Here's a tessellation that I've not seen done. The idea came from trying to find a new way to repeat right triangles around an open back hexagon. I used some rhombuses and it worked out to be a pretty cool pattern, if I do say so myself.  There are a bunch of triangle twists on the other side that are pretty fussy to fold.  In order to correctly twist the triangles you need to fold a little bit of the paper over on top of the edges of the open back hexes. It's difficult. Use strong paper and do it on a dry day.  There are also small hexagon twists on the back as well.  You could also say that the pattern is alternating right triangles and rhombuses around small hex twists with open back hexes in the gaps.  It's just a matter of perspective.  I do have my crease pattern, but need to take a photo of it. Will add it soon.  Updated to add diagram.

This tessellation began with the idea of three rhombus twists around a triangle on the other side.  I wanted to find a way to repeat that pattern.  I used open back hexagons to further that goal. From there I was left with large gaps that needed reconciling.  It turned out that a series of seven triangles worked to resolve the void.  Oh, this was an incredibly tedious tessellation to fold. The creases felt never-ending.  Getting all six triangles to work in all the gaps was an arduous task.  At times, I thought to myself, I'll never finish this.  Strong paper and an obsessive personality eventually resulted in the completed tessellation.  You can see from the first photo that I oriented four of the triangles upward.  The second photo shows the other three in the series on the back side.  This type of design has a lot of flexibility.  The shapes can be arranged in different variations of up and down.  Crease pattern diagram incl...

 This tessellation is the result of me messing around with repeating linear rhombuses and trapezoids. It kind of looks to me like the rhombuses are launching rockets. Hence the name.  One side is strictly rhombuses and trapezoids.  The other side has quite a few triangles.  These collapsing folds are very versatile. There are so many pattern to be found.  Creating one is often just a matter of putting a few shapes together and filling in the gaps with triangles.  I used pretty flimsy paper, so it's not nearly as perfect as I would like it to be.  Given how obvious the various shapes are, a crease pattern hardly seem necessary, but I'll include one just the same. 

This is a tessellation by gatheringfolds that she called 'Epicycles'.  Every so often, I like to solve someone else's tessellation to give my mind a different perspective on things.  It really does help reset my creative process so that I can come up with new ideas of my own.  It also keeps me sharp in recognizing how to extrapolate the structure of other people's finished designs.  And it's a nice respite from the sometimes arduous process of thinking up and sorting out a completely unknown tessellation from start to finish.  It's an elegant design of open back hexagons and rhombuses.  There are a lot of designs that utilize these two shapes in conjunction with one another. This one is particularly interesting in how the rhombuses twist in a way that almost makes them look as if they're dancing.  The reverse side is exclusively open back triangle twists.  My diagram follows. 

This is a tricky little an offset hexagon stars tessellation. The idea is pretty basic. Just the stars and then some rhombuses. Folding it, however, is a little more complicated.  The shapes that fill in the gaps on the reverse side are somewhat unusual. Actually, it's more how you have to twist them rather than the shapes themselves.  I've been messing around with less standard tessellation techniques lately. Really searching for unique ideas and arrangements.  I certainly could've done a better job in my execution. Perhaps a second attempt at another time will yield a more impressive final result.  Still, the idea is intriguing.  Diagram included below. 

Some tessellations are obvious and some are not. Some are simple patience. Others are mostly stubbornness. This tessellation falls somewhere in the middle between those extremes.   This builds on the concept of rhombuses around an open back hexagon.  This time the outer edges of the rhombuses are connected to triangles using flagstone style collapse folds.  This creates some interesting shapes in the remaining negative spaces. They are unusual and tricky, but totally foldable.  I used tant paper and 32 pleat triangle grid.  This one needs strong paper.  I have a diagram somewhere. Will upload it at a later date. 

 This is a really interesting tessellation that I found. It has a lot of overlapping layers, which is always cool to find and fold.  I actually came up with the pattern for the back side and later decided I liked the other side better for the front view.  It uses open back hex twists as the beginning point. Some small natural trapezoids emanate from them. Then there are triangles twisted off of the trapezoids.  Everything is rather close together and tightly twisted.  A single module is pretty easy, but tessellating it is exponentially more difficult.  My first attempt with ordinary paper was unsuccessful. I had originally thought to make the repetitions closer together and only realized they wouldn't fit in the midst of that try.  I moved the repeats a pleat further out and was successful using tant paper.  The third photo shows pretty clearly how the trapezoids and triangles twist out from the central hexagons.  It also shows how you need t...