This is a really cool tessellation that I created . It's trapezoid based tirangle shapes connected by offset small hexagons with alternating small triangle twists around them.  Inspired by a previous tessellation I had created called 'Twister' I set out to create a new one that utilized the same trapezoid triangles in a new way. This is the result.  When I had finished mapping it out, I wasn't entirely sure if it would work. It seemed logical, but some of the gaps were unfamiliar to me in the context of flagstone style tess . Which is essentially what this is.  I guess, technically it's a hybrid of flagstone and classic twists. It's intriguing to think about what other hyrbid folds might be out there waiting to be found.  At any rate, it looked promising. So I forged ahead.  Relatively certain, but not 100% sure. Turns out it works beautifully. A lessson to trust your experience.  This is a difficult tesssellation , but it's also a fun one. The way th...

This is an unusual tessellation that I recently designed . It's a dense collapse of various shapes that is based off a an open back hexagon with small right triangles around its edges. From there it just gets even weirder. I collapse some teardrop shapes around the center and add triangle twists. In order to repeat the pattern I used some oblong rectangle type shapes. It's all very unorthodox, but it does work.  It was an interesting exercise in how tightly shapes can be manipulated.  I would label it as a difficult tessellation to fold. It's full of strange shapes and troublesome overlaps.  I used thin paper because I knew that everything was very close together and I figured that would make it more feasible to execute the many overlaps. Which it did. However, it also made it hard to keep the smaller shapes as neat as I would've liked.  Would this work better with thicker paper? Maybe. Probably.  You can see my center is slightly askew because one of the smal...

 This is a rather simple tessellation that I recently dreamt up. Open back hexagons with triangle twists a few pleats away. Nothing terribly interesting there. But then I add some six sided pyramids and triangles twisting off of their short sides.  It kind of reminds me of the fold where triangles are twisted on an offset small hexagon. Like in this tessellation , just to name one. But it is different for sure.  The back side of this tessellation is pretty humble as well. Basically just repeating trapezoids connected by triangles.  I have a crease pattern. Need to take a photo of it. Will hopefully upload it soon.  * name of the tessellatino is from the Tool song 'Third Eye'.  Added crease pattern.

 If you're a fan of rhombuses, like I am, you'll be interested in this tessellation. It layers standard rhombuses and longer parallelogram style rhombuses around open back hexagon twists.  It's not too difficult. Intermediate level for sure. The trickiest part is just making sure that you crease the folds for the parallelograms correctly. Those 1.5 pleat creases can be a little elusive. Especially if you don't use them often.  The intersections where three parallelograms meet can be a little finnicky. There's only a small natural triangle joining them.  Other than that, it's smooth folding all the way.  Crease pattern is below. 

 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...