Just Rhombii by Joel Cooper/Peter Keller

 This is the just rhombi flagstone tessellation originally designed by Joel Cooper. It's quite literally all rhombuses on the front of the paper.

I did mine with a 32 division grid.

Peter Keller did a photo tutorial on how to fold it on his flickr account.

There's an extra flourish at the center that I've not attempted. I just wanted the field of rhombuses.

His tutorial is a photo series of how he folded the design. It was quite helpful in understanding the structure. But personally, I prefer a crease pattern for understanding how to fold tessellations. That's just how my mind figures these things. So I mapped one out before beginning my attempt.

A very basic rendition of the creasing pattern can be found in the last image of this post for those that are interested in using it to help them attempt the design.

All the rhombuses are mountain folds. All the hexes and triangles are valley.

I folded my version very differently from the tutorial. When I fold flagstones I approach them in a very simple way. I do all the preceasing to set things up. Then I just work my way outwardly from the center easing all the folds into place.

I first set the initial hexagon twist and the inner most set of rhombuses. After that, it's just a gradual conditioning of the paper. Working outward in a circular fashion. Slowly coaxing all the iterations into their proper places. When they're all relatively set, they go under some heavy books to flatten overnight.

First photo is a backlit rendition. Second is the solid.

Last photo is the crease pattern. It's a relatively small version, but it's still quite plain to see how the design repeats ad infinitum whatever size grid you choose.