This is an open back hexagon twist based tessellation that uses short/wide triangle shapes to create some interesting geometry in the spaces between the repetitions.  The central triangle shapes are essentially a single edge of an open back hex twist.  I had a crease pattern, but I don't know what I did with it.  Will have to see if I can find it to add at a later date.  I really like the movement on this particular design. It almost feels like it's in motion, even though it's just a still piece of paper.  Coming up with it was pretty ordinary. Just decided to combine some familiar shapes in a different way. 

 This tessellation is one that kind of came to me quickly. I didn't spend much time conceiving of it. I am, however, quite pleased with the end result.  It has a similar look to some other tessellations I've seen, but I believe its architecture is different. That difference does make for some subtle variations in how it looks compared to the aforementioned similar designs.  It looks tricky, but actually, it's pretty frustration-free to execute.  The central points are small hex twists. From there, just some rhombuses and open back triangles. Repeat as needed.  The front has slightly curved right triangles.  The reverse side (second pic) is pretty interesting in its own right.  The crease pattern for this tessellation is at the bottom of this post. 

  This tessellation uses a combination of alternating rhombuses and triangles around small hexagons.  It's pretty dense and not an easy one to fold.  When I first mapped it out I had alternating rhombuses and standard triangle twists, but that idea was a little off.  You can see from the picture that the triangles actually turned out to be a little different than the usual kind, Which I actually thought was pretty neat.  I believe the geometry really wants rhombuses on both sides. I'll probably try it that way in the future.  Still, I'm pretty pleased with this configuration,  Crease pattern is at the bottom of this post. 

 This is a tessellation by ArseniyK. I haven't solved one of his in quite a while. His designs are quite sophisticated. They can be both difficult to figure out as well as next to impossible to execute. This one is no exception.  The front side didn't give me too much trouble solving it. However, the reverse side was a little more elusive.  I mapped out the front on some grid paper and was confident when I began folding.  As I went along it got trickier and trickier to get things into their proper places.  It was very late into the collapse that I finally realized I hadn't noticed a key element. I had been twisting the small hexagons on the back side not realizing that they needed to be stars. When I was nearly done with the front side, I finally saw it and was able to correct and adjust.  It's such an intense fold that my first attempt with semi-thick paper was a complete failure.  When I tried again with kraft paper, I was able to complete it. However, this paper does

This is 'Hybrid Hex Weave' by gatheringfolds. I do a lot of her designs because she's generous enough to share them with the world and take lots of photos. More photos makes solving the mystery a little easier.  I'll admit that I was initially a little puzzled by the natural triangle that occurs in this particular tessellation. I mapped it out just fine, but I wasn't entirely certain how to execute it.  Undaunted, I forged ahead. When the other elements were in place and it came time to actually make that shape work, experience took over and it nearly solved itself.  A lot of tessellations are weaves. Twists of triangles, hexes and rhombuses on the other side create a layered look on the opposite side. It gives the appearance of multiple pieces of paper interlaced, when in fact, it's all done using a single uncut sheet.  To look at the front of the design, it's not always obvious how it's constructed. When you can see the other side the structure is much

 This is a Joel Cooper tessellation called hex weave. I actually had the front photo for a while and fiddled with solving it, but got stuck and moved onto other things.  Some time later I came across another photo from someone else and decided to try that tessellation.  Turns out that second photo was the back side of Joel's hex weave.  Seeing the backside, there wasn't much solving involved. It was pretty obvious.  It was only after I started folding it that I realized that the two photos were from the same design. Pretty neat how that worked out the way it did.  At first glance, I thought it was standard open back hex twists, but I quickly discovered it was irregular open back hexagons. They're 1.5 pleats per edge.  Then there are rhombuses off of their axes.  When you go to sketch out the repeats you find  triangle twists in-between them.  It's a very elegant design.  My crease pattern sketch is at the bottom. 

 This is a tessellation that I discovered recently that builds off of what I call offset hexagons. A small hexagon that doesn't twist along the grid lines. Instead you twist it by bisecting the grid lines.  It's a technique that's used in many origami tessellations by many origami artists.  The second photo of the other side illustrates it pretty well.  In this case, I used that starting point to create right triangles emanating from it.  Since I couldn't just repeat the central module because it's asymmetrical, I used some triangles to make the transition to the next repetitions.  Originally, I was going to use small triangle twists, but instead opted for open back triangle twists because I thought it would work better with the paper I was using.  It was a soggy kind of day and this paper isn't particularly sturdy. I kept it as neat as circumstance allowed.  I'd love to try it again with the small triangles using a denser paper. I'd also be interested t

  The idea for this tessellation came from solving a few different ones by gatheringfolds. A different take on some common origami tessellation elements.  It features small hex twists with alternating triangles off of them. The triangles alternate between front and back.  It also has some pyramids and another common tessellation shape whose name I don't know. It's all illustrated in the crease pattern sketch at the bottom of this post.  It's a symmetrical tessellation. The front and back are mirror images of each other.  It feels very familiar, but I don't believe I've seen it before. That's not to say it hasn't been done before. Just that I don't think I've seen it myself prior to having conceived of it.  It's nice how many repetitions fit on a 32 pleat grid. 

 Contained is an origami tessellation by gatheringfolds. She is quite active on instagram and I often try to figure out her creations. Solving the puzzle of someone else's tessellation is something I quite enjoy. Honestly, I enjoy the process of solving them a lot more than I enjoy the actual folding of them. I enjoy that part too, just enjoy the solving a little bit more.  This was a tricky one for sure. Her generous uploads of many photos made the structure pretty easy to determine, however, the execution is a bit finnicky. It's very densely layered. All the shapes are quite close together. Sturdy paper is required.  The centers are open back hexagon twists. There are triangles off of their axes.  Each of those triangles connects to a small hex twist on the other side. That hex twist has a triad of triangles on the front. From there it's just repetition.  Not all origami tessellations require pre-creasing of all the folds. Sometimes I am lazy and just crease as I move out

 This is a tessellation by gatheringfolds that I solved. I can't remember what she named it. I went looking for it again on her instagram and I couldn't find it the second time around. I really tried. Several times.  So I just went ahead and gave it a name for the sake of titling the post.  It's a pretty interesting configuration. Hex twists at the center. Double triangle twists. Then a nice triad of around a pyramid.  Solving other people's tessellations is always a fun puzzle.  Once I've solved how to fold, executing it is also a pleasing exercise.  It's also a great way to find inspiration for your own ideas. Even if they take elements from other designs, you can still find unique variations.  My crease pattern that I worked out for this tessellation is at the end of this post.  There are some remnants of other tesses in the crease pattern photo. But I think it's still pretty easy to understand. 

This tessellation was created as I was working on solving a tessellation by gatheringfolds. I had figured out her starting point and the central module. It was at that point that I got lazy and decided I would just do repeats of that.  Later on, I did go back and did complete solving her full tessellation. I just haven't folded it yet. A post for another day! Inspiration comes in many forms. Sometimes, even laziness.  The repetitions on the first side are just offset rhombuses when you strip it down to its essence. It is, however, a nice exercise in folding 1.5 grid shapes. Those shapes between 1 pleat and 2 pleats can be useful in many ways. They can be confusing when you first encounter them, but they're not so very different from any others.  I like how neatly and tightly everything nestles together.  The other side has some nice narrow arms with triangle twists on the ends. I found those interesting as well, as they didn't quite twist in the usual way.  As usual, I have

 This origami tessellation was solved from a picture that I had saved to my google photos several years ago. I don't recall from where I obtained the original pic or to whom the credit for the design is due.  I believe I tried once or twice before to figure it out and was unable to do so. I only had a photo of the front side, so that made it a little bit harder.  I was kind of stuck on the idea that it was a small hex twist on the back to create the rhombus star on the front. That however, isn't the case.  When I wasn't even really trying, it struck me that it might be a collapsed star instead.  From there, it was pretty easy to solve it and finally fold it to completion. That was satisfying! On the reverse side the rhombuses twist in the opposite direction as the hex star.  As with any respectable origami tessellation, it is folded from a single sheet of paper.  I did trim it to a hexagon before I started, but there are no other cuts.  My crease pattern is included below. 

  This tessellation is unusual for me in that it's incredibly tricky. I came up with the starting point quite innocently and then it got way more complicated from there.  It began with a classic star around an open back hexagon and then went down an infuriatingly difficult rabbit hole.  By then, I was too deep into it to turn back. I had to complete it.  My first attempt with thinner paper failed.  My second attempt with kraft paper was successful. I just wish kraft paper took better photos.  I did my best to get some nice back light photos, but with such thick paper it's a struggle.  It's a pattern I've not seen before, so that's always rewarding.  My crease pattern is at the bottom. Attempt only if you're feeling particularly brave. 

 This tessellation was born from me thinking about another tessellation I'd seen by Arseniy K. I wasn't actively looking at nor trying to solve his. I was just remembering the central starting point and wound up with this variation. His had some extra triangles that I didn't use.  It's offset small hexagons circled by rhombuses. Then there are some triangles off of the tips of the rhombuses. At that point it all repeats. More rhombus are created on the backside by the layout of the repetitions.  It's a pretty tricky tessellation to fold. Definitely one of your harder ones.  I used some pretty thin copy paper and was obviously able to complete it, but it probably would've helped to have a slightly sturdier stock.  Have a crease pattern. Forgot to photograph it. It will be forthcoming in the near future.  Update: crease pattern image added at the end of this post.