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...

This tessellation is probably from at least a few months ago. If I remember correctly, I had trouble getting a good photo of it and then kind of forgot about it.  Anyway, I found it. Thanks to a power outage during the snowpocalypse. I went combing through my folds to see if there were any that I'd neglected.  It's a somewhat unusual configuration. Which are my favorite kind.  The center is a classic set of six triangles wrapped around a small hexagon on the other side. Then I connect vertically facing right triangles to them. Next, I add opposite facing right triangles and repeat the center.  In the gaps, I found that I was able to add open back hexagons in a tucked format to complete the design and flatten it.  It's definitely not my most precise fold. It could use some cleaning up in the seams. But the idea is sound and the concept is unique as far as I know.  I kind of wish it could be folded with thinner paper. It looks like it would back light nicely...

 Here is a very recent flagstone tessellation that I created.  I've been messing about with trapezoids a lot lately.  A lot of times I have the beginning of an idea and it takes a little while to bring the whole concept to fruition. In this case though, the pattern came to me out of nowhere and solidified pretty much  immediately.  It's kind of nice when it happens like that.  It's an interesting series. Or, I think so, at least. The pattern stands out when you look at it vertically. A rhombus with a trapezoid at the top and the bottom. When that repeats, it does so one shape shifted upward or downward.  I've actually found a few other patterns of a similar nature that I've yet to fold. Hopefully, they will be coming soon.  I remembered to take a photo of the crease pattern after I had completed folding this tessellation . So you'll find it below. 

 This is an unusual flagstone tessellation that I came up with a little while back. I, then promptly forgot that I had already folded it and proceeded to fold it again a couple weeks later. That's what I get for not uploading things promptly. If I had, I would've seen it here and known that I'd already done it.  Still, it was kind of a fortunate mistake because it came out much better the second time around.  What makes this particular tessellation interesting is that I used isosceles triangles attached to open back hexagons, but then doubled them up. So they look like rhombuses that have been bisected.  From there, it's just some triangles and repeat.   It's a difficult one to fold. There are a lot of overlapping things happening on the back of this one. It's hard to get narrow gaps on the front because of this. But it can be done with some persistence.  Looking at the finished tessellation , I'm confident that there are numerous other possibilitie...

 Here's a new twist based original origami tessellation that I just completed the other day. It's pretty simple . I needed something to do on a rainy day. Thin paper and uncomplicated tessellations are perfect for those soggy days when more complex tesses just won't work.  Turns out if you connect six trapezoids to each other you get the central molecule seen above. It was a discovery to me.  From there I just added some small hexagons and repeated the trapezoids.  Where I had some additional corners, I added the triangle twists just for fun. They're not required. You can just leave the corners.  The reverse side is kind of neat. Lots of intersecting and tucked shapes.  I don't currently have the crease pattern for this tessellation . I only worked out the center before hand and kind of figured out the rest on the fly.  But I'll unfold it and add one sometime soon. Update: crease pattern added. Filed under: February 2026 Origami Tessellations

 I had totally forgotten about this tessellation. Honestly, I've probably forgotten many. Hopefully, I'll rediscover them again soon. They're all waiting in a pile for me to do so.  This is a sort of unusual flagstone . Which I've just realized that I have done before. I did it in purple paper then and called it interlocking diamonds .  I was sure as I was folding this one that I had done a similar, but different tessellation. Using all isosceles triangles and no rhombuses.  It's possible I've done that as well, but I can't seem to find it. It's also possible that I thought of doing that, but decided it was too hard. I might've also done it, but didn't like the finished product.  At any rate, it looks way better done with white paper. It backlights really well.   The crease pattern already exists in the original post.

 Something much less intense. Just some fun with classic twists. A bunch of triangle twists and a bunch of rhombus twists in a slightly strange configuration.  Some of the triangle twists are hidden. You could do corners instead, but I like how it looks with the hidden triangles.  Back view is kind of interesting.  This is an easy tessellation . Sometimes it's relaxing to just breeze through something simple.  I meant to fix the edges that aren't quite matched, but apparently, I forgot. Had to upload it anyway. Trying to catch up. So far behind on adding the new stuff.  Crease pattern is included below. I'm pretty sure this is the right one. Do let me know if it's not.