Browsing a MiniNeo eZine that I follow, I noticed a rather interesting looking hexagonal flower and thought it worth a try:

You triangle grid a hexagon into 16ths, then put a hex twist in the middle, then add the swing-back on petals and tidy up the tessellation to make a swirl.

The manipulations that follow add symmetry and then open up layers of petals in a great final reveal.

I folded this from a hexagon cut from an A3 sheet, and it is large and lovely – it looks a little like a water lily flower. I think I will fold this again with prettier paper.