This is a tessellation from quite some time ago that I don't think that I ever posted. Not sure why. It's a pretty cool pattern. It's similar to my 'Space Invaders' tessellation , which some people really seem to like. So perhaps, this one will be of interest as well.  So, it starts out with an open back hexagon with right triangles around, just like 'Space Invaders' does. But then, I tuck the short edges of the right triangles into each and that's how I get the repeats.  There are not so willing rhombus twists in the gaps, but it does work.  It was difficult to get a good photo because of the dark color of the paper, but the full size image is decent.  This design kind of takes some liberties with what I would call a flat fold. It doesn't really twist neatly or as expected, but I managed to make it behave. There are a lot of micro triangles which make it an advanced fold . The finished pattern is worth the trouble.  Crease pattern included.

 This origami tessellation from several months ago is a much simpler variant of another that I did back in August 2025 called Proximal Measures .  It uses the same starting point of parallelograms twisting around a small hexagon on the other side.  Then I add some triangle twists off of the tops of the parallelograms. Some large triangles fill in the gaps between the repeats.  Although I conceived of it in the reverse, I have the hex side as the front and the parallelogram side as the back. Just because I like the one side more.  I don't still have the original crease pattern. But I will try to remember to create a new one and add it soon. Update: added crease pattern.  Filed under: March 2026 Origami Tessellations . Although, it was probably done back in August or September 2025.

  Was messing around with a technique that I'd seen many years ago, but had never actually done myself, until now.   Essentially, it's collapsed hexagons and then you use the flaps to create little pinwheel shapes. This is much more evident in the second photo.  Then I added a whole bunch of triangle twists simply because it was possible. Because, why not, right? This is also shown in the second photo.  The entire tessellation was conceived of as shown in the second photo.  But when I was finished and took the pics, I really liked the other side (first photo) much better. It happens to me a lot.  I don't think that I ever drew a crease pattern for this. I did a little mini tester of the center and then just went for it with a full size grid. Freestyle.  I'll try to remember to unfold it and add a diagram sometime soon.  Filed under: March 2026 Origami Tessellations

 This tessellation uses rhombuses twisting around an offset hexagon. Then, I add parallelograms overlapping the rhombuses. Because, why not, right? Next come open back hexagons tucked into the parallelograms. And some triangles tucked into them.  It's at that point that the pattern repeats.  This is an intermediate level origami tessellation . I had a hard time with it because I did it on a very rainy day. But even with soggy paper, it all worked out just fine.  Looking at the back side you can see how the triangles tuck into alternating edges of the open back hexagons. You can also see how the triangles are connected to each other.  It's a pretty straight forward pattern. If your paper behaves anything like mine did, it's going to fight you on staying in the collapses. But, keep working them. Your persistence will pay off. Crease pattern included. 

 This is a another flagstone tessellation that I did a month or two ago. I was exploring rhombuses interacting with parallelograms and did several that played around with those two shapes.  This one is simply alternating them in a linear pattern. I like how the rhombuses form rows of diamond shapes between the parallelograms.  It's not hard to fold at all. It's very basic for a flagstone .  Don't have the original diagram anymore. Will try to remember to add one soon.  It's pretty simple to reverse engineer, though. Just follow the shapes.  Other side is all triangles. 

 I did this flagstone tessellation probably at least few months ago. I don't think that it's been uploaded previously.  It's a linear style pattern of triangles and rhombuses. I did two rows of rhombuses and one row of triangles. Looking at it, I wonder why I didn't just do one row of each.  Another nice variant might be to change the direction of the rhombuses as the rows are repeated. Something for another day, I suppose.  It's a pretty typical flagstone tessellation . Everything is connected on the back using triangles.  In my opinion, linear flagstones are easier to fold than the circular kind. The shapes just seem to fall into place with a lot less coaxing. That's just my experience.  I doubt that I still have the original diagram. It's pretty easy to decipher. Just connect the shapes on the front in the usual way and add triangles in the gaps as needed.  Still, on principle, I will try to remember to draw a new crease pattern for it and upload...

  This particular tessellation was kind of a let me see if I can do it sort of idea. I knew that it wouldn't be one of those pretty design. It's just an exercise in execution. Several layers on top of each other that make sense in theory, but are rather difficult to make happen.  I did make it happen, for the most part. It turned out as expected.  It's from quite some time ago. So, I don't remember too much about it. Don't have my original diagram.  I do know that it starts with open back hexagons. And then I add those very small natural trapezoid off of them.  I think that I added some rhombus twists after that. Not entirely certain. I will have to unfold it to be sure.  If you're interested in testing how much stress your paper can take, this one will do it.  If you want to see how many layers of folding you can successfully wrest from a single piece of paper, this one is for you.  It's absolutely an advanced tessellation . A test of your mettl...

 Trying to keep things not too repetitive... so I have a somewhat different tessellation this time around.  The idea of small natural rhombus stars is not a new concept. I've done some in the past. Lots of other people have done them as well.  I'm not sure whether this particular iteration is unique or not. Unlikely, but who knows. Not me.  It was, however, new to me.  In this case, they have a hexagonal like connecting points between them. Which actually makes it very simple to do the repeats.  I left rather large gaps figuring that would help me create a neater finished fold. They could, of course, be spaced much closer together if desired.  It's not an easy fold because you have to twist the little rhombuses around the hex twists on the other side.  I've done these types of tessellations with both thick and thin paper. Either one works depending on how delicate you are as you work it.  There are a significant amount of overlapping folds...

 This intermediate tessellation is from a while ago. It's from my layering phase. It seemed like a really cool idea when I mapped it, but I wasn't that thrilled with the final product. Which is probably why I didn't upload it when it was new.  I recently found it in a box of old tessellations and noticed that it hadn't been posted. Just because I'm not that thrilled with it doesn't mean that someone else won't like it.  I like the concept... I think I just chose the wrong color paper. That doesn't seem like a very important decision, but it can have a big effect on how the finished model looks and photographs.  The center is rhombuses tucked into each other. Then I add trapezoids tucked on top of them. All well and good so far. It gets a little strange after that.  I add opposite facing trapezoid and repeat the center. The remaining gaps have an odd assortment of shapes. There are natural triangles, double wide triangles and tall isosceles triangles....

 I had the central idea for this tessellation a week or two ago. But, I had some trouble determining how to repeat it. Eventually, when I wasn't even really thinking about it, it finally came to me. That was so satisfying.  And I  was finally able to fold it to completion just the other day.  The crux of the pattern is trapezoids weaving around rhombuses.  It's not too difficult to fold . It just requires a lot of prep.  The back side is nothing remarkable. Just a whole lot of triangles.  My crease pattern is below. 

 I thought that I had already added this tessellation , but I couldn't find it here. Probably had trouble getting a good photo and then it got left behind. It's probably from a few months ago.  It's here now though, finally.  It's a fun little flagstone . Center is a pinwheel of trapezoids. Then I add another trapezoid vertically with the opposite orientation and connect them all in the same way. This creates a large pyramidal shape where a large double sized triangle can be placed in the middle. And repeat.  It's one of your simpler flagstone designs , but it's a pretty neat pattern.  I don't have the diagram anymore. Still, it'd be very easy to map out. Just follow the shapes. On the reverse side... small hex twists at the centers of the pinwheels. All small triangles everywhere else.  If I remember, I'll sketch a new crease pattern and upload it. Update: drew a new crease pattern. It's at the end.

 I've been meaning to post this tessellation for a while now. It's very different from my usual modus operandi. Or it looks that way at least. It actually uses fairly common shapes and techniques even though it looks like I did something crazy.  The central shape is your typical open back hexagon. It's twisted with small natural trapezoids off of it. Then there are six sided triangle shapes to connect the next array of repetitions.  Because of the way things are connected everything on the back kind of lands on top of each other. And with the multitude of layers it has, it is very hard to flatten. But it can be done, sort of.  The first time that I did this origami design I used larger connecting shapes (as reflected in the crease pattern below). And I also folded over the hexagons on the back into their centers thinking the design would flatten better that way. It did, but it altered the look considerably. I didn't really like how that turned out.  So, I deci...