Spinning Saws Origami Tessellation

Let's talk rotated grids

Rotated grids are a powerful tool for folding display-ready tessellations.

Since I figured out the mathematical underpinnings of this tool last year, I've considered rotation for every single display-style tessellation that I've folded.

But when I talk about rotated grids, many people's eyes glaze over.

It's not obvious to non-tessellators whether a piece has been folded on a rotated grid or not - and even experienced tessellators can struggle to identify rotation if they're not familiar with the technique.

The bottom line with rotation is that I use it to align repeating elements of the pattern with the edge of the paper.

This alignment is fairly rare in the tessellations that I design, and it's important to achieve alignment to have consistent borders the whole way around.

Look Closely

Where are the positions of rotational symmetry; the 6, the 3, and the 2?

Can the twists be separated into clusters, with flexible spacing in between?

What twists are used? In what order and on which sides?

What are the different loops that form the tessellation?

These are the questions that come to mind as I'm looking at the structure and shape of Spinning Saws.

Multiple views

As with all tessellations, you can view Spinning Saws from the front, the back, and each side with light.

Unlike other tessellations, you can actually see the line of thought that led to this one!

Check out my video on designing with crease pattern building blocks to see the genesis of this design and get these blocks for yourself!

Learning Sequence

Spinning Saws is an example of what I call the Hex-Rhomb-Tri-Rhomb Expanded tiling.

Unlike the Hex-Rhomb-Tri-Rhomb tiling, the triangle twists are not positioned in locations of 3-fold rotational symmetry and there is more than one type of loop in the tessellation.

The twists form clusters that can be spaced arbitrarily far apart, which makes this tiling easier to fold than its seemingly-simpler counterpart.

Folding this tessellation requires mastery of closed hexagon twists, open triangle twists, rhombus twists, placing triangle twists on the back side (triangle wraps), and practice using these three twists together in other tilings is highly recommended.