Infinite Pyramid Origami Flagstone Tessellation : Origami Tessellations

Infinite Pyramid Origami Flagstone Tessellation

This is a flagstone tessellation that I came up with recently. I had the idea for the starting point and was determined to create a pyramidal pattern that could repeat outward from it.

It took a few tries to determine how the corners would work, but it came to together nicely in the end.

It consists of trapezoids and rhombuses on the front side.

On the back side there are many triangle twists. This is pretty standard for a flagstone tessellation.

As with any flagstone tessellation, it is somewhat labor intensive. But overall, it is not hard to fold. I wouldn't say it's easy either, but it's pretty doable with a little patience.

I've been obsessed with triangular patterns lately. This is just one more example of what you can do with them.

The photo of the reverse side shows the dense array of triangle twists needed to complete the design.

I used 28 lb printer paper trimmed to a hexagon. It was folded into a 32 pleat triangle grid.

Other than trimming the paper into a hexagon, there are no cuts. Only folds.

It's not necessary to trim the paper to a hexagon. The same can be accomplished leaving it rectangular.

I just find it easier to reach the center with my stubby fingers when working with the hexagon.

I also think the hexagon results in a nicer finished design.

My crease pattern sketch is included at the end of this post.

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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