Tiled this out on a larger scale, thanks to some 1/64 paper folded by Mawelucky. (thanks again!)
As previously stated here, this is a "deltoidal trihexagonal + quasiregular rhombic tiling". ouch. that's a mouthful, isn't it?
I like it because it has my favorite shape (the delta rhomboid- looks like a strange piece of pie) and one of my other favorite shapes, a 6 pointed star made up of diamonds.
the reverse has another shape I like, which is a pentagon in the form factor of a regular hexagon, but with one side pulled out into a point.
extending this pattern to a larger scale (and a full tiling) required a little bit of changing; I oriented all the hexagonal twists (at the center of the stars) in one direction, and made some other pleat adjustments accordingly. So there's a good amount of rotational symmetry here around the central large hexagon twists, as well as different rotational symmetry around the smaller hexagon twists.
The pictures for this fold didn't turn out terribly well, so hopefully I'll come back at a later date and replace them with improved shots taken at home.
Let me know what you think!