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...

 Here is the tessellation that I referenced in an earlier post called ' Alternate Realities '. In that post I explained how I had mapped out a certain design, but when I went to fold it, I sort of lost track of the pattern. I wound up folding a slightly different tessellation by improvisation.. That was the 'Alternate Realities' tessellation .  This tessellation is the original idea folded to completion. It's similar, but different.  It has the same starting point of teardrop shapes pointing outward from an open back hexagon. It diverges from there. Where I add small hex twists on the back to create a triad of the teardrops. At that point, I am able to repeat the central pattern.  It doesn't fit entirely on my 32 pleat grid, but if you had a larger grid you could fully repeat the center and keep repeating as long as the size your grid would allow.  It's an intermediate level origami tessellation . If you follow the crease pattern included below, it's n...

 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

 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...