solvingorigamitessellations.com The tessellation consists of many overlapping rhombus twists. They overlap a little differently than my usual designs. Rhombus collapses overlapping are a pretty standard technique. However, in this case, we overlaps twisting rhombuses. The results are quite different.  To be honest, I don't recall how exactly I made the pattern repeat. I'd have to refer to my original diagram, which I have not yet taken a photo of.  It's quite a dense pattern full of many overlapping folds.  When I drew it, it seemed like a pretty simple idea, so I used thin paper. It turned out to be more intense than I anticipated. This thin paper worked, but just barely. A thicker paper would be advisable.  When I come up with twist based tessellations I usually try to created ones like this that are non-standard. There's no shortage of already existing twist based tessellations. But the really tight and dense ones, such as this,  are usually still undiscovered.  s

solvingorigamitessellations.com  If you like flagstone tessellations then you'll like this one. It's a cool one.  I actually mapped it out as rhombuses pointing at each other and then away from each other. Using some triangles to make it work.  When I finally folded it, the pattern came out more like vertical rhombuses flanked by triangles with a row of horizontal rhombuses between the repetitions.  That's how I see it anyway. I'm sure others will see it differently.  However you might perceive it, it's a pretty fascinating design.  All these years later. Hundred of tessellations folded and it still blows my mind what can be done with a single sheet of uncut paper.   It's a somewhat difficult tessellation   to fold. As are most flagstones. In addition to the shapes featured on the front of the paper there are a lot of triangles to work out on the back.  I used 20 lb white printer paper. And my crease pattern diagram is included at the end of this post.  I would

  solvingorigamitessellations.com This is one of those tessellations that when you come up with it you think that you've really hit upon something unexpected. And you have. But it's also one of those tessellations that is very difficult to actually fold .  It's well worth it though. The finished product is a dazzling array of rhombuses twirling around small offset hex stars.  It's a densely packed fold that's hard to execute and time consuming, but those are my favorite kind! I actually folded it quite randomly as my baseline. Then after it had a chance to rest under some weight, I went back and rearranged the mountain and valley folds into the final pattern.  For tricky tessellations such as this one, that seems to be the least frustrating way to go about it.  This is an original tessellation that I designed.  Crease pattern available at the bottom for those who might want it. 

 This is another tessellation designed by gatheringfolds that I reverse engineered and then folded. She calls it 'Hubble'. After the telescope, I'm guessing.  It was neither very easy nor very hard to figure out. The central array of seven hexagons was easy enough to determine. As were the triangle twists around them. I did get stuck for a little bit on the next layer. The two different kinds of connections that the rhombuses had to the hexagons took some fiddling to determine.   It was a very low humidity day when I folded it. So the paper was pretty crisp. I used ordinary printer paper. Widely spaced twist fold designs such as this almost always work very nicely with standard paper.  Her original model used a larger grid and therefore had more repetition. But my small grid fits the first part of the second iterations. It also still illustrates how to fold the entire pattern regardless of what size grid is used. See my diagram included below for more detail. 

  This is an intermediate level tessellation that I recently created. It's a kooky kind of pattern that starts off very simply.  The center point is a small offset hexagon with rhombuses around it.  Next I add some open back hexagons and sets of three trapezoids.  Some rhombuses take up the remaining spaces.  This pattern repeats six times around the center.  At that point, I was getting close to the edge of the paper.  The open back hexagons repeat again. Then I just filled in the remaining space with more trapezoids and rhombuses. That third level has its own pattern. If you had larger paper and were to go for a forth level, that would need a slightly different pattern yet.  It's a little different from a traditional origami tessellation which repeats the same pattern infinitely. I'd  call it a progressive tessellation.  As you move outward the pattern changes slightly, but it can keep going and going for as long as you want. It's just a matter of reconciling the sp

I have learned that the contents of this post have been plagiarized at a site called openai24 dot com.  Thank you to Peter Whitehouse for informing me of the situation.  I have informed the hosting company/domain registrar of the copyright violation and hopefully they will take action sometime soon.  Please know that this is my original design and I am the artist who conceived of and executed it.  If you're feeling as outraged as I am by this blatant theft feel free to leave a comment on their site condemning their actions. Or write an email to their hosting company (namecheap dot com) to express your displeasure.  Thank you.  So, I decided to buy some fancy tissue foil paper from France. I had this tessellation idea that I wanted to do, but I couldn't quite get it done using any of my usual papers.  From what I had read online, tissue foil is supposed to be really great for tessellations because it's both thin and resilient.  This tessellation is my first time using it. 

I amended my Chasing Infinity tessellation post to include information about a recent case of internet plagiarism.  That post as well as this one were copied and posted at the site openai24 dot com. No credit was given. It was blatantly stolen.  This is the original. I am the artist and rightful owner of the content. .  I have filed a formal complaint with their hosting company. I have also left a comment on their site about the same.  If you're feeling up to it leave a comment on their site expressing your disdain. Or send a message to their host (namecheap dot com) condemning their actions.  Thank you all. And thanks to Peter Whitehouse for alerting me to the theft.   This little tessellation is unique for me in that I didn't really plan it. I just folded a 32 pleat triangle gird and mapped it out right on there. No fiddling. No testing. Just draw and fold. I'm not really sure what came over me, but it worked out well.  I even used ordinary 20 lb printer paper. Nothing

 Here's an easy tessellation that looks really cool when finished.  I have the nagging feeling that I've done this one before, but if so, I haven't been able to find the previous version.  It uses just one shape for its foundation. I'm not sure if there is an official geometric name for this shape. I was pretty good at geometry and I don't recall anything like that.  It's a six sided and triangle like shape. Obviously it's not a triangle, as those have only three sides. But when you look at it, it makes you think of a triangle.  I just took that shape and used the cross-grid edges to connect them to each other. In doing so, some large hexagons formed on the other side.  That's it. That's all there is to it.  My crease pattern is included below if you'd like to fold it. 

This tessellation is all rhombuses on the front. It starts with a small hexagonal twist with rhombuses around it. From there it progresses by adding additional rhombuses  until I'm able to also add some open back hexagons. The pattern of repeating the open back hexagons and rhombuses can then continue repeating.  When you break it down to it's components, it's essentially two base ideas combined into a single design.  You've got the small hex with rhombuses offset around it and then you have the larger hexes with the small rhombus spiral going around them. I just added enough extra rhombuses to transition between the two.  It's an intermediate level origami tessellation. Nothing too crazy.  I found it particularly interesting because I was able to do all rhombuses on the front and almost all hexagons on the back. There are some rhombuses on the back too. But there are no triangles at all. Which is a little unusual.  I do have my diagram that I used to create it. I&#

This is an interesting little flagstone tessellation that I designed. It's a linear style of alternating trapezoids. I also used some regular rhombuses as well as double length rhombuses to help the pattern repeat nicely.  It's not a design I've seen before, which is always nice to find.  It repeats very nicely on a 32 pleat triangle grid.  I used tant paper. I'm pretty positive it would also work with any somewhat thicker printer paper.  This is an idea that I've had for a while, but I kept thinking that it was too simple and I wasn't motivated to actually fold it.  It also took a little fiddling before I realized how it would tessellate neatly.  Eventually, I worked it all out and was quite pleased with the end result.  It's a little difficult to fold, as are most flagstones. But with sturdy paper it is a mostly pleasant experience.  My crease pattern is included below for those that might wish to attempt it.  It's worth noting that when you

 This is a triad based flagstone tessellation that I recently created.  The starting point is an open back hexagon with alternating trapezoids and rhombuses  collapsed around it.  From there that pattern can be repeated by adding an opposite facing trapezoid off of each central one.  That, however, leaves a lot of empty space to reconcile.  I did so using a series of additional rhombuses as well as a few triangle collapses.  It's all just a matter of making the space work for you.  The reverse side, as you would expect of a flagstone tessellation, is a vast array of triangles.  It's somewhat different from any tessellations I've seen before. It's an interesting study in how far you can go in manipulating the paper if you're able to discern what combination of shapes will rectify the gaps in your ideas.  A starting idea is a wonderful thing, but working out how to take it all the way to completion is where the real magic is done.  This ability comes mostly from

This is a pretty easy tessellation if you're looking to get a feel for the process.  Open back hexagons have trapezoids collapsed around them. It's a really easy starting point.  Then we just add some rhombuses tucked into the points of the trapezoids.  At that point, the pattern can be repeated.  Large pyramid shapes fill out the remaining gaps.  If you're looking for an easy tessellation to get yourself familiar with some basic techniques of the genre, this one would be a good place to start.  I did draw a crease pattern. I haven't taken a pic of it yet. Will add it later on.  Update: added crease pattern at the end.  But all the shapes are right there in plain sight. There are no tricks or secret sneaky folds. It's a very straightforward tessellation. It shouldn't be too hard for even a beginner to figure out.  If you decide to fold this, leave a comment and let me know!

 This is a fun little tessellation that I came up with in an effort to be able to fold something new during high humidity.  I talk about humidity a lot in regards to folding various tessellations. The paper absorbs the moisture in the air and becomes soft and difficult to fold. Particularly for your more intricate patterns. Simpler designs, however, are still perfectly executable under most any weather conditions.  This tessellation is a prime example.  I used ordinary 20 lb copy paper on a drizzly day and it turned out very nicely.  The premise is rhombuses twisted around a small central hexagon. From there some small triangles twist off of them. Then just repeat.  This tessellation is actually a variant of another tess I did not too long ago called Flowers in the Garden Tessellation . Both begin the same, but diverge slightly in how they repeat.  On the reverse side there is just an array of open back hex twists.  So, not so simple as to be boring, but not so difficult as to be a pro

This is a tessellation that I did not that long ago. I called it cotton candy because I had used pink paper and it made me think of that.  I came up with the crease pattern again without realizing that I already had. And then proceeded to fold it again before finally noticing it was a previous design.  The first time I folded it, it didn't turn out as nice as I would've liked. This time around though, it came out much neater and looking more like I expected it to when I conceived of it.  It's an unusual design that puts together several different shapes in a way that isn't typically used.  To access the diagram refer to my first fold/post of this tessellation called cotton candy .  There are also additional details in that post about the nuances of executing this particular design.  If you happen to fold it yourself let me know in the comments.