Crossroads Origami Tessellation

Just stick more twists in between!

The ways that variations can be made are kinda endless.

You can change the spacing, switch a twist to the other side, change a position from closed to open or vice versa.

Or, in some cases, you can stick more twists in between the twists in your tessellation!

That's exactly how Crossroads came into being - it's an expansion of Square Knots Weave with open squares stuck on the back between each of the original twists.

Symmetries

Check out the symmetries on this one - which positions are actually 4-fold?

Does that change if you just consider the pleat structure and ignore how the hybrid square twists are squashed?

If we take the actual folded structure, only the closed square twists have 4-fold rotational symmetry and the open squares on the front are in 2-fold positions.

However, if we ignore the direction the hybrid twists are squashed then both the closed and open squares on the front are 4-fold rotationally symmetric and the 2-fold position lands on the hybrid square twist.

And if we were to choose to squash the hybrid twists differently, we could create the opposite effect - the open squares could be the 4-fold ones and the closed squares would be 2-fold!

We could also remove all rotational symmetry from the pattern by squashing the hybrid squares chaotically - but the pleat structure would remain the same.

Alignment

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The alignment tension in Crossroads (just like it was 2 weeks ago for Hybrid Rosettes) is whether to align the natural tiling breaks or the repeating elements to the edge of the paper.

By letting the repeats cross the paper diagonally, I end up with a clean border and don't need to fold all the way to the edge (although I got pretty close here).

Tessellations are infinite, and you get to choose the piece of infinity you want to fold.

Just because a crease pattern ends at a particular place doesn't mean that that's where you should stop too.

The choice is yours.

Learning Path

Ok, so I know this tessellation looks a bit intimidating, but there's actually just six things to learn to get there.

1. Closed square twists
2. Open square twists
3. Folding square twists on opposite sides of the paper
4. Hybrid square twists
5. Folding hybrid square twists with other square twists
6. Folding hybrid square twists with other twists on the opposite side

That'll get you to Crossroads - and it doesn't require meeting the devil at the crossroads at midnight to sell your soul. ;P

If you fold Crossroads, I want to see it! Tag me @gatheringfolds on Instagram or Facebook to share your work. :D