Siren's Call Origami Tessellation

Entrancing Patterns

There are some patterns that when I see them, I know I have to fold them.

Usually I keep a queue of about 10 of these patterns, but sometimes one skips to the front of the line.

Siren's Call is one of those.

I knew I'd have to fold it as soon as I finished the prototype - who could resist those solid lines in backlighting - but I didn't have the math needed to rotate the triangl-centered grid to aligned the pattern to the edges and neither of the standard options were close enough!

So, I made an attempt at the math, folded the tessellation, and achieved alignment - but it wasn't the alignment I was looking for.

I'm still not sure if I got lucky or if I did the math wrong, but I am sure that I'll figure it out eventually.

Symmetry and Clusters

This tessellation's structure is unusually well-concealed.

Since the twists are so dense, the closed twists on the back don't appear closed anymore and the clusters are difficult to distinguish because they overlap.

If you look closely at the symmetries, though, you might spot the structure too: two different clusters of four triangles placed on opposite sides of the paper.

The cluster on this side has a closed center twist with open corner twists, while the cluster on the back has an open center twist and closed corner twists.

Basically, this tessellation is a mashup of Emergent Hexagons and Stars in Stars - both of which I also found incredibly attractive!

Backlighting and the back side

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See if you can shift your perspective from the twists to the lattice fo dark bars and back again.

This is the feature that I found incredibly alluring when I discovered Siren's Call - can you see it?

Learning Sequence

Ok, so this tessellation shouldn't be the sixth one you ever fold, but there's still a sequence of skills to practice on your way to mastery.

1. Closed triangle twists in clusters of four
2. Adding open triangle twists to clusters of four and practicing triangle-centered grids
3. Using open and closed triangle twists on opposite sides of the paper
4. Using mixed-twist clusters of four on opposite sides of the paper
5. Bringing these mixed-twist clusters closer together
6. Mixing different clusters of four on opposite sides and close together