This is an odd flagstone tessellation that I folded not too long ago. The main premise is triangles and rhombuses alternating around a small hexagonal twist on the other side.  In order to keep the pattern going there are also several series of just triangle twists around hexes.  Visually, it's a strange pattern to try to follow, but it is a consistent pattern that can be repeated indefinitely.  If you look closely, you can see the distinct smaller patterns. They kind of bleed into each other, but they also exist on their own.  Just another interesting wrinkle in the flagstone tessellation universe.  I would rate this as a difficult tessellation , as I feel all flagstones are somewhat difficult until such time as you become quite familiar with them. At that point, they may become intermediate or even easy. It just takes a lot of practice and depends a great deal on your affinity for such folds.  Paper matters too. A good quality paper can be the dif...

 So, I'm trying to catch up on posting all the tessellations that I've completed in the last month or so. They're all there in my google photos waiting patiently while I dilly dally with other things.  I really like this particular tessellation . Both the front and the back are pretty intriguing patterns. Which, I think, is a little unusual.  It uses interconnected trapezoids on both sides. On one side six trapezoids form large triangles with a small triangle trapped in the center.  On the other side three trapezoids form smaller triangle shapes.  It's pretty neat how the geometry works out with that lopsided kind of symmetry.  I actually conceived of this tessellation on paper as the second side. But once I'd completed folding it, I found the other side (first pic) much more exciting.  Crease pattern included.  Filed under: Origami Tessellations September 2025

 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 is a crazy one. I don't really remember how I arrived at this particular pattern. Most likely, I was just messing around with a small experimental grid to see what caught my eye.  I guess that I was feeling especially bold at the time I landed on this idea. This ia definitely an advanced origami tessellation .  Some of the shapes in this one are almost impossibly small. At least, for the size of paper that I normally use. Which in this case was standard 8..5 x 11 inch printer paper. I figured tant paper would be too thick to let me make such teeny tiny folds. And also, that it would be too thick to allow for all the overlap that was required. For the most part, that worked out to be true.  Of course, the converse of that is, such thin paper stresses easily and doesn't stand up well to too much fussing and cajoling.  Anyhow, it turned out mostly successful. Could've been neater, but considering how tricky it was, I'll call it a win just that I was able to finish ...

 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...