One Space Away
The dominant feature in backlighting of Groovy Triangles is a Star of David made with open triangle twists on alternating sides, while the dominant feature of Emergent Hexagons is a honeycomb structure of solid dark bars.
This is something I've found with other closely related tessellations too.
In equilateral triangle tiling tessellations with clusters of four twists, there are several spacing considerations: between clusters, within clusters, and global lines.
In Groovy Triangles, the spacing within clusters is as dense as possible, with spacing between clusters one more than the minimum, and no larger variations in spacing.
Look closely at Groovy Triangles - what do you see?
Can you see that half of the twists are on the back and half are on the front?
Can you see that there are three open triangles clustered around each closed triangle?
Can you see that that exact cluster is repeated on the back?
How many clusters do you have to go through to get back to your original cluster?
Where are the positions of 3-fold rotational symmetry?
Are they in twists or in empty spaces, on grid intersections or grid triangles?
What parts could be tighter together? Further apart?
Most of these questions are geared towards understanding the structure so you can fold it on your own - with or without a crease pattern.
Since Groovy Triangles has the same cluster of four triangle twists on both sides, it ends up showing the same pattern on both sides.
Now, when I say "same pattern", I don't mean "exact duplicate" - the pattern on the other side might have a different rotational direction and position than the pattern on the front, but all the structural descriptions must stay the same.
In fact, if I started describing this tessellation I'd need to tell you which direction a specific twist rotated before you could match the side of the tessellation you're looking at with the side I'm looking at.
Of course, there are subtle distinctions in the physical piece - I keep all of my "hard" grid lines on one side - but without those differences it would be impossible to tell which side is which.
Groovy Triangles uses simple twists in a complex structure.
Both closed and open triangle twists are needed, as well as folding on both sides and folding clusters of four twists.
In order, the skills needed are:
- Closed Triangle Twists - triangle intersections
- Open Triangle Twists
- Folding on both sides - triangle wraps
- Clustering 4 Triangles
- Clustering 4 triangles with both open and closed twists
- Clustering 4 triangles with open and closed twists on both sides
There are many ways to gain these skills - my YouTube video on triangle twists is a good start and my courses, especially Basic Twists Bootcamp and Tessellations by Tiles, go deeper into these topics.