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...