Here's a really intriguing tessellation that I found. I was fiddling around with right triangles around a hex twist and discovered that layout could be combined with small offset hex twists on the other side. 

So at the center you can see that the right triangles twist around a standard hexagonal twist on the reverse side. 

As you move outward toward their tips they twist around an offset hex twist on the other side. But only three points from the right triangles converge at that location. Along the other three axes there are small triangle twists on the back side. 

It'll be more obvious in the crease pattern sketch. 


There is a little trickery on the back side with getting the many triangle twists to work well together. Bisecting some of the folds is required. That is illustrated pretty clearly in the photo of the reverse side. 

There's also an unlit view of the front, which offers more perspective. 

Plus, I made a short video showing the tessellation rotating to back light. 

As always, it's folded from a single hexagonal shaped sheet of paper. No cuts. Only folds. 

Crease pattern sketch is included at the end of this post.