looking and folding different than I thought it would. For me, it was more difficult than some of his other flagstones. The transitions between the repetitions proved somewhat troublesome. By the time I figured out the nature of the connections, some were already too far gone to truly perfect. Origin Crease Pattern  I have been attempting to come up with some new original designs. I have a few in the works. We'll see how that unfolds.

I saw this tessellation on flickr. I'm pretty sure. I can't find it anymore. I don't know to whom it belongs. But I thought it was nice, so I went ahead and figured out how to fold it. It's a pretty straightforward design. It wasn't very difficult to figure out. It was a fun fold though. With a very nice end result. I have all these designs in my head which I'm struggling to bring to fruition. So it was nice to take a beat and just relax with something simple. I did do a single module crease pattern. I haven't yet photographed it. But will post it later. First pic is the front. Second is the rear.

Here's an interesting origami tessellation that I worked out. I struggled to photograph this in a way that showed its complexity. In the northeastern winters it can be hard to get enough light. Small hexes on the rear collapse into the next concentric hex on the front. From there open back triangle twist surround each. Off of the first ring of triangles the tessellation repeats quite simply. The next array of hexes lands directly off of that first ring of triangles. Similar to a flagstone tess. No spaces. The outer triangles of the central module are also edges of the surrounding modules. When the folding is complete that's when the hard part comes. Trying to arrange the flaps on all those triangles so everything flows in the same direction and lands neatly is a bit of a Machiavellian madness. I folded over one side of each triangle in a counter-clockwise direction. This created the pinwheels. Many of the fold overs do run into each other. But it is not difficult to m...

This tessellation was conceived as a doodle. I came up with the center first and then added the arms. To work out the flatness, large triangles were added on the reverse of the design. It's an open back hexagon twist center. Triangle twists off of that. Those pointy rectangles radiate off the triangles. Then there are offset open back triangle twists on the back to reconcile everything on the front. Also, the portion of the triangle twists that land on the hex pleats are valleys, while the other two sides are mountains. It's kind of a flagstone variant. I do seem to come up with very convoluted designs lately. I folded this using some large, standard origami paper and it was a nightmare. It took so long. But once the first two modules fell into place, I couldn't not take it all the way. Thicker paper would've sped up the process, but coulda, woulda, shoulda. The second image is a doodle of the crease pattern. That's how I determined the layout. In the do...

 This is an idea I had that looked a little better in the design stage than it turned out in execution. In hindsight, I maybe, should've left more space between repetitions. Or folded it more neatly. Still, I think, the design might have benefited from some spacing. Some dead space between the florets would've probably accentuated them a little better and made for a crisper fold. Hex twists on the rear and then overlapping hex twists on the front. 

Miniature stars all connected by criss-crossing veins. Smallest hex twist on the grid at center of star. Triangle twists fall as close as possible to the hexes. Each star is separated by two pleats. I had tried this design in the past and was not successful. This time all the steps fell into place quite easily. You'll need to fold the triangles individually and really enforce their creases. Then you can go about the task of collapsing each star one at a time. You will need to collapse each star as a unit. You cannot fold the hex and the triangles separately as they land too snugly. As you add stars out from the center the connecting pleats will not naturally lie flat. You'll need to bisect them for a flat tess.

So I found another interesting origami tessellation on flickr that I was pretty sure I could recreate. It was some basic ideas that were arranged quite cleverly in a really elegant final design. I started out trying it on a 32 pleat grid. It wasn't big enough and I tried putting the repetitions closer together, but they still didn't really fit. So I sucked it up and made a 48 pleat grid. I was able to print a fairly large hexagon on standard printer paper and cut it out. This yielded a somewhat larger one than I would've gotten had I used the fold and cut method of creating a hexagon. Still I wound up with rather small pleats and pretty tiny triangle twists. But I persevered. Eventually I got what is shown in the photo.

Robin Scholz Triphilia variation. I didn't even realize there were more steps... so I stopped wehre I did. Did the hex spread. Turned that into triangle twists. Folded over those flaps and inverted. I had been wondering where I'd first seen this design. At least I finally figured out its origin. It's a lot of folding, but worth it. And none of the steps are very difficult to understand. There's a final step where you squash the backside of the design. I didn't realize that. I'll need to try that at some point. It's a brilliant variation on a classic origami tessellation. Simple, yet complex. As any good tessellatin should be. Update: I completed the additional steps to recreate the true triphilia tess. Last photo shows it backlit. This is one of those tessellations that has many simple steps that take up a lot of your time. It really requires a higher level of devotion to the craft. The final result is pretty spectacular.