While working on coming up with new tessellations using a pyramid of rhombuses like I did in my Pythagora's Tessellation , I came up with this one.  I was quite pleased with myself at having found this one. It's pretty neat how the rhombus stars and the rhombus pyramids are each a part of the other. So, I mapped it all out and dutifully folded it.  It was only after I was all finished that I happened to look in an old folder of mine and found an image I'd saved that was essentially the same design.  I had downloaded the picture a very long time ago, so I don't recall where I got it or to whom it belongs. There was no signature on the image itself.  The tessellation in the old picture didn't really do repeats. Whereas I take it all the way to the edge.  If I had to guess, I'd say it was probably a Peter Keller. It looks like something he might've done.  So, this tessellation of mine is unintentionally, both a quasi solve and a quasi original.  A...

 This is an interesting little tessellation that I came up with rather quickly. Funny thing that I discovered about it after I'd plotted it out, is that it's pretty much the inverse of a tessellation by gatheringfold called 'Emergent Triangles' .  Her tessellation is rhombuses around large hexagons and then small offset hexagonal twists with alternating rhombus and triangle twists.  This tessellation is open back hexagons with triangle twists around them. Then it's alternating rhombus and triangle twists around a small offset hexagon.  Similar, yet different.  I wasn't thinking about her design when I was coming up with this one, although, I'm sure it was somewhere in the corners of my subconscious.  An interesting fold any way you look at it.  The reverse side almost looks like a flagstone with its endless arrays of interconnected triangle twists. A stunning pattern in its own right.  My crease pattern is included below.  During my mapp...

 Having recently folded my Laughing Envelopes tessellation  inspired by a technique I saw used by Arseniy K and Dirk Eisner, I had the idea for this original tessellation . While it's a different central point, it uses the same kind of principle of tucking and folding.  Though it doesn't look like it, it actually uses open back hexagons that are tucked and folded over to create the arrays of overlapping small hexagons.  The thing that I find particularly interesting about this design is that you can take a step further. The layered hexagons can be converted into overlapping triangle twists.  Unfortunately, I used ordinary printer paper and it was pretty weakened by the time I had completed it as shown in the first photo.  I did manage to do the triangle twists on the six central hexes, but the paper was too weak to allow for continuing it with the other iterations. But if your paper is sturdy enough, it could certainly be done.  I still need to take a ...

 It's time for a new flagstone tessellation. This one begins with three trapezoids around a small triangle twist on the back.  From there I repeat the trapezoids in three directions. Adding a repeating and widening pattern of triangles and more trapezoids in the other three directions to fill the ever expanding space. I consider all flagstone tessellations to be difficult . Just because of how everything has to converge almost silmultaneously. And also because the reverse sides are always full of so very many triangles. However, it's also worth noting that flagstone tessellations work more seamlessly with the triangle grid than other styles of difficult and advanced tessellations. So, if you're hoping to step up your tessellating game, I would say this is the style with which to start.  Crease pattern included.   Filed under: March 2025 Tessellations

  When I posted my Cats in the Garden Tessellation , I said that I wanted to try to create more tessellations using that same foundation. This is my next creation using that same starting point.  The idea is pretty simple. Triangle twists with wings. They spin around open back triangle twists on the opposite side.  solvingorigamitessellations.com In this tessellation I used open back hexagons in the repetition of the pattern.  This neccessitated some unusual shapes in the remaining areas which are quite apparent in the second photo. I found it tricky to find those unusual shapes during my mapping, but eventually I got it all figured out.  The pattern itself isn't all that crazy. I'd say it's an intermediate level origami tessellation . Especially if you're folding it using the crease pattern, you shouldn't have much trouble at all.  Crease pattern below. 

  As promised, this is my additional manipulation of my Inclined Planes Tessellation . It's the same design posted previously, but taken a few steps further.  Essentially, all I did was take a bunch of the folds and reverse them.  Reverse folds are pretty common in standard origami. Like when you're folding a cat or a sheep. They are less prevalent in origami tessellations , but they are sometimes used.  A reverse fold is just as the name implies. You turn it inside out. It can be employed in many ways to change the structure of a tessellation.  However, with your typical twist based folds, reversing is just a matter of chocie during the inital process. Many of the folds are an either/or type of deal.  With some more complex tessellations you may only have that option after the folding is complete. As is the case here.  Robin Scholz's triphilia is a really good example.  This tessellation is another one that takes that same approach.  Fil...

 This is an original layered tessellation . It looks pretty humble at first glance, but it's actually somewhat complex. I took a few photos at unusual angles to illustrate the depth of the layers.  It's twist based, but not so simple as your typical twist tessellation.  I created it starting with open back hexagons. Then there are small natural trapezoids off of their axes. At that point I layer on long hexagon shapes. I then use them to fold triangle twists. At that point the design is repeated.  It's an intermediate level tessellation . It's not all that hard to fold once you know the structure. I used basic printer paper and had very little trouble.  The reverse side just looks like open back hexagons with little points sticking out from them. Those little points are actually the small trapezoids that are partially covered by the edges of the hexagons.  The entire tessellation layers upon itself rather neatly. It's a very interesting find for me.  ...

  This tessellation is a little different than my usual stuff. I use triangle twists in a different way to create shapes that otherwise wouldn't be possible to overlap as they do using a standard triangle grid.  The method is similar to how you would use reverse rabbit ear folds, if you've ever done them.  Another interesting thing about this particular tessellation is that I actually plan to work it further to create yet another design. I just haven't finished that part yet. Close, but not yet. Soon, I hope.  For now, this one is nothing to sneeze at.  The reverse side looks rather humble. Which belies the truth of its construction.  I created it by doing triangle twists off of small hex twists on the back. But then I folded over those triangle twists on top of themselves.  If you look at the diagram (shown below), it all looks rather simple, but it holds a few secrets.  It has standard small hex twists with triangle twists 2 pleats away and t...

This original tessellation builds off of the concept of twisting triangles and/or rhombuses around a six sided pyramid. In this case I did open back hexagons with triangle twists and then added the pyramids with more triangle twists.  This results in the need for another shape off of the other three edges of the pyramids. It's an oblong rhombus. Instead of the typical rhombus, its edges span 1.5 pleats.  It's an intermediate tessellation . It's pretty straightforward, but I wouldn't call it easy simply because of the unusual rhombuses it uses.  Crease pattern is below.  Filed under: March 2025 Origami Tessellations

  This tessellation is kind of a funny story. I had reverse engineered how to fold 'Orbits' by gatheringfolds and had started to fold it. Without really thinking and not paying enough attention to what I was doing, I instead repeated only the first two layers of it.  I was half way through the fold before I realized that I had left out some of the steps.  This is the tessellation that came of that blunder. It's essentially her original design simplified to just two significant elements.  There are the small offset hexes with alternating front/back triangle twists and there are the open back hexes.  Like 'Orbits', it too is a symmetrical design that is a mirror image of itself on its opposite side.  I don't have a separate crease pattern. But to fold it, just use the one for ' Orbits ' and only use the elements in the lower right corner of the diagram.   Filed under: Match 2025 Origami Tessellations

This is an original tessellation that is somewhat atypical in that some of the folds land squarely on top of each other. It's a little hard ot do, but it is possible.  Why do it? Because it can be done.  The actual architecture is very simple. If you look at the crease pattern below you'll understand what I mean. All the intersections are very straightforward. However, gettting everything to work together nicely is a little bit of a conundrum.  After you have it all flattened, then there's the additional task of arranging the folds in some sort of coheerent pattern. That's the real trick to this one. Try it. You'll see. It's fun though, to fiddle around with all the possibilities. There's no right answer. It's just a matter of how you want it to finish.  It's probably a difficult level tessellation . You just have to be delicate with it. It'll take some finesse.  I think this is my crease pattern. It's a little wrinkled. I may have altered t...

 This tessellation is a sort of  a semi-original . The center point is something I saw on the Insta feed of Arseniy K. But I then took the rest of the tessellation in my own direction.  When I first saw his tessellation , I was struck by how creative his central idea was. It just made me want to use that as a jumping off point.  This is the result.  The idea of his that I loved so much is rhombuses around an open back hexagon. But instead of twisting off the axes of the hexagon, the rhombus are situated right up against it. With this setup you can tuck half of each rhombus kind of under itself to create the central pattern.  It's a finnicky design with lots of overlaps and tricky intersections.  Even after I mapped it out on some grid paper, I still needed to do a first fold using basic paper just to get a better understanding of how the folds would all work together.  It was only then that I moved on to the fancy paper and executed the fi...