Big Wheels and Little Wheels Origami Flagstone Tessellation : Origami Tessellations

Big Wheels and Little Wheels Origami Flagstone Tessellation

I had seen a pic of a tessellation someone had done that was the classic circle of flagstoned triangles surrounded by large blunt pyramids.

This led me to wonder what other shapes might possibly be able to tessellate around that familiar circle of triangle twists.

That is how I arrived at this configuration.

It begins with the familiar flagstone circle of triangles emanating off of a small hexagonal twist on the reverse side. It's from there that I wondered how open back hexes would work as the next layer.

It turns out that they work out quite nicely.

Oddly offset parallelograms form on the back to reconcile the shapes on the front.

I had been fumbling around with ideas for flagstone open back hexes for a while and not really finding anything useful when this idea came quite suddenly. It all just coalesced pretty rapidly.

I used kraft paper thinking its sturdiness would be helpful, but it was actually really difficult to fold a true flagstone using such thick paper. I suspect it would've turned out a little nicer had I used slightly more flimsy paper.

But perseverance paid off and the final result eventually came to fruition.

A crease pattern is below

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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