Some interesting things can be done using simple triangle twists as the main component. In this case, I create an open back hex twist and then add some simple wings to it. I then use those wings in conjunction with the folds of the hexagon itself, to create a series of circular triangular twists that surround them.  It's a densely packed design. It's a little tricky to get the triangle twists to cooperate.  But overall, it's not terribly difficult to execute.  I didn't draw a crease pattern prior to folding this. Just did a small test on a little square of paper. However, should I remember, I will try to make one some time soon. When I do, I will update this post to reflect that.  The result on the reverse side is an interesting weave formation highlighted by 'halos' of the shapes from the font.  It seems to me there are still a lot of designs yet to be discovered that are based upon the humble triangle twist. Updated to add the crease pattern at the end of the

 This is a wonderfully simple design that really highlights the beauty of uncomplicated folds. It's trapezoids around open back hex twists. There are 1.5 triangle twists in the other gaps.  When I first mapped it out, I thought that the trapezoids were too close together and it wouldn't work at all. That I must've done something wrong.  But it looked logical as I'd drawn it on the grid paper, so  I went ahead with it and found it worked perfectly.  I'm a big fan of how he excels at nestling shapes together in unexpected new configurations.  This design was not difficult to fold. It also fits nicely on a 32 pleat grid.  My crease pattern sketch is included below.

 Another wonderful design by one of the origami tessellation masters. This one had a very apparent structure. Had no trouble mapping it out on some grid paper.  On the other hand, it was incredibly difficult to fold. I just found it very fussy to execute. Which, personally, I both love and hate.  I had to keep referring back to the original photo to keep track of the mountain and valley folds. But once I got the center situated correctly on my rendition, I was able to use that as a guide.  Basically, its center is an offset hex twist on the back with rhombuses on the front of it.  From there he adds two triangle twists to the tips and sides of each rhombus. Those triangles then form around an open back hex twist on the reverse side. Repeat as needed.   A brilliant structure. The crease pattern sketch I created is at the bottom of this post. 

 This is a flagstone tessellation that I came up with recently. I had the idea for the starting point and was determined to create a pyramidal pattern that could repeat outward from it.  It took a few tries to determine how the corners would work, but it came to together nicely in the end.  It consists of trapezoids and rhombuses on the front side. On the back side there are many triangle twists. This is pretty standard for a flagstone tessellation.  As with any flagstone tessellation, it is somewhat labor intensive. But overall, it is not hard to fold. I wouldn't say it's easy either, but it's pretty doable with a little patience.  I've been obsessed with triangular patterns lately. This is just one more example of what you can do with them.  The photo of the reverse side shows the dense array of triangle twists needed to complete the design.  I used 28 lb printer paper trimmed to a hexagon. It was folded into a 32 pleat triangle grid.  Other than trimming the paper in

 Here's a really intriguing tessellation that I found. I was fiddling around with right triangles around a hex twist and discovered that layout could be combined with small offset hex twists on the other side.  So at the center you can see that the right triangles twist around a standard hexagonal twist on the reverse side.  As you move outward toward their tips they twist around an offset hex twist on the other side. But only three points from the right triangles converge at that location. Along the other three axes there are small triangle twists on the back side.  It'll be more obvious in the crease pattern sketch.  There is a little trickery on the back side with getting the many triangle twists to work well together. Bisecting some of the folds is required. That is illustrated pretty clearly in the photo of the reverse side.  There's also an unlit view of the front, which offers more perspective.  Plus, I made a short video showing the tessellation rotating to back lig

 I finally got around to fully solving this tessellation. I had partially solved it in a previous attempt that I posted, but this time I took it all the way. Or at least as far as my paper allowed.  When comparing the original pic with my rendition, I can't really tell for certain if I recreated it in the exact same way. But the front configuration is the same.  As far as I could tell, it required a lot of squash folds where the intersections might otherwise overlap. The same could be accomplished by tucking one fold into the other, but the elegant solution would be the squash folds. Which is, what I'm guessing he would have done.  Now, my grid ran out for me to fully repeat the design, but I went as far as I could.  I actually found it easier to solve the back side and map that out and fold it that way. Your experience may vary.  I have a crease pattern that I drew. Since they were only partials, I didn't map the very edges in my crease pattern sketch as my paper had run o

  This is a fun one. A neat little example of one way you can fold rhombus twists in a linear fashion. It's much less complicated than most of the tessellations I've been doing lately. However, it does feature a folding technique that I rarely use. In fact, that I rarely seen used at all.  It's called a rabbit ear sink fold. I learned about it years ago in Eric Gjerde's famous tess book. I'm not a fan of the fold. They're kind of a pain to do, but they're sometimes useful for creating points. As is the case here.  It's a simple tessellation, but it's a cool pattern. I think so anyway.  Crease pattern is included at the end. 

 Surprisingly, I didn't have much trouble solving this tessellation by Arseniy Koom. It just kind of made sense to me right away.  Go figure.  It uses an interesting right triangle shape which I would like to explore for other possibilities.  Besides that, the other shapes are very standard. Open back hexagon twists and small hex twists.  It all comes together rather neatly.  I guess, technically, it's a flagstone. Since there are only those narrow seams between everything.  Also the triangles connect to the open back hexes in the same way you would normally execute a flagstone.  Because of this, the reverse side features a plethora of triangle twists. What I found unique about this particular tessellation is that some of the back side triangle twists are overlapped by other folds. That makes it somewhat difficult to get everything situated neatly.  It definitely requires patience and fairly sturdy paper.  My crease pattern is at the end of this post. 

 This is an insane flagstone tessellation that I came up with a little while back.  Originally, I only had the beginning of the idea. It was just recently that I was able to flesh it out to completion.  At the center is a triad of alternating rhombuses and triangles around a central triangle on the reverse side. The entire pattern is based on the fact that three sides emanate from the rhombuses, while the other three stem from the triangles.  Somehow, with a little persistence I was able to figure out how the two different patterns would coalesce.  It's a crazy intense fold full of what seems like endless shapes on both the front and the back.  At many points during the execution, it felt as if I would never finish. But finish I did.  The front is both many rhombuses and many triangles. The back is just an endless sea of triangles with a handful of rhombuses.  I do have a crease pattern that I need to upload. Will do that soon.  If you wish to fold it, be prepared to dedicate a lot

This tessellation puzzled me for a while before I realized that what I thought would be hex twists were actually triangle collapses. Once I realized that, it was smooth sailing from there.  In his post he had the second photo as his front. But I liked the other side so much that I posted it first and used it to inspire the title.  Essentially, it's right triangles on one side around collapsed triangles on the other. As you repeat the pattern you get the large hex twists.  I gave it a title for the purpose of this post. His post didn't have a title for it.  It wasn't too hard to fold. It wasn't that easy either. But his ideas are always intriguing and unique. Had I'd used nicer paper the right triangles (second pic) probably would've nestled together more neatly, but the other side (first pic) came out really great.  There's also an unlit version of the first pic as well as a basic crease pattern below. 

This is a linear origami design using trapezoids and triangles. Instead of your typical triangle grid tessellation that repeats circularly, this one is all horizontal and vertical repetitions.  The top of each trapezoid tucks into the base of the one above it.  The triangles collapses serve as a means to make the trapezoids repeat horizontally. The triangles tuck into each other the same way the trapezoids do.  I really like this collapsed style of tessellating the paper. It allows for far more repetitions in smaller space than classic twists.  As far as a crease pattern, it's probably not necessary. Like I said before, it's just trapezoids and triangles. A very uncomplicated design with a lot of repetitions.  I did a very quick sketch before folding, but it was kind of mixed up with other ideas.  If I remember, I'll draw a quick, new one and post it here later. 

 This tessellation is pretty simple in structure and yet, yields an impressive finished product.  It's just open back hexagons with  rhombuses tucked into them.  Even though the shapes are quite spread out, it still has a wonderful result on a small 32 pleat triangle grid.  It's one of your less intensive origami tessellations. There is not a lot of pre-creasing.  Once you get the hang of the collapses, it's a breeze to complete.  It is, however, important to work the reverse side as you go. You can't just fold the front shapes. Working the back side is essential to getting everything nestled nicely into place.  A crease pattern isn't really necessary. The shapes are very apparent. I do have one though. It's included at the end of this post. 

 This tessellation comes from my idea for intermingling trapezoids and rhombuses. I just kind of started with the central pattern and worked my way outward.  Collapse style tessellations such as this one offer a plethora of new ways to configure the various shapes you might choose to incorporate.  You can also mix twists and collapses in a single tessellation. This one however, is all collapses.  Collapsed tessellations are pretty easy to map out on grid paper. The connections between the shapes are pretty straightforward.  They can be a little tricky to execute. Especially on the back side. They have a lot of folds in common with flagstones, although they are not quite as intense. They also tend to result in a lot of shapes to fold. Even on a 32 pleat grid, you can often wind up with many repetitions. So patience is a must. All the work is in the preparation. By the time you've finished all the pre-creasing, you'll feel like you've done so much. But at that point, the actu

 This tessellation began as an idea for trapezoids around a collapsed triangle. As I was working the paper, it became clear that additional trapezoids were needed.  I began working three around the triangle center, but quickly discovered that additional ones were needed. With the central six sorted out, it was just a matter of repeating and using the grid to follow the geometry for how it would all coalesce.  It's a pretty easy pattern to fold, so long as you're okay with doing small triangle collapses.  I haven't seen it before, so it may be new. The negative spaces are large pyramids.  I've included my crease pattern at the end for those who might be interested.  There's also an unlit closeup of the back side to help clarify how it's folded.  .