When I mapped out the hexes with the rectangles off of them I didn't realize how many triangle twists it would actually require.
I knew it might need them, but there were just so many. They readily formed both on the back and on the front.
So many. But I had a pretty sturdy piece of paper, so I went ahead and persevered. It was not at all easy.
Everywhere that three rectangles converge on the front a triangle twist forms on the back. Triangles also form on the front as you work the other shapes. The edges were a little bothersome. They don't come together as nicely as the inner portions. But it's not the sort of tessellation where you can not go all the way to edge. If you want it flat it has to go all the way with the same shapes.
I actually used a flat head screwdriver to help push the triangles into place as they were partially formed by the rotations of the hexes and rectangles. It was fussy and tedious, but it worked.
Lots of photos including backlit and unlit. Also a basic diagram that got me started. The diagram only shows the rear triangles. It doesn't show the front triangles, but they are fairly obvious.