My previous square grid triangles tessellation gave me an idea for another. It's not that different. It seemed way cooler in my head. I wanted them pointing at each other as well as going in opposite directions. Same basic principles. Just reverse a few things. I thought about leaving no gap between the flat sides and decided against it. But maybe that would've been more interesting.  Honestly, I didn't want to do all the extra folding that would've been involved. 

 Decided to do some square grid tessellation work. Just to keep up my understanding of it. Thought triangles might be interesting. I've casually wanted to do something with triangles on the square grid for a while now.  Used what I learned from this tessellation as a jumping off point since the triangles are really just half diamonds and the flat side is the same as a single side of a square.  It came together rather uneventfully.  It needs a lot of small diagonal folds in both directions. A little bit tedious in the prep work.  The actual collapse is pretty simple. However, it does overlap some on the backside. As you get closer to finishing the collapse you'll need to tuck certain folds under others. The specifics  will become apparent as you approach completion.  I do have a rough crease pattern that I haven't yet photographed. Will add it at a later date.  Update: Adding crease pattern....

 This tessellation was inspired by the way in which a small hexagon can be folded offset from the grid creating triangles very closely surrounding it. Like in the ninja stars tessellation . I figured why not see how it works out if I turn those triangles into rhombuses. Sounds logical, right? It worked out pretty nicely.  A very straightforward construction. Completely non-irritating to fold.  Still you wind up with a pretty picture for your not so hard work. The negative spaces are a larger version of the shape seen in the ringing bells tessellation . If there's a name for this shape, I don't know it. I guess it's a trapezoid variant of sorts.  I went with two pleats between where the rhombuses meet each other. You could go only one pleat. That's how I drew the crease pattern included below. I'm pretty sure you could even go no pleat and wind up with an even more compact version of the pseudo-trapezoid in the negative space. 

  This is an idea that I had a while back, but it seemed next to impossible to actually execute.  While it's not a very clean fold, it's satisfying to have done it. Slightly better paper might have yielded a somewhat neater finished product.  It's a very small, very densely structured design.  It's rhombus flowers, like the classic just rhombii flower flagstone . However, it's the tiny rhombuses natural to the grid.  Collapsed hexagons are at the center of each 'flower'. Small triangles negotiate the spaces in-between. Crease pattern is included below.  . 

So I came upon an interesting tessellation someone had created and I went about reverse engineering it. I thought from the single module I had come up with that I had it all figured, but I missed a few details which later revealed themselves as I went ahead and folded the larger incarnation.  Upon realizing, I returned to the original photo and figured out the steps I'd missed. A fold for another day.  My 'mistake' actually resulted in a pretty nice finished design. Pictured here first front, then back.  Central small hexagonal twists have double length rhombuses two pleats off of their axes. Repeat. Very large triangles form on the reverse side. They bisect three of the grid's tiny rhombuses.  It's an uncomplicated and relaxing fold. For what it's worth, those seem to be the sort that yield the most brilliant photos.  I have a very messy crease pattern photo. There are other ideas in the background, but the red lines still adequately illustrate the design.