Here's a new tessellation I conceived. It may have been done before, but I haven't ever come across it in my many googlings for origami tessellations. It's pretty straightforward as far as tesses go. Open back hex twists on one side. As seen in first pic. Go to the other side. Fold the rectangular/pointing border. As seen in the second pic. I always create designs as a single module and then figure out how to tessellate them after that. This has pros and cons. Most times it works out pretty well. Occasionally I cannot figure out how to repeat the design in a tessellated format. I did have a little trouble determining how to gracefully tessellate it. But a little patience and trial and error solved the riddle. The basic crease pattern appears in is the last pic of this post. It illustrates where the folds go. It also shows how to arrange the repetitions so that they map out elegantly on any size triangle grid. I did mine on a 32 division grid, but a larger...

 This is the just rhombi flagstone tessellation originally designed by Joel Cooper. It's quite literally all rhombuses on the front of the paper. I did mine with a 32 division grid. Peter Keller did a photo tutorial on how to fold it on his flickr account. There's an extra flourish at the center that I've not attempted. I just wanted the field of rhombuses. His tutorial is a photo series of how he folded the design. It was quite helpful in understanding the structure. But personally, I prefer a crease pattern for understanding how to fold tessellations. That's just how my mind figures these things. So I mapped one out before beginning my attempt. A very basic rendition of the creasing pattern can be found in the last image of this post for those that are interested in using it to help them attempt the design. All the rhombuses are mountain folds. All the hexes and triangles are valley. I folded my version very differently from the tutorial. When I fol...

 I totally had no clue what I was doing when I came up with this. I saw the tessellation in the second image on flickr and started trying to reverse engineer it, but I got sidetracked by the open back triangle twists. I had it figured it out in small format, but wasn't thrilled by the construction technique. While it's an attractive design, it didn't turn out to be something I was keen on doing in its larger format. So I abandoned that and I decided to simply use it as an inspiration for a new design instead. I came up with this mixed up assortment of triangle twists. They stagger off of their hexagons. Some are only one pleat away, while others are two. That's what creates the assortment of thin and thick connective veins. The third photo is really interesting. Because the center twists are different from the outer twists it creates a puffed up appearance which was unexpected. My original intent was to have iterations of the central design. But I veered of...