I recently did a couple of refolds of previously folded flagstones. All hexes and hexes surrounded by triangles. I had different paper this time around and was interested to experience the effects and results.  A sturdier paper certainly makes it quicker and less frustrating to execute a complex design. It also offers the possibility to forgo the flat fold and do something three dimensional.  Such was the case with my refold of hexes and triangles. Although the paper 'wants' you to go to the reverse side and flatten those triangle twist, you absolutely do not have to do it.  In fact, leaving them unflattened reveals a really nice pattern. 

I first saw Ryan's Tessellation by Christiane Bettens at the back of Eric Gjerde's Awe Inspiring Tessellations book. That was years ago. I found a tutorial for folding it on flickr and was able to recreate it quite nicely.  I didn't have this blog at the time. I was still very new to origami tessellations. So I never documented the process. I only took one pic that just sits in my google photos unused. It's a circular series of triangles and rectangles around large hexes on the reverse side. The triangle points push under where they meet with the long edges of the rectangles.  Skip ahead about 5 years. I decide to fold it again. This time instead of an iso-area fold, I go, as I'm prone (compelled) to do, all the way to the edges.  I take several nice pics of both the front and the rear lit and unlit. I neglected the back the first time around. It's just as interesting as the front really.  That first pic is actually the rear side back lit. I think that's my

This pattern was kind of a flash idea that I mapped out very quickly. I did not do a test fold. I just drew it directly on the gridded paper that I used to create the final model.  It's actually an idea I had a while back, but when I drew it out it seemed too dense a pattern to actually work.  When I revisited the idea it was obviously the same exact density, but I decided to forge ahead nonetheless.  I did not fold it flat. Which is something I usually try to achieve. But I had slightly sturdier paper and the three dimensional back side did not give me any problems at all. In fact, the unflattened reverse side came out quite beautiful.  I'm certain it could actually be flattened neatly if one were so inclined. My paper, however, not quite that sturdy.  It is open back hex twists and what I call the bell shape. They are connected by pushing under the offset edges and a single arm between them.  This technique and the shape are fully mapped out in my dance of the triangles tesse

There's an odd shape in the grid that I've worked with a few times before. It kinda looks like a bell to me. It alternates between a one pleat bisect and two pleat natural. It's a shape that lends itself to a pretty straightforward flagstone type of fold.  On the bisected edges you push the the extra under.  In this case I just used this one shape and repeated it.  It was a lot easier to fold than I thought it would be.  On the backside some very large hexagons form.  There is a little bit of fuss folding on the back. The corners of the hexagons need to be flattened at some unnatural angles. This is easily accomplished with a pointy metal nail file.  I don't have a crease pattern specific to this, but there's one from a similar fold that will make it pretty clear. The one for my Dance of the Triangles Origami Tessellation will illustrate both the shape and the folding technique. It just has some extra triangles in it. 

I discovered this elongated rhombus shape at the gatheringfolds website. I can't believe it never occured to me before. It seems so obvious after the fact.  It's basically just two rhombuses stacked on top of each other. That shape led to this configuration. A central small hex twist on the rear with the elongated rhombuses spinning off from it. Some double wide triangle twists between the repetitions.  It's a very simple design, but I really like it.  For this one, I did keep the crease pattern. So if you're just looking to fold without having to figure it out, you can do that.