v2 of my cube features easier-to-print joints, more durable construction, and a design that should be more compatible with a range of print settings. Revision details at the far bottom of this page. I highly recommend this over the previous version - there should be no comparative downsides.
A small test file has been included so that you can try out your print settings before printing the entire model. You can try rotating it to print in all 3 of the required joint orientations if you wish.
Prints at 0.2 mm layer height and takes about 3 hours. Requires about 11 m (32 g in PLA) of filament. Please let me know your results!
This thing is optimized for 0.2 mm layer height. Please try that first before any other resolutions. It's also optimized specifically for a 0.4 mm nozzle width, so no guarantees it will work well if you're using another size.
10% infill is more than enough to support the top surfaces if you have good cooling. Go up from this number if you prefer a bit heftier of a cube, which makes it a bit more fun to play with IMO (100% infill cubes are a hit with my coworkers).
Some other tips for best print results: use the part cooling fan at 100% (except for your first 1-2 layers), turn the model diagonally in your slicer so that X and Y axes move together for most of the moves, use 2+ vertical shells/perimeters for strength (3+ for the rounded version), and print at the coolest temperature you reasonably can for your material to avoid stringing or unwanted lamination.
Cura users: Be sure to disable "Ignore Small Z Gaps" under your "Shell" settings or this will not slice properly and the joints will be fused together!
Break free and loosen it up
The cube's hinges should all turn freely straight off the print bed (though the vertical joints often come out tighter than the horizontal ones). The previous model required some "wearing in" to feel loose, but v2's joints should require much less work.
Autodesk Fusion 360
This model was designed in Fusion 360. I used cubes with 3 mm fillets/chamfers along with conical joints, plus a lot of handwritten calculations to ensure even tolerances throughout the part. For example, the radius of each cube is equal to the outer radius of each pin, so that the corners do not interfere when rotating (as they did on many other models I tried printing).
v1 -> v2 changes
-a version with 45° chamfers instead of fillets on the non-joint edges to avoid warping/curling
-slightly reduced cube edge radius and increased joint width for more rigidity when turning
-new conical joint design to reduce unsupported overhangs
-fixed thin wall error in previous file
-prints a bit faster since fewer shells are required