This is a natural hexagon tessellation. All the folds follow the triangle grid.  I haven't come across a lot of tessellations of this nature. Or any really, other than my own.  They are a little simpler to fold than some, but they are not easy or for beginners.  The finished product is as interesting as any I've seen.  The actual execution process is more about working with paper curling up on itself than coaxing unnatural configurations.  I love all kinds of origami tessellations. They are all wonderful and interesting in their own right.  But these natural tessellations are more than worth exploring. 

 This is a tessellation idea that I had a while back, but hadn't brought to fruition. But at last, I've made it a reality.  It's open back hexagon twists with tilted rectangles nestled against their edges. On the reverse side there are 1.5 triangle twists. By 1.5, I mean the triangle twist that exists between a single pleat twist and a double pleat twist.  It photographed much more impressively than I thought it would.  It was kind of a pain in the ass to fold. Probably more so because it's spring/summer where I am. Origami is easier in the cold months. The paper is so much more cooperative and resilient.  But inspiration cannot be quelled by the weather. 

  Looking back over tessellations that I had folded years ago, I came across one by Lydia Diard that I did in 2018. Back when I was stull new to origami tessellations I followed her flickr and learned a lot.  While I was successful in understanding the structure of the design, it was pretty poorly executed. I also did not save any crease pattern or hint at how it was done. Arg! This led me to try to figure it out all over again. It was actually a little harder this time around because I'm not really familiar with her folding style anymore, like I was back then.  Nevertheless, experience with many different designers and styles was enough to carry me through to solving it for a second time.  It's a fiddly little folds design at which I do not particularly excel, but I forged ahead all the same.  This time I created a crease pattern with basic flow instructions. It's not really a fold that can be expressed fully in just a crease pattern. So I added some notes as w...

This is a tessellation by Arseniy K @arsenikoom that I solved. His version had more distance between repeats. It also featured a some rectangles joined by a triangle.  I chose to just do a straight up repeat of his central module. Firstly, because it would repeat better on a 32 pleat grid. I don't use paper that allows for larger grids. Even 32 pleats is pushing it with the paper I use. All my origami tessellations are folded with ordinary 8.5 x 11 printer paper. I use 20, 24 and 28 lb. papers, depending on the design and the time of year. 20 lb. paper works fine in winter, but not so well during summer months. Occasionally I use kraft paper. But kraft paper is difficult to fold because it's so thick. It also doesn't backlight well at all.  Back in the day, I used to just fold a triangle grid on the rectangular paper without trimming it. Nowadays I stick with trimming it down to a hexagon. It makes it quicker to fold the initial grid. It also makes it easier for my stubby f...

 I came up with this tessellation just fiddling around with collapsing triangles around an open back hexagon.  I remember having the idea to do this technique using regular rhombus shapes, but I have yet to follow through on it.  For whatever reason, this elongated shape compelled me to finish the idea and complete the fold.  There are no twists in this tessellation. It's all collapses.  The central collapse is a bit tricky. If you look at the crease pattern there are triangles up against the central hexagons that have to be mountain folded toward the center of the hexes. Similar to how the triangles are folded over the central square in a Fujimoto clover.   The  outer triangles are pinched closed.  The funny thing is, I often struggle the most with my own designs.  Often finding it easier to execute the creations of others. 

This is a variation on numerous rhombus flower twist tessellations I've encountered on google, flickr and instagram. In this case the hex twists and the rhombus twists are on opposites sides of the paper.  This yields an interesting center to the flower twists that I haven't seen before.  The center portion is also rhombus twists around a hex. They are just arranged so that the outer iterations spin correctly. Everything is pretty tightly spaced, so it's a somewhat finnicky fold.  The layout is very straight forward, but actually nestling all those rhombuses so close together takes some patience and some decent paper.  The reverse view is kind of interesting in its own right. 

 I've folded many designs by @gatheringfolds. I enjoy figuring out her tessellations and re-creating them. Did her Stars in Stars tessellation a little while back and this is another variation on that concept.  Change up the spacing on the same shapes and you wind up with a different design.   The interesting thing about these particular configurations is how the front and back sides are mirror images of each other.  Most origami tessellations have front and reverse sides that are entirely different.  Obviously, the shapes folded on one side determine what shapes are necessary on the other side.  Sometimes there is room for variation in reverse sides even when front sides are similar. However, with these triangle triad bases models, the back side and the front side are mirror images.  That certainly makes solving a little easier. 

This tessellation began with the idea for the central module. I was obsessing over doing some sort of circular design with alternating rhombus and triangle twists.  The single instance was easy enough to conceive, but it didn't work as a straight up repeat.  A little bit of work on some grid paper yielded a flatly foldable solution. Just follow the creases and they will show you the way.  The crease pattern is a little deceptive because some of the twists need to be folded over on themselves in order to make the design work.  Other than that, it's a fairly easy fold to execute. Nothing really tricky about it.

 This particular tessellation was one of those sudden ideas that just come to you out of the blue.  The front side are all natural shapes to the grid. No additional creases. Small hex twists with double length rhombus wings off of them.  The back side is open back hexes, but then the flaps are all folded to the centers. There are also small triangle twists to make everything flatten properly.  It was fairly easy to fold even with tightly spaced repetitions.  It was a tiny bit tricky to get the flaps folded into the centers of the open back hexes neatly, but nothing too bad.  It folds and looks like somewhat similar, but different tessellations I've seen and done, but I don't believe I've seen this exact configuration.  What's also nice is because it uses such small grid shapes you get a lot of repeat out of a small 32 pleat triangle grid.  A crease pattern is included at the bottom of this post.

 Figuring out and folding the creations of other origami tessellation designers is one of my passions. While coming up with my own creations is very satisfying, I tend to think, I'm a little bit better at reverse engineering the finalized ideas of others. Bonus: doing so usually provides inspiration for new ideas.  There are a number of designers whom  I follow and regularly try to solve and fold their models. Madonna Yoder aka @gatheringfolds, is one of them.  When I want to solve a tessellation that is intriguing, beautiful and satisfying, but isn't infuriatingly difficult, her designs are often what I choose.  In this case, I did her Dancing Pyramids Tessellation .  Apparently, I spaced it a little differently (as she informed me). Lol. That was unintentional, but just fine by me. As long as I'm able to solve the puzzle, I'm happy.  This particular configuration of a sextuplet of three triangle twists on the front and three on the back has a lot of ...

 Sometimes for inspiration I'll go into my old saved photos of tesses that I've found on the internet. Some are quite old and I don't recall how I obtained them or from where they came. One such photo I had saved caught my eye and I knew that I hadn't ever attempted to re-create it before now. So I thought I'd finally give it a go. The original design was more spread out and used a larger grid. The hexes and the rhombuses had a pleat of space between them. I had to shrink things somewhat to get it to fit nicely on a 32 pleat grid. This however, also made it a lot more difficult to fold the rhombuses around the hexagons. Then again, I've always been a sucker for tightly packed tessellations.  I didn't bother to create a crease pattern. It's a pretty straight forward fold. 

 In my previous post I alluded to a new tessellation that I came up with while trying to figure out an old tessellation I had folded several years ago. This is that new tessellation.  The other tess used triangle twists exclusively. In this one I switched the small triangle twists to be triangle collapses instead. The rear side actually looks nearly identical, while the front side is pretty different.  I also did some triangle with points on top and some with their points tucked underneath.