I've been wanting to design a non-planar preassembled mechanism for awhile, but it took Prot0typ1cal's Venus Box to inspire me on what to make. That is a beautiful design, but the more I thought about it, the more I thought it should be possible to print without assembly. Combining that spherical box idea with my earlier iris box concept lead to this design.
You can see how it works and how to free it up after printing here: https://youtu.be/-m8uWz-qf7Y
I left 0.3mm of space between the moving parts. If that's not enough, you probably need to calibrate your printer a bit. Common errors include temp too high (makes strings), filament diameter too small in slicer (makes overextrusion) or belts loose (makes positioning less accurate). The first layer will also have to be quite accurate, as it needs to stick enough to keep the leaves in place, but not so squished that everything fuses together. As anyone who prints my designs knows, these are not for the faint of heart, so don't feel bad if it doesn't work on the first try.
Believe it or not, pretty much everything in this design adheres to the 45 degree rule, which is why it prints well without supports. If you open this with a program like 3D Builder, you can separate the pieces and see how the internal mechanism is designed. You can also open the source file in OpenSCAD, as it includes an animation of approximately how the pieces move (I'd recommend lowering $fn to 30 so that it doesn't take forever to load).