Here's a fun and straightforward origami tessellation that I knocked out fairly easily at work one day. Just a basic hex flower that repeats. On the reverse side it results in a stars pattern. For a simple design it has a really lovely end result. It's not difficult to see that it's just hex twists with teardrop shaped petals attached to it. To create the repetitions I simply added additional hex twists off the center that connected to the central axes. Only caveat is to leave enough space between to fit the petals of the repeaters. To the best of my recollection I left 4 pleats between. I wanted to leave more, but the paper size/grid size didn't allow for it. I actually saw a similar design that left more space between each, which looked really nice. But bigger grids required bigger paper or at the very least more patience. I was actually more struck by the pattern that formed on the back side of the paper. It was an unexpected surprise.  A gorgeous series of ...

I came up with this design and it was definitely legit from a structural perspective. All the folds worked together in perfect synchronicity. It's a very tight design though, so actually folding it was a challenge. At first I had the hexes and the triangles all on the front. While I was able to complete the central module, the paper was practically dust by the time I started trying to collapse the surrounding repetitions. So I decided to try moving the hex twists to the back of the design to make more room for the very closely packed triangle twists on the front. It was still very difficult to fold. But that did do the trick. It's definitely not a tessellation for the faint of heart. But after some maniacal persistence I was able to finally coax the paper into the places I wanted it to go. The funny thing is, it's a very humble looking pattern when you first draw it out. It looks like it will be easy. But because of the way the triangle twists overlap one another...

 This is another tess that I found online. I believe I found it somewhere on flickr. So... someone else's concept. They didn't provide a crease pattern or instructions. At first, I was overcomplicating it. Then I tried drawing out the pattern, including the shadow effects. That's when it became clear to me. Arranging the hexagons as they did in a 3D cube pattern has quite an impressive effect. But, the folding of the design, is actually quite basic. There's really only one technique involved beyond the usual triangle grid. The last image shows a rudimentary crease pattern. It's simply large hexes all connected by triangles. To fold the design you perform a sort of waterbomb fold on each triangle. That enables you to flatten the hexes. The lines in the triangles that surround the central hexagon illustrate how to fold them. You squeeze together the outer edges of the triangles in mountain folds collapsing along those inner vertexes as valleys. If you lay ...

This is a fun design that was inspired by a Lydia Diard design I folded not long ago. It's a similar structure. It begins with an open back hexagon twist at the center. That is then surrounded by more hexagons. The interesting part is how they connect. Single pleat veins are squashed and flattened where each corner of the central hex meets the surrounding hex petals. This creates the appearance of another layer hiding behind the hexes. The hexagons can continue tessellating out from each other infinitely. This design would be really stunning applied to a larger grid. The front and back of the design are shown. The third image is a very crude crease pattern formation. It illustrates pretty clearly how the vertices of the hexes are flattened and connected.

This is a tessellation I attempted to recreate that I had found somewhere on the Internet. You can find lots of them, but many lack crease patterns or instructions on how to fold. That's become a fun new aspect of my origami habit. Trying to figure out how to recreate tesses from their folded pics. I really like how this one looks when I take the photo with back light, but no flash. This technique really brings out the structure of the folds. Giving a 3-D appearance to otherwise flat designs. This is a flagstone of large open back hexagon twists on one side connected by their surrounding triangle twists on the other side.  The second photo shows the reverse side of the same design. The third photo is a very basic crease pattern I created on a smaller piece of paper with a much smaller grid. It's simple, but should be quite helpful to those familiar with this form of origami. That's generally how I suss out the larger designs. Figure it on a smaller scale and...