This is a reverse engineer of Joel Cooper's Sunflower Tessellation that I found in his flickr albums. It's old. 2006 old. But it was new to me. Not super complicated to figure, unlike the stuff he does nowadays. It's a slightly unusual approach to rhombus and hex twists.  As far as the actual execution is concerned, it was of intermediate difficulty. Neither easy nor crazy difficult.  It does backlight very nicely, which is always a pleasant surprise.  Joel doesn't tend to upload crease patterns for his folds, but I did save mine. So if you're looking to just fold it without figuring it, you can do that.  I just used slightly better than average printer paper. Nothing fancy. It was quite adequate. 

 I'm pretty sure that I tried to do this one a little while back and didn't quite achieve success. Didn't quite figure the reverse side the first time around. This time I got it quite easily. At least the concept and architecture anyway. The actual execution was another story.  It started out really difficult working from the front side of the paper. However, once I moved to the rear it became a lot easier. Not easy really, but less frustration, more just folding.    Folding the back side really is the key. Alternating triangles and rhombuses. The rhombus points are 'eaten' by the triangles flat sides.  Similar technique to that used in Scholz's Triphilia tessellation.  I did save a crease pattern sketch. It's not terribly detailed, but it should be helpful if you're interested.

  Lately, I've been coming up with tessellation ideas that don't truly fit the grid and therefore don't result in a flat fold. Three dimensional origami tessellations are nothing new to the world at large, but they are still kind of new to me.  I've done a few. This is my latest. It turned out pretty nice.  It combines flagstone and 3D.  Unfortunately I was using discarded paper with a print out on it. So that distorted my photo of the bottom shape a little.  For a long time I took the approach that  going 3D was a cop out. If I couldn't find new shapes and patterns in the paper that naturally flattened, then I wasn't really succeeding.  But, after having stumbled into a few 3D folds, I kind of came around to the idea that they're something new and exciting. A different sort of challenge.  Rather than grind on the same old same old, why not embrace a new experience and explore its possibilities. . 

I saw someone's tessellation somewhere on the internet. Don't remember to whom it belonged. Went looking for it, but did not find it again.  Had previously downloaded the photo and decided to try to replicate it. Once I zoomed in on the pic it became mostly obvious how it was constructed.  Their fold was much neater than mine. My paper simply wasn't up to the task. But I was able to complete the tessellation. It's just a little janky, but still legit.  I actually like the backside a little better than the front. Which is why I made that the first photo.  It's a small hex twist on the back, then do some rhombus twists one small natural rhombus off of the center. Triangle twists off of the rhombuses. Some half offset triangle twists form in the gaps. If you've ever folded that triangle twist between small and two pleat, it's that, but only half of it.  A unique and interesting flagstone for sure.   

 I came up with this odd shape that I really haven't seen before in other origami tessellations. It's not ground breaking. It follows the same basic principles as other grid shapes. It's a flagstone fold for sure.  It was new to me, so I just went with straight up repetitions. But it seems perfectly logical that it could be combined with triangles and other shapes in various configurations.  It was a pretty hassle free fold. Although, working the back side was definitely required.  It helped a lot to go to the back and tease those folds.  The opposite side takes an interesting picture too. An unusual tiling.  I do have a crease pattern sketch, though it's a fairly uncomplicated to figure without any assistance. 

I decided to try working with a dodecagon shape. Fiddled around with variations of it. First attempt, went with just straight up repetitions.  It doesn't fold flat. I seem to be on an island of non flat folds lately, with no means of escape.  Three dimensional tessellations are cool if you have the right paper, but I really don't. Still, I forge ahead nevertheless.  A little trick that I've come up with to help finish them is using light weights over time to help convince the paper to do what I want. A few newspaper fliers and a kitchen towel overnight. Not so heavy as to crush it, but just enough force to make a mild impression.  To create the dodecagon shapes you follow the grid for one pleat and then cross it for the next and repeat until you've come full circle.  They are connected via the cross pleat sections in a traditional flagstone style.  This results in smallest grid triangles on the reverse side. They do not flatten. So be prepared to fuss with ...

Something a little different this time around. It's a three dimensional fold.. I'm generally not a 3D folder. Instead, I gravitate toward the fold it flat style. I like the challenge of figuring out how to make it work out that way.  But I randomly came up with this and it's kind of neat.  I was able to work it out that everything kind of locks in place.  It's a sort of riff on the classic flagstone of the same format. Open back hexagons and triangles make six pointed stars.  I've included below a really primitive crease pattern.  Basically you create folds off of the hex's points. You pinch them to lock the structures. 

So I saw a tessellation by Matthias Schwar on flickr. He called it double triangle flowers . I liked it. However, when I went to fold it, I realized that clean, full repetitions would not fit on a 32 pleat grid. So I modified it slightly to accommodate my (by tessellation standards) rather small grid. This is the result.  I often consider what wonderful designs and patterns I might be missing out on executing because I don't go beyond 32 pleats.  The reason that I don't is simply that I don't have large enough paper.  I could purchase larger paper, but the idea of just using ordinary paper feels organic to me.  If I did buy larger paper exclusively to fold more elaborate designs I would probably psych myself out worrying that I might make a mistake and waste it.  There's also the issue of working with larger paper. It's already not that easy to work with standard size paper. I have small hands and stubby fingers.  Pontificating aside... All in all, a pretty...

Fiddling around with triangle twists and shapes that might complement them is how I wound up with this particular configuration.  It turned out to backlight really cool.  I was inspired by someone else's tessellation  that I had previously recreated. Their idea just set me off on the path to this one.  It came together rather quickly. When unlit appears as flagstone type small hexagons around larger hexagons. Triangle twists to make it all work.  Backlit, you can see it's actually natural rhombuses.  It's a pretty straightforward fold. Not too difficult at all.  I did draw a single module crease pattern. If I can find it, I will upload it and it will make everything pretty clear, if it isn't already.  Update: adding crease pattern

  There are a lot of origami flagstone variations on the rhombus fold. I've folded quite a lot of them. Both those imagined by others and a few I've sussed out on my own.  This is one I've never encountered in all my google searches and flickr hunts. Maybe because it's too simple. Maybe because it doesn't backlight nicely. Who knows why no one else (to my knowledge) has folded it.  I actually just came across it accidentally. Just started drawing on the paper not really knowing where I was going with it.  The front design, which is the one I drew on the paper before folding, is very simple. An endless wave of rhombuses all swimming toward some mysterious shoreline not yet visible.  I didn't give much thought to the other side. I came to realize during folding that triangles were popping up on the back. Makes sense. I should have foreseen this from all my other experiences with similar designs.  What's unusual with this configuration is that the triangles ca...

  I recently did a couple of refolds of previously folded flagstones. All hexes and hexes surrounded by triangles. I had different paper this time around and was interested to experience the effects and results.  A sturdier paper certainly makes it quicker and less frustrating to execute a complex design. It also offers the possibility to forgo the flat fold and do something three dimensional.  Such was the case with my refold of hexes and triangles. Although the paper 'wants' you to go to the reverse side and flatten those triangle twist, you absolutely do not have to do it.  In fact, leaving them unflattened reveals a really nice pattern. 

I first saw Ryan's Tessellation by Christiane Bettens at the back of Eric Gjerde's Awe Inspiring Tessellations book. That was years ago. I found a tutorial for folding it on flickr and was able to recreate it quite nicely.  I didn't have this blog at the time. I was still very new to origami tessellations. So I never documented the process. I only took one pic that just sits in my google photos unused. It's a circular series of triangles and rectangles around large hexes on the reverse side. The triangle points push under where they meet with the long edges of the rectangles.  Skip ahead about 5 years. I decide to fold it again. This time instead of an iso-area fold, I go, as I'm prone (compelled) to do, all the way to the edges.  I take several nice pics of both the front and the rear lit and unlit. I neglected the back the first time around. It's just as interesting as the front really.  That first pic is actually the rear side back lit. I think that's my ...