I came up with this design and it was definitely legit from a structural perspective. All the folds worked together in perfect synchronicity.
It's a very tight design though, so actually folding it was a challenge. At first I had the hexes and the triangles all on the front. While I was able to complete the central module, the paper was practically dust by the time I started trying to collapse the surrounding repetitions.
So I decided to try moving the hex twists to the back of the design to make more room for the very closely packed triangle twists on the front.
It was still very difficult to fold. But that did do the trick.
It's definitely not a tessellation for the faint of heart.
But after some maniacal persistence I was able to finally coax the paper into the places I wanted it to go.
The funny thing is, it's a very humble looking pattern when you first draw it out. It looks like it will be easy. But because of the way the triangle twists overlap one another all of the connects are very dependent upon one another.
It's almost impossible to just fold a portion of the design and flatten it. After you get the center set, you have to half set the outer iterations and then keep going around and easing them all into place as a single unit.
First image is front side back lit, then rear back lit, then front unlit.
Somewhere I had a small crease pattern starter module. If I can find it, I'll post it here at a later date.
I found my starter crease pattern.
Here are some images of the crease pattern and partial collapses to illustrate how the design works. For the iterations you simply repeat the same central pattern off of each of the veins radiating from the triangle twists.
The first image is just a very simple pattern for one iteration. The successive images show the design in partial stages of collapse.