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.
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.
This can be printed with no support material.
Printed with PLA on blue painter's tape, extruder @ 180°C, bed at 50°C.
I printed it with typical 40% honeycomb infill. I did change the infill angle to 90 degrees, since the solid fills (along the "vertical" rises) are already at 45 degrees relative to the X-Y axes, the 90 degree infill angle makes the fill pattern 45 degrees relative to the part's perimeters up the four rising "corners". For the circular portions, of course, it makes no difference.
I also used a 0.75mm Z-lift on retract to avoid hitting anything while making the large fast movements. Since the print failures I had printing t 40760 were primarily caused by breaking the part (the thin vertical portions) because the tips of the overhang tend to curl up, and the extruder hits one and snaps the part (see photos; yellow).
I first tried to print it with ABS (see photos; black); that was with a .5mm Z-lift on retract.
After that failure, I decided to go back to using PLA (as with 40760), with better luck (see photos; orange).
It still gets dicey at the times where it's closing the vertical circles; I had to babysit and assist the print on the outer 3 spheres.