So, I had this idea for a tessellation doing teardrop shapes pointing outward from an open back hexagon. I had it all plotted out and ready to go.  I started folding it and the center came out as intended, but then I kind of lost track of my reference points for what was meant to come next.  I had originally intended to repeat the central pattern.  Rather than just give up, I decided to improvise the rest of the fold. What I wound up with is the tessellation shown above.  A week later, I was able to fold the original idea to completion. That will be a post for another day.  Both designs use a starting point with which I'm quite fascinated. It involves folding a standard open back hexagon, but then you twist small, natural trapezoids off of it. They land so close that it kind of layers everything on top of each other. This in and of itself doesn't offer much to look at, but it opens up many possibilities for where to go from there.  You can see a dia...

 This is another right triangle tessellation. However, in this case, I decided to do a linear pattern.  I had this idea a while ago, but just recently worked out how to execute it properly.  It's a flagstone tessellation . Everything is nestled edge to edge.  The triangles connect to each other in both a mirror pattern and by offsetting for each new row.  As I was in the midst of folding it, it occurred to me that a really cool variation would be to leave bigger spaces between the rows. I think that would look pretty cool.  In this case, everything is tucked as close together as possible with just a lot of triangles on the back side.  It's a little more difficult than a typical flagstone tessellation because many of the folds on the back overlap each other. It works just fine, but it takes some finesse.  Crease pattern included.  Filed under: July 2025 Origami Tessellations

 This is a reverse engineer of a  flagstone tessellation designed by Joel Cooper. I do not know it's name. I was not aware of its existence until I was emailed by a reader (Jessie) asking for help solving how to fold it.  I sent them a couple of diagrams. The first of which, I thought at the time was good, but was not right at all. Sorry! The second time, I was pretty close, but later realized, it was still not quite there.  Finally, I decided to just try folding it myself to see if that could help me figure it out once and for all.  The mostly successful result is shown above. It's somewhat scruffy because I was still solving as I was working the paper that I used to fold it.  I will unfold it soon and use it to create a finished crease pattern. Then I'll upload it here.  The design is three interconnected rhombus stars which are surrounded by open back hexagons. The design is repeated by adding new triads of rhombus stars.  I found it a confusi...

 Here's a different approach to right triangle tessellating. It starts out with the typical center point of an open back hexagonal twist and right triangles twisting around it. However, moving outward I just looked for connecting axes. Then I mirrored those axes to create the connecting shapes.  This creates a much simpler design that is easier to conceive and also easier to fold.  It can be folded using basic paper. It's a busy pattern when backlit.  It's an intermediate level tessellation . It's pretty easy to understand. And not too difficult to execute.  The reverse side is also an interesting pattern of subtle tucks and large shapes.  You can use the crease pattern below if you wish to fold this particular original origami tessellation for yourself.  Filed under: July 2025 Origami Tessellations

 Here's a really interesting flagstone tessellation that I recently created. I used my 'Drunken Stairways' tessellation as a jumping off point for how to configure it. But while that used hexagons and trapezoids, in this case, I used hexagons and rhombuses.  It's kind of a back and forth pattern of the rhombuses situated around the open back hexagons. It repeats pretty straight forwardly.  It's not hard to do, provided you follow the crease pattern.  It does remind me though, of just how many possibilites exist in the combination of a handful of basic geometric shapes.  There are so many more patterns to be found. It's fun to think about.  Crease pattern included. 

  This original tessellation continues my exploration of ways to use right triangles. It starts off with the same set of six right triangles twisting around an open back hexagon. At that point the central design is repeated by connected opposite facing right triangles to the first set.  The short edges of the triangles are joined by tucking into small equilateral triangles. . This tessellation combines elements of flagstones, twists and collapses.  It's a somewhat difficult tessellation because the different methods of connecting the shapes kind of go against the natural flow of the grid.  When you're folding an origami tessellation that uses a singular technique everything sort of wants to work together.  When you mix and match methods, they don't always play nicely together.  It's definitely doable though. It's difficult, but not terribly so.  I have a crease pattern. I forgot to photograph it.  Will add it soon. Update: Crease pattern added. ...

 I may have done this tessellation before. I'm not sure. When you do as many tessellations as I do, you tend to lose track and ocassionally repeat yourself.  Update: Renamed this tessellation when I realized I had already used its first title for a previous design.  I tried to see if I could find an older version of it, but I wasn't able to do so. That doesn't mean that I absolutely haven't folded it before, but no matter.  It felt new when I did it this time around.  Better to fold it a second time than to possibly miss an opportunity to fold something new.  It's one of your easier to fold designs. It's a six-sided polygon with triangles twisting off of three sides. When you repeat that pattern you also create open back triangles on the reverse side. That's it. That's all there is to it.  It makes a pretty neat pattern though. A good tessellation for the intermediate folder to hone their skills.  I folded this back in May, but was hesitant to u...

 This is an original tessellation that I did a while back that has been languishing in my google photos waiting to be published. It's unusual compared to my typical designs. I don't recall how I arrived at it, but somehow I did.  It was a rather difficult one to actually fold. And I so happened to decide to fold it using 28 lb printer paper. Which, probably didn't help matters. It kinda works and doesn't work at the same time. I'm still not sure. I was able to get it done. It's a strange assortment of odd shapes and very closely tucked typical ones.  Looking at the crease pattern that I used, it's somewhat bizarre. But I like how it backlights.  Still I kinda wish I had used different paper cause it's not as neat as I would like.  Crease pattern below.

 This is a pretty cool little flagstone tessellation that I recently folded. It features several different classic configurations all rolled into one finished product.  You've got your six tirangles around a hexagon at the very center. Then there are some three rhombus cubes too. In addition to that, we also have some rhombus stars as well.  If I remember right, this was actually an accident. I had mapped out a different configuration where the center point repreats after some rhombuses flowing off of it.  But when I went to actually execute it, I drew out a slightly different (this) pattern on the paper. I didn't even notice until I had started the creasing process.  By that point, I figured, just go with what I have and save the other design for another day.  The crease pattern I created is for the other idea, which I haven't folded yet.  Not that I remember where I left it. Hopefully, I'll find it and be able to do the original idea. If I think of ...

This original origami tessellation is a little different from what I've been doing lately. It's nice to change things up occasionally.  It uses a technique that I learned a long time ago when I folded a tess by Arseniy K called razorblades .  It's right triangles situated around an open back hexagon.  However, in this case, I used that same central point, but changed the shapes that link up with it. I connected the right triangles via flagstone style collapses to additional open back hexagons. Then I repeated the center. In the remaining spaces the right triangles alternate around the hexagons in an interesting forward and back pattern.  I have a diagram. I'll included it at the end of this.  This is a difficult tessellation because of what needs to happen on the backside in order to make the front work.  In the razorblades tessellation there were large triangles to connect the repetitions. It was a very straightforward pattern. Because of the different...

 More fun with trapezoids in flagstone tessellations .  The idea for this was a triangle twist with three trapezoids spinning around it So even though the center is six triangles, that was just a way to make the shapes around the edges work.  Although, I would imagine that if you wanted to you could conceive of a design where the center point could repeat instead.  The six triangles with the trapezoids eminating out from it. That would be an interesting variation.  The back side is almost exclusively triangles except for the one center hexagon.  As far as flagstone tessellations go, this is one of the less difficult ones.  Crease pattern included.  Filed under: June 2025  Origami Tessellations

 This is one of your simpler ideas as far as tessellations go. A standard six sided shape with triangle collapses tucked into it. And repeat.  The main shape, besides the triangles. is a common one you might find it many origami tessellations. It consists of one cross grid crease, then one that follows the grid and continue until  you close the loop.  It's kind of a simplified version of the Bells tessellation I did several years ago using the same two shapes. In that case, I connected them using collapses, instead of tucks.  In that one there were only small triangles. In this one, there are small and open back triangles.  As you explore various shapes and folding techniques you'll find that many patterns can be recreated in similar, yet different ways. That's the amazing symmetry of the geometry.  Looking at the reverse side you can see the collapses of the small triangles as well as the larger ones. Because of the multitude of small triangle colla...