Big Thick Gyro Cube v2
Multiple extruder update
I uploaded separate files for the "odd" and "even" spheres to make it easy to print in multiple colors if you have a dual extrusion printer.
I also separated the supports object so you can include or exclude as you desire, or assign it to a support-material extruder.
v2 Update
Since most printing problems occur at the worst overhangs (closing the vertical circles), I made a second version that includes some support (vs. letting the slicer do it, which generated far too much). This version is the "with supports" file.
Oh, and I cracked sphere #2 (second smallest one) snapping in sphere #1 (smallest) into its nib holders; so I also notched the female nibs on one side a bit, which make it a little easer to assemble.
I printed the version with supports scaled to 70% that turns out to be just slightly larger than thing 40760.
With the supports, I was able to print the object completely unattended. It was easy to break out the bulk of the support, and carve the remainder off with a knife; the smallest sphere was a little tricky to trim off.
After several failed attempts to print thing: 40760 (see photo; yellow), I decided to design my own from scratch.
The spheres in this version are 5mm thick (less fragile during printing the "vertical" portions), and the "holes" have been cut with a flat inner edge, making the vertically printed holes close at the top better and have a cleaner edge.
It is also larger overall (to accommodate the thicker spheres); you'll need at least a 150x150x150mm print volume to print it full-size.
It has nice big nibs with shallow departure angles to avoid any overhang issues.