This is a hexagon of rhombuses and triangles that are nestled together along their matching fold angles. There is a concentric hex collapse at the center.  The tessellation repeats quite naturally. A larger grid and sturdier paper would really have done with model a great service.  We ran out of better quality paper at work, so my tessellations have suffered somewhat for it.                                            Still, the idea is solid. It would be really nice if someone with better paper and a bigger grid decided to fold it. 

This is hex collapses repeating. Kind of interesting. Nothing ground breaking here, but pretty cool still the same.  It's no doubt, been done before. It was new to me, though.  I was thinking about spread squashing the flaps open for a different look. That was the initial plan. Still, I like how it turned out before that.  I used hexes on the back in between the touching 'petals' to connect them flatly.  The photos that follow are front squashed unlit, rear lit and spread squashed lit. 

There's a neat technique that uses the fold angles of various shapes to have one flow into the other seamlessly. Unlike twist folds which just spin off the axis of another twist, these folds share the same fold angles.  It's similar, but a little different. It allows for slightly different arrangements and configurations of the shapes on the grid.  This type of fold relationship is also somewhat easier to execute. Each shape flows directly into the next.  Unlike twists, the patterns are more linear than round.  This one is rhombuses and open back hexes.  Instead of a typical circular pattern, they form rows because of the nature of their angular connections.  I've used this technique before. It offers some different structures while still using the standard shapes. 

I've done a bunch of tesses lately, but getting nice photos has been difficult. Either it's too late or it's cloudy or there's no time at all.  I'm not complaining, just saying.  This one is a riff on a tessellation in Eric Gjerde's famous origami book. That one is hex twists with open back triangle twists off of it.  In my variation I decided to see how it would look if the hexes and triangles were on opposite sides of the paper.  There was a lot of precreasing involved. Those triangular veins needed help folding. And it's a somewhat unnatural flat fold  But, not too crazy difficult and a pretty cool result.

Messing around with rhombuses yielded this interesting pattern. It utilizes reverse rabbit ear folds to create triangular points which connect the running rows of rhombus twists. The triangles form in the spaces between the rhombuses. Then there are mirror triangles to facilitate the the next row.  It kinda looks and folds like a square grid tessellation even though it's done using a triangle grid.  It's a fairly easy fold.  I do have a crease pattern. Just need to take a pic and upload it. Update: photo of crease pattern added below.