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...

 This tessellation is a somewhat random idea. It's really only a pattern in the most liberal sense.  Basically, I started with rhombuses around open back hexagons.. Then I added small offset hexagons and repeated the two ideas as best as I could. Once you add a few offset hexes you can then repeat the larger hexagons. The pattern of rhombuses and triangles is rather unorthodox, but it does work.  It's anyone's guess how to arrange the moutnain and valley folds in order to create a consistent design.  It's make for a pretty picture though.  It's a lot of work, but it isn't very difficult.  My crease pattern is included below, but it's not all inclusive. I think I had to work some shapes out as I went along. 

 This is an odd one. I was just fiddling with small shapes I could nest around an open back hexagon. As I was trying to decide exactly how to repeat the pattern, I looked at the other side and decided I liked it when the spaces on the back were right triangles. So I went with that configuration. And here we are.  While the beginning idea for this tessellation was the narrow parallelograms around the open hex, the true inspiration point was when I looked at the other side to determine how to make it repeat. It was then that I saw that I could create negative space right triangles nested against the hexagon.  At that point, it was just map it and fold it and just like that another origami tessellation was born! I debated calling the back the front and the front the back. It's all subjective, I suppose. I like them both equally in their own way.  This is an intermediate level tessellation . Nothing too difficult. Nothing too easy either.  Crease pattern included....

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...