Rectangular Twists Origami Tessellation : Origami Tessellations

Rectangular Twists Origami Tessellation

This tessellation came to me out of nowhere and coalesced very quickly.

When I mapped out the hexes with the rectangles off of them I didn't realize how many triangle twists it would actually require.

I knew it might need them, but there were just so many. They readily formed both on the back and on the front.

So many. But I had a pretty sturdy piece of paper, so I went ahead and persevered. It was not at all easy.

Small hex twists, but they rotate on the bias of the grid. This is to accommodate the small rectangles that shoot off from them. For a flat tessellation triangle twists were necessary.

Everywhere that three rectangles converge on the front a triangle twist forms on the back. Triangles also form on the front as you work the other shapes. The edges were a little bothersome. They don't come together as nicely as the inner portions. But it's not the sort of tessellation where you can not go all the way to edge. If you want it flat it has to go all the way with the same shapes.

I only precreased the hexes and rectangles. I think if I had tried to precrease the triangles as well that the paper never would've lasted.

I actually used a flat head screwdriver to help push the triangles into place as they were partially formed by the rotations of the hexes and rectangles. It was fussy and tedious, but it worked.

Lots of photos including backlit and unlit. Also a basic diagram that got me started. The diagram only shows the rear triangles. It doesn't show the front triangles, but they are fairly obvious.

Comments

Infinite Triangles Origami Tessellation

This is just a flash idea I had. There was no planning involved. No inspiration. I just started folding and followed the lure of the creases in the paper. Upon seeing the finished result, It kind of reminds me of Robin Scholz's Triphilia tessellation, but the construction is definitely different and I was not thinking of that as I was crafting it. The similarity is that you can arrange the layering of the triangles into different patterns of your choice. I went looking and discovered I had folded this a few years ago and called it Triangle Temptations . I didn't realize this until after I'd completed this model. Apparently, according to my original post, I'd seen someone else fold it on flickr and recreated it. This happens sometimes. You hit on an idea and it's something you've done and forgotten. They linger in the back of your brain and come forward unexpectedly. That previous version differed from this one slightly, in that it used double sized cross g

Micro Rhombus Stars Origami Tessellation

This tessellation is micro rhombus star twists. I'm pretty sure I've seen this done with larger size rhombuses, but not with ones this size. They are the smallest natural rhombuses of the triangle grid. The center is achieved by collapsing a small hexagon. On the other side there are small hex twists and open back triangle twists. Since the shapes are rather small, it's a little bit difficult to fold. It's probably more of a cool weather tessellation. Humidity does the paper no favors on such small designs. But the ideas come when they do. Reverse view and crease pattern images follow.

What If Caviar Could Talk Variant

This origami tessellation is a variant of one by Arseniy K. He named his 'What If Caviar Could Talk'. After I had solved his design, I decided that I wasn't up to reproducing it exactly as he had folded his. Perhaps another time, in the future. So I changed things up a little to make it slightly less difficult. Both designs have a foundation of open back hex twists with triangle twists around them, He used micro rhombuses between the repeats. In my case, I used larger natural rhombuses instead. Still a difficult fold to execute, but much less so. It still required thick paper. I used tant folded into a 32 pleat triangle grid. You can see from the photo of the reverse side how densely packed everything is. It's a few layers deep. So be prepared to wrestle with that. My crease pattern for this iteration is included at the end. To fold his, sub out small natural rhombuses in place of my larger ones.

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