I'm still obsessed with variations on 'encapsulated' triangles.  This pattern is interesting in that it contains a shape that is partially rhombic, yet rectangular on its other end.  This results in a pattern where some of the triangles are dominant and others are submissive.  It's just an interesting set of shapes that naturally coalesce on the grid.  It's an intermediate difficulty fold on medium grade paper. Crease pattern is fairly obvious, but I have included it below.  Reverse side does require a little finesse to make it work. It fits perfectly on a 32 pleat grid.   

Building off of some other recent configurations, I came up with this one. You've got the classic rhombus, the triangle and also an elongated rhombus. They alternate to form circular hexagonal shapes.  The back side is a little tricky. There is some freeform diagonal cross creasing required. Nothing super complicated. It's not something you would want to pre-crease. It's easier to just pinch into place as you work.  I was very conscious of trying to fit my idea into my typical 32 pleat grid as my previous idea did not.  Been toying around with the idea of using kraft paper. This seems to be the most economical and sturdy choice for tessellators.  The shapes in this tess are folded in the Scholz style. The points are pushed into and under the cross grid pleats of the adjacent shapes. It's a pretty popular and well documented technique.  Reverse side folding is important and critical to effective completion of the model.  I didn't save a crease pattern, but y...

So I came up with this tessellation pattern that I really like. I haven't seen it before. That always excites me. Unfortunately it just misses fitting on a 32 pleat grid with any full repetitions. I tried using a 48 pleat grid, but my paper just wasn't sturdy enough. I mapped it all out, but was only able to do the 32 pleat version with the paper that I currently have. .  Some fancy elephant hide paper might be in my future. Depends on how much I obsess about it.  It would also be really cool to see someone else fold it. If some industrious folder were so inclined.  It's a pretty cool design. It's tricky to execute and a somewhat complicated pattern.  The idea started with this single module. It came together rather easily.  How to repeat it didn't come as quickly, but I eventually found it hiding there in the grid and was able to map it all out in detail.  It was really disappointing however, to discover that I wouldn't be able to fold it in all its full r...

I screw around with variations on classic shapes and techniques. This is one such result. Close knit rectangles. Similar to the wall of rhombuses flagstone I did recently. Same idea. Different shape. It's good practice for honing your folding technique.  It's a pretty simple design that illustrates another way in which shapes on the grid naturally coalesce.  It's a 32 pleat triangle grid. You might think square grid for rectangles, but no.  I'm back to flat folds after a brief flirtation with the 3D variety.  I can't imagine too many would need it, but there is a crease pattern included below. 

  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...