This is an interesting study in how triangle twists can connect using different sized hexagons.  Twist based origami tessellations are not my strong suit, but every now and then, I hit upon something pretty cool. Like this one.  Essentially, it starts out very typical. Open back hexagon with six triangle twists on the axes.  If you're familiar with tessellations, then you've probably seen and done this a number of times.  How it becomes more interesting is that from there I add small hexagons with six triangles around them. But those triangles alternate front/back. I like to refer to them as offset hexagons because they don't twist by the natural lines of the triangle grid. Instead, they twist based on the triangles that surround them.  At that point, the pattern is repeated.  This tessellation is even more unusual because I didn't really plan it. I just drew the pattern rather spontaneously on the paper right before I folded it.  That is why I...

 I don't think I've done this one before. It's a pretty straightforward flagstone tessellation that just kind of came to me pretty suddenly as I was trying to think of something new.  It consists of just two shapes on the front. Hexagons and rhombuses. On the back, it's triangles all the way.  Unlike the majority of flagstones, this one is a linear pattern. I've done several linear flagstones that I can recall, but I do believe this one is new for me.  Take a look at the link that follows if you want to see more linear flagstones tessellations I've created.  This one is, essentially, alternating rows of hexagons and rhombuses repeating vertically and horizontally.  It's one of your easier to fold flagstones. There's nothing particularly tricky about it. Just crease and collapse.  My diagram further illustrates exactly how to do it.  Filed under: September 2025 Origami Tessellations

 When I was first learning how to do origami tessellations , I read Eric Gjerde's book and did probably all of the tessellations in it. One was called 'Negative Space Stars'.  As soon as I came up with this design, I was immediately reminded of that tessellation. It's totally different, but features the same vacant space concept.  It's pretty simple as far as tessellations are concerned. Still, it's a fun little design to spend a little time doing.  The back side is pretty interesting too.  My crease pattern is pretty bad. It has some other ideas in it. To fold this tessellation follow the blue lines only.  Use thin paper. There are a lot of overlaps. It's easier with thinner paper. 

 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....