I'm very far behind on uploading new origami tessellations that I've completed. There are a lot and I hope to steadily catch up in the near future.  I've been doing so many lately that it's sometimes hard to remember which goes with which diagram or how I arrived at that particular idea.  This tessellation is one of those that I don't really recall. It's certainly an interesting finished product and I'd like to remember how I got there.  I was searching through my photos for a crease pattern and couldn't find one. I guess that I forgot to take a picture of it.  Still, I wanted to add it here before it gets any older  and my list of things to upload gets even longer.  I will look for the crease pattern and see if I can locate it. If not, I will unfold the tessellation and create one from that. Because, honestly, I'm curious to find out how I came to create it.  I do remember that I conceived of it as the second photo. However, upon completion...

 When I did my 'Rotational Discretion' tessellation , I mentioned that the same pattern could be done without leaving any gaps. This tess is the fulfillment of that assertion.  At first glance, your eye might be drawn to the center where you'll see a six pointed rhombus star. However, if you change your perspective just a little you might see the series of multi-shape triangles rotating around the center. They are comprised of 3 each of rhombuses and small triangles.  As the tessellation repeats the same thing occurs. You get those six rhombus stars, but at the same time each of those rhombuses is a single piece of the larger multi-shape triangle patterns.  It's an interesting study in how the shapes of the grid can create and be a part of more than one pattern at the same time.  This is a difficult tessellation simply because all flagstones tessellations are. But once you get the hang of them, doing more and more, they do become much easier to execute....

This is one of my typical crazy twist tessellations. Whenever I try to come up with twist based original tessellations I always wind up with wacky configurations that overlap in unusual ways.  I really hit upon something interesting though, with this one. I found a three triangle tuck that works with very closely twisting rhombuses.  There are some really cool things you can do with rhombuses and triangles if you're willing and able to execute some unusual overlaps.  This is a difficult origami tessellation , if only because those triads of triangle twists are not for the faint of heart.  But it's also a relatively natural tessellation. The paper and the grid were pretty willing to accommodate it.  I didn't have too much trouble with it even though I used basic printer paper.  The back view of this tessellation is rather unremarkable compared to the front.  My diagram for how I folded it is below.  Filed under: August 2025 Origami Tessellations

 This original origami tessellation is a little different than my usual. It uses isosceles triangles in a triad pattern.  It's a somewhat difficult tessellation . There are a lot of small and fussy folds. At the same time, it's a pretty simple pattern. That could probably be said of many origami tessellations.  Another way to describe them would be to say that they are the edges of large hexagons. Their long side spans  two natural small rhombuses of the triangle grid. The two shorter sides follow the grid.  I positioned them around a triangle twist so that they collapse to form a larger triangle.  In order to repeat the pattern, they alternate around a small hexagonal twist. This principle is illustrated much better in the crease pattern included at the end.  The final piece of the puzzle are the shapes that form in the remaining gaps. They are slightly unusual, but not undocumented. They do appear, here and there, in various other tessella...

 This is an interesting variant on your typical flagstone tessellation . I arranged a series of three rhombuses and three triangles into larger triangle shapes. Then used a wider spacing to repeat the pattern so that they stand out more than if they were tucked closely together.  I have done other tessellations using this same configuration in different ways. Although, I don't remember their names in order to reference them.  Everything could theoretically be tucked right up against each other for a different take. I or someone else may or may not have already done that. I can't quite recall for sure.  Either way, I think the wider spacing makes for a pretty neat design.  I would classify this as a lower level difficult tessellation . Good for intermediate folders looking to advance their skills.  The back side of the tessellation is an intriguing array of closely tucked rhombuses surrounding triangle twists at each center point.  It's easy to forget w...

 This original origami tessellation idea is based off of natural parallelograms around collapsed hexagons. From there, I realized I could add small triangle twists that land between their top edges.  Originally, I mapped it out to be spaced further apart to make folding it easier. Then, I realized if I pushed everything closer together I could fit complete repetitions on my 32 pleat grid. So, I went with the denser configuration.  I used basic printer paper, thinking it would make some of the tinier folds a little easier to execute.  In hindsight, I think that a stronger paper might've been more suitable.  One side came out very nice, while the other could've been better.  If you want to try to fold it, I'd recommend a sturdier stock.  Crease pattern included at the end.   The crease pattern shows my original, more widely spaced concept. The little t's show where I moved the repeats closer.  It's a somewhat difficult tessellation , more...

 This tessellation is a very simple idea that I really can't believe I hadn't thought of before.  It's two classic configurations combined into one complete flagstone design .  The pattern alternates between six pointed rhombus stars and six triangles around a small hexagon. That's it. That's all there is to it.  My 32 pleat grid didn't allow for too many repeats, so I just tried to create clean edges. But it could keep going on a larger grid.  My original diagram that I used to start wasn't totally accurate, so I adjusted as I worked the fold. I will add an accurate crease pattern sometime soon.  It's a somewhat difficult tessellation to fold. Because all flagstones are sort of difficult. But it's nothing that can't be done with a little bit of patience.  Updating to add crease pattern... Filed under: August 2025 Origami Tessellations

 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

 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. ...

 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 an odd little tessellation that I recently created . It was conceived of as a collapsed hexagon to which I then added a multitude of triangle twists.  It became quite messy with so many triangles overlapping each other everywhere.  However, as I was folding it, what I discovered was that the other side became an interesting set of unusual shapes in a flagstone style pattern.  It's bascially a small hex flower with oddly shaped petals. Then there are open back triangle twists to connect the repetitions.  I was so focussed on all the various triangle twists on the other side that I didn't even really consider what might be happening elsewhere.  I used thin printer paper thinking it would be easier to fold all the overlapping triangle twists. Had I taken a step back and seen what was happening on the reverse side I mgiht've opted for a sturdier paper and gotten a neater finished product.  It's a somewhat difficult tessellation to fold because of how...

 This is a linear flagstone tessellation that I just recently created and folded. The idea for it came to me while I was thinking about some other tessellations that I've done that use trapezoids in an alternating directional pattern. And I thought to myself, what if I could do something similiar in flagstone style. And this is what I came up with.  Essentially, it's a cantilever pattern of trapezoids and hexagons.  Some might feel it's a difficult tessellation . While others might see it as only intermediate . I always find flagstones rather intuitive to fold. Sometimes it almost feels as if they sort of fold themselves.  But while the bulk of the folding process might flow rather smoothly, actually getting everything tucked close together can be a completely different situation.    If I had an iron, I would probably use that. But I don't have an iron, so I just use a heavy book and a dumbell. But not before I've spent far too much time pushing and cajoli...

This is a collapse based origami tessellation that I created pretty recently. It's all interlocked rhombuses and triangles in a back and forth repeating pattern.  This style of tessellation can be pretty difficult to do when using small shapes. Collapsing a multitude of small triangles requires patience and persistence.  On the other hand, these types of tessellations are fairly easy to conceptualize. Everything just tucks into everything else. There are no gaps to figure out how to reconcile. They pretty much take care of themselves.  Looking at the revesre side, I almost like it better. I do love the look of how those points converge in the y shape. And it shows the details of the work so much more clearly.  A crease pattern isn't really needed. Just fold all the shapes on the front tucked into each other. This tessellation holds no secrets.  Filed under: May 2025 Origami Tessellations

* This is a tessellation that was folded by 'Jessie'. We had a little e-mail exchange. They were interested in folding the ' hexagons and trapezoids tessellation ' designed by Peter Keller. I had previously posted my fold and solution for this tessellation back in 2022.  The crease pattern I had originally posted was pretty basic. So, they emailed me to ask for something a little more extensive.  I drew one and sent it to them the next day. And the day after that they emailed me again to show their completed tessellation (as shown above). It turned out quite well. Kudos to Jessie.  For better tightness on flagstone tessellations you might want to use sturdier paper or wait for a low humidity day. Otherwise, a really nice effort. Keep on folding! The  extended crease pattern is below. My original posting of Hexagons and Trapezoids fold and solution.  * photo used with permission from the creator.