I don't really remember this intermediate tessellation from a few weeks ago. Had to unfold it to determine the structure. Looking at the finished photo doesn't really reveal any clues as to its origin.  But the truth is, that it's actually quite simple. Not that easy to fold, but the architecture is not that complex.  Basically, it's open back hexagons with rhombus twists tucked into them. I connected the repetitions by mirroring. In other words, I took the way that the rhombuses in the center connected to each other in the center and created opposite facing angles my chosen distance away. The actual molecules are not mirrored. They flow the same as the center.  Doing this creates an obstacle. The joining folds want to flow in opposite directions. This happens with rhombus twists because they naturally twist in opposite directions when connected to each other using certain methods.  To overcome this, I folded some shapes 'backwards'. This let me fold everythin...

 Here's kind of a cool flagstone tessellation that I created recently.  It looks somewhat random, but it really isn't.  The center point is six rhombuses around a small hexagon on the opposite side. Pretty typical tessellation starting point.  Then I add some long parallelograms off of their edges. The other gaps are a series of interconnected trapezoids.  I didn't have enough paper/grid to actually do the repeats, but I do believe it is possible with more surface area.   My crease pattern actually shows dual ideas.  It shows both the pattern folded in the above model as well as another idea for where to go with the same starting point.  In the case of this particular model I just repeated the sets of trapezoids. The crease pattern however, has another idea. One which I haven't yet folded. Where you can alternate the sets of trapezoids with parallelograms and large triangles.  In theory, you could fold my original origami tessellation ...

 This is an interesting hybrid  flagstone tessellation that I recently designed and folded.  It uses a few different techniques and patterns. It was pretty hard to actually fold. Some of that difficulty can be attributed to weather conditions and the paper being softer in warmer/more humid seasons. But it's also a tricky configuration to execute even under favorable circumstances.  There was a good chunk of time while I was collapsing it that I was doubtful that I would be able to successfully complete it. Fortunately, it did work out. I was able to bring it to completion. Even if not quite as neatly as I would have liked.  It starts out innocently. Just a common set of six triangles attached to an open back hexagon.  Then I add a right triangles  and mirror image right triangles to the edges of the original center triangles.  At that point the secondary pattern emerges where the regular triangles and right triangles can be twisted around an offs...

 Every once in a while I'll come up with an unusual configuration of rhombus twists that I use to create a new tessellation . Unlike traditional twist based rhombus tessellations, these designs will feature awkward patterns and unorthodox overlaps.  I just enjoy trying to come up with functional patterns that seem like they shouldn't work.  This tessellation is a new one in that style.  It features overlapping rhombus twists around a large hexagon. Some triangle twists help make the pattern repeat.  The back view is mostly unremarkable. Although, there are some interesting micro right triangles.  Whenever I create tessellations like this I'm always hoping for a surprise interesting pattern on the other side. Sometime I get one and sometime not so much. Still, a good  fold regardless.  My crease pattern is a little messy, but it mostly gets the point across. Filed under: April 2026 Origami Tessellations

 This is a recent collapse style, somewhat difficult tessellation that I created. It starts off twist based. Three triangles twisting around another triangle on the other side.  Then I tuck some trapezoids into those three triangles. From there I'm able to add two different molecules that repeat.  One is an open back hexagon. Three edges have the trapezoids and the other three have triangles. Those triangles can then repeat the central point.  The other is twisting three trapezoids around a triangle on the other side.  There's a healthy dose of tucks and twists to keep most folders excited.  Getting everything situated is tricky. There are a lot of micro triangle twists on the reverse side.  I'm a big fan of these kinds of tessellations . They're intricate, yet easy to understand.  Crease pattern included for those who dare!

  This is a new flagstone tessellation that I did last week. It uses trapezoids and triangles in a linear pattern.  The pattern is particularly interesting because of how the smaller subsections of the shapes each continuously mirror on diagonal paths. A pair of two triangles one way, then mirrored, then again and so on.  Same with the trapezoids. up, down, up, down on a diagonal plane.  Back side is all triangles.  Another interesting feature of this tessellation is that some of the triangles on the back side only worked right in certain gaps. While there were a few choices of the spaces to put then into, if you chose the wrong one, you were left with gaps that didn't quite work.  I can usually tell if a gap will work if it has certain features. Either it nestles right up against the shapes on the other sides. Or there's only a micro rhombus gap on one side. Or there's a small hex gap, but one edge is cut off.  I've tried to illustrate these conc...

 This is one of those tessellations where I pack an absurd amount of triangle twists into a small space and see what the result is. More often than not, you'll get a pretty interesting design on the opposite side.  This tessellation starts its life with an open back hexagon. From there, it's pretty much a chaos of triangle and rhombus twists. Not really chaos, but it kinda looks that way when you see the other side.  My grid wasn't large enough to actually repeat the center, but I think it can be done if you have more pleats to keep going.  I did this one quite some time ago, so I don't really remember how it came to be exactly. Although, I do remember that I was kind of fixated on folding the edges of open back hexagons in on the center.  My crease pattern is below. I think I remember that I made a small mistake when tracing it. I believe there's a missing triangle in the right mid edge section.  I like to fold twist based tessellations using thinner pap...

 I've been meaning to add this particular origami tessellation for at least several weeks now. I just had a lot of trouble getting a good photo of it. It's still not a great pic, but it was the best that I could get.  I had hoped using thinner paper would allow for a nice backlight pic, but it didn't work out that way. So, I just went with a standard photo instead.  It's kind of an unusual pattern for me. There's a large natural triangle at the center with three small triangle twists rotating around it. Then on the other side there are three sets of three triangles twisting around it.  I repeated the center three times and then filled in the other three areas with a different collection of triangle twists.  It's a fully twist based tessellation.  I can't really decide if I like the front of the back better. Although, I do remember that the design the the center of the back was my original inspiration. Interesting how things evolved so much from there....

 This is an odd one. It's kind of like multiple patterns mixed into one. I really don't know why I did it this way other than just experimenting. Thinking about it, I would probably like to take the multiple patterns and do a few different tessellations with them in the future.  For now, this is what I have.   I'm sure that if one had a large enough grid and took the time to work it out that it could easily become a truly tessellating design in and of itself. It's both random and intentional. Kind of interesting in that way.  What I really like about simpler twist based tessellations like this is that you can do them successfully regardless of what paper you use. And the weather doesn't matter much either. They are a great way to teach yourself how the shapes rotate on the angles of the grid. As well as how the various shapes can and cannot interact with each other.  Crease pattern included. 

 This origami tessellation uses the fact that trapezoids can create overhang in order connect to the next set of shapes. That's one of the things that I find so interesting about them. You can arrange them in ways that a lot of other shapes simply can't do.  In this particular tessellation, I did alternating trapezoids and rhombuses around open back hexagons. The gaps between them left space open for me to add opposite facing trapezoids. Which allowed me to repeat that molecule.  The repeating process created the more standard six trapezoids around a hexagon in the other spaces.  It's a nice, fluid design that highlights the versatility of the trapezoid shape in tessellating.  If you're a fan of flagstone tessellations , this is a pretty cool one.  Crease pattern below. Created the pattern last week. Just fold it the other day.  Filed under: April 2026 Origami Tessellations

 This is a twist based origami tessellation using trapezoids and hexagons. I think that I created it two weeks ago and just gto to folding it about a week ago.  The most notable thing about it, is that even though it uses hexagonal twists, it's actually a linear configuration.  This was achieved by connecting the hexagons to each other rather than just repeating the trapezoids all around them.  This happens pretty naturally when you connect the trapezoids vertically and look for a way to repeat the design horizontally.  It's also a mirror symmetry design. Each side is a mirror image of the other.  It's a pretty easy tessellation to fold. Any ordinary paper will work fine.  My diagram is below. 

 This is the tessellation that I reference in the previous post. I had the central idea. That came to me quite easily. It wasn't hard to figure out how to repeat that. However, when I did, I was left with a rather large gap that I didn't know how to fill.  I played around with various sets of shapes and still wasn't sure what would actually work.  When you're stuck, sometimes it's best to just take a step back and work on something else for a while. So, I did.  A week later, I was thinking about it again and came up with a new plan to reconcile those empty spaces. I still knew that it wasn't quite right, but that I was almost there.  At that point, I decided I would go with what I had so far and see if I could figure out the final answer as I folded it.  This isn't an approach that I usually take. It risks wasting fancy paper and a lot of grid folding time. But, occasionally, this is the only way for me to figure trickier things out completely. It doesn...