I saw this tessellation on Lydia Diard's Flickr page and I really liked the pattern. It's simple, but elegant.  It was pretty easy to reverse engineer. It's based on a 32 division triangle grid, but you need to add additional folds to connect the hexagons. This is most apparent in the second photo. Those connections will not naturally flatten. They need to be spread squashed. After some trial and error with how best to achieve the desired result I arrived at the following method. I first folded all the large hexagaons. Reinforcing the creases and then unfolding. Then I folded the narrow sections that would connect them. At that point it was easiest to pinch the corners of the hexes while spread squashing the connecting veins. Using the grid to help create pointy sqashes at each axis point of each hex. If you're familiar with tessellating and intermediate origami techniques it should not be hard to figure out as you go. The first photo is the front ba...

 This tessellation is the result of repeating as closely as is possible the classic dual hexagon collapse. You have the smallest hexagon and then the next largest concentrically. The small hex is a valley fold and the larger on is a mountain. You collapse the large one on top of the smaller one and flatten. It's a pretty standard origami maneuver. In this case I just repeated it as often as possible on a single sheet of paper. It's very similar to the spread hex tessellation. In the middle I  squashed the flaps that formed from the collapse. You wind up with a lot of overlapping pleats that you can arrange as you see fit. Or you can do some more squashes. They can also be turned into triangle squashes. The other side gives off a nice star effect as seen in the third image. To create the crease pattern simply layout the concentric collapses in offset rows with one pleat between each repetition. All of the folds, except for the squashed on the central star, conform...

 I was trying to reverse engineer a tessellation from Lydia Diard. I'm still not sure how I figured out the steps to recreate it, but somehow I was able to do so. Just folder's instinct I guess. I did a mini one flower version to figure out the basic structure. Then I did a bigger version where I screwed up the tiling. That version led me to discover how to properly tessellate the design. Her flower iterations were a little bit closer together though  Wish I'd done that. Then I could've had whole repetitions around the edge. Funny thing is, although it's a pretty simple set of folds, it was quite difficult to execute. Or it was for me. Once I did the central portion, it was not easy to do the outer iterations. You can't really flatten the paper during the process. So it's not easy to keep previous folds intact while you're working on new ones. Some of the fold are quite small. So prefolding, unfolding and refolding wasn't a successful ...