Atypical Symmetry Pattern
Most of the time when you see a tessellation with only hexagons and triangles, there's only one hexagon and only one triangle and they alternate back and forth.
But that's not the only way!
Using the Hexagons and Triangles 6-fold Islands symmetry gets you a choice of a second hexagon too.
You can choose an open or closed central hexagon, a triangle of any type on any side, and then a hexagon of any type on any side too!
I figured out that all of the options work by playing with my crease pattern building block templates, and so can you - sign up to get the free templates here.
Shrinking Violets is an example of the Islands symmetry, with the open hexagon twists in positions of 3-fold rotational symmetry.
I chose a closed hexagon twist for the center, closed triangle twists on the opposite side at tube pleat spacing, then open hexagons on the same side as the central hexagon.
These choices give a visually pleasing result that doesn't create too many challenges for folding - try it for yourself!
If you'd like a crease pattern, you can get it here.
The Islands symmetry on the Hexagons and Triangles 6-fold tiling is a tricky one to align.
The repeating 6-fold parts of the pattern are not aligned with a natural tiling break, so you must choose between aligning the closest repeats with the edge ( which means folding all the way to the edge) and aligning the tiling breaks with the edge (so you can leave a border).
In this case, I chose to align the direction of closest repeats.
This alignment is done with a rotated grid, tailored specifically to the tessellation at hand.
You can learn to align your tessellations too - and the math doesn't even go beyond fractions!
Check out my rotated grids blog to learn more.
The path to folding Shrinking Violet isn't as long as you might think - with the right tessellations, you could get there in 6 steps.
The skills needed are as follows:
- Closed triangle twists
- Closed hexagon twists
- Open hexagon twists
- Triangle wraps (triangle twists from the back)
- Open hexagon twists with triangle twists on the oppsite side
Many tessellations, even recently discovered ones, can be taught in relatively few steps to a beginner.
This is not to say that these tessellations are easy, just that there are few skills to practice to get where you want to go.
And it's no wonder that folders struggle to recreate what they learn at conventions too - if intermediate skills are skipped or the tessellation is taught in precrease-and-collapse form it will be very difficult to fold again.
That's why I use a skills-based approach whenever I teach tessellations.
I focus on applying concepts instead of teaching specific patterns so that my students can actually understand what they're folding and why.