I think I've tried to do this before. It seems familiar. But I couldn't find any pictures of such a tessellation in my personal archive. I suspect I may have attempted it and failed before.
On this occasion, I was able to complete the project.
It's a fairly simple pattern, but because everything is so close together it's a little tricky to execute.
You can see from the crease pattern pictured further down that the triangles are only one pleat off of the axes of the hexagons. This makes everything fit together rather tightly. There's a lot of overlap.
After completing the center, it gets temperamental. You can partially fold sections, but everything is interdependent for the most part.
Good preceases are a necessity.