I haven't posted an advanced tessellation in a while. So here is a new one. It's an unusual pattern that also features some very small folds. There are tiny rhombuses and compressed triangles with which to contend. It is an original origami tessellation that I just recently created. The main shape is a six sided polygon of alternating edges. One pleat bisecting the grid, then one pleat following it and so on until you close the loop.  One the other side are open back hexagons and some oblong six sided parallelogram-ish shapes.  When I folded it the small rhombuses weren't actually on the front at first. It was after I had completed it that I realized I could reverse some of the folds to bring them up to the top.  There are some very tight folds and also some very small ones, which is why I believe this to be an advanced tessellation .  Evenso, I actually used thin printer paper because I figured thick paper would never let me make some of the tighter/smaller fold...

 This is a wacky one. A just to see if I can pull it off kind of tessellation . For the most part, I was able to do so successfully. Could be better, but it's a tough one .  It's basically just layers upon layers of elongated hexagonal folds around open back hexagons.  I used thin paper because I figured I would never be able to layer everything using anything thicker.  When I first plotted it out using a small grid of only 16 pleats it seemed so easy and worked beautifully. However, as with many tessellations , adding more repetitions made it exponentially more difficult.  The crease pattern looks pretty innocent, but it's anything but.  As I was folding it, I found myself wondering if maybe medium thickness paper might've been a better choice.  Most of the folds are mountain folds with the exception of the open back hexagons and a set of convergence points. In the diagram the blue dots indicate where the paper should be tucked under. When I drew it I...

 This is a simpler tessellation . For when you're feeling like something a little less intense. Or for when it's rainy outside and the paper is feeling especially flimsy. This will do very nicely.  It's a pattern of small and large triangle collapses as well as rhombus collapses.  If you examine the reverse side, it's not quite as easy as it appears. There are a miltitude of very small folds required, but even as small as they are, they're not too hard to pull off.  There no need for a crease pattern for this tessellation . The front view reveals all the shapes rquired and exactly how they connec to one another.  I used regular printer paper folded into a 32 pleat triangle grid. It worked fine. While thicker paper may make the execution easier, a tessellation such as this one really benefits from the translucency of thin paper when you go to take the finished photo.  When I looked at the finished tessellation it reminded me of the old paper chess game that ...

 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.