Original design as a challenge to develop a unique opening box. When done, resembled one of Bender's eyes. A co-worker said it looked like a Venus Fly trap, so named it "Venus Box".

A cam actuates 4 doors by rotating the spherical cover (or base). Remains securely open or closed. 4 inch diameter, the whole thing snaps together, and prints without supports.

Print Cam at 0.3 or lower, with 2 shells and 20% infill.
Print Cover at 0.3 or lower, 2 shells, 20% infill.
Print the doors at 0.2 or lower, with 3 shells and 20% infill.

NOTE: Trim the triangular nuggets off the door hinges, they're only there to help the build.

Slide the doors together, posts go into the hooked holes, don't snap these together.
If you print the Cam at 0.3, use sand paper, file or soldering iron to smooth out the stair steps on the 4 lower race faces (cam tracks) before assembling.

Enjoy :)

EDIT 5/20/16: Added Parasolid files
EDIT 5/24/16: Added "NT" (no trim) door files, without the triangular build helper nuggets.
EDIT 6/13/16: Added COVER2.STL that has more snap, print only if your cover is loose.
EDIT 6/14/16: Thingiverse Featured. "elegant Venus Box" :)
EDIT 1/9/17: Added COVER3.STL for even a tighter fit for multiple material type prints.

https://youtu.be/-EtzOVkyGRA