I decided to revive the venerable iris box by redesigning it in OpenSCAD and making it printable with fewer parts and less assembly. It's also somewhat larger (though now the dimensions are easily adjustable with OpenSCAD), the tracks are redesigned to give more rigidity when closed, and it now opens and closes according to righty-tighty, lefty-loosey. The ring is also aesthetically redesigned and the base interior tapers down the wall thickness to give a little more internal volume.
Print the three parts (base, ring and leaves). Note that unlike v2, the base is printed right-side up and the ring is upside down. You can also test the mechanism with testbase, which takes much less time to print than the full base. You can test the tolerance by clipping a leaf onto a ring peg to make sure it turns easily but doesn't wiggle. Remove before beginning assembly.
While holding the ring upside down, place each leaf onto it as shown in the picture and hold them there with your fingers (don't clip them on yet). Put this assembly onto the base, putting the ring pegs into the larger openings in the base. Press down and apply a little left torque to the ring (some wiggling may be necessary) until the base pegs fall into the leaf tracks. Now it should be possible to twist the ring back and forth a little, so twist it all the way right. Next, line up the leaf keyed holes with the ring pegs and pop each keyhole onto each peg. You can usually only get them on half way at first, then the second time around they'll go on all the way.
These STLs made a very smooth mechanism on my TOM, but if your calibration gives you different results, then adjust the parameters in the scad file (peg clearance diameter is probably the most important).
UPDATE: I found the mechanism to be a little sticky when the box was half-way open, which turned out to be because I miscalculated the clearance for the geometry. I've fixed the error (this version is much smoother), so the scad file and IrisLeaves.stl are new.