The author of Thing 31685 mentioned it was inspired by a circa 1893 puzzle book, which led me to read that book online. There, I stumbled on the "Spots" puzzle, http://archive.org/stream/puzzlesoldnew00hoff#page/98/mode/1up , in which an oversized die is cut into nine simple blocks. The surprisingly difficult problem is to reassemble the die.
My version takes advantage of the fact that 3D printing can easily build more complex shapes. First, the dots are not merely painted, but are conical hollows. Second, rather than having the internal edges be simple cuts, I have introduced an interlocking pattern of conical hollows and bumps. This makes the assembled die hold together somewhat, but the puzzle is at least as difficult to solve because the internal and external hollows look identical -- I even painted them identically.
I also made the die face pattern match the modern dice I had at home. All dice have opposing faces sum to 7, but the book's face pattern is slightly different from my design.
In the 20131213 version, I've added a little 3D-printed box to hold the assembled die and rotated a few of the pieces to make print quality less slicer-dependent (no holes on top, because cura doesn't place fill wisely). The box serves to hold the assembled die together and as a reference for the dot placement while assembling the puzzle, but the box itself is also a little puzzle -- how does it open?
This is a very easy print using either PLA or ABS with typical settings and minimal fill. I designed it to be printed at 2/3 the scale given here, but such small parts simply do not feel as nice when attempting to solve the puzzle. The parts given here build a die which is roughly 45mm on each side. There is a tolerance built-into the design to allow for some roughness in the print, but the design can be scaled up or down quite a bit without major issues. The paint inside the conical hollows of the blue version is simply flat white latex, which sticks well enough due to the texture of the extruded PLA; the black die is made out of ABS with white appliance touch-up paint. The black hollows of the white version were dyed using a black permanent marker. The 20131213 version has the same die parts (in a potentially better-printing orientation), but also includes a box for the die which has dots to be painted the same way.
By far the easiest way to assemble the die puzzle is to closely examine the assembled-with-gaps 3D design I've included here just for this purpose -- don't try to print diepuzzle45mmAssembled.stl . The file to print for puzzle+box is diepuzzle20131213_flat.stl , but you can print just the puzzle as diepuzzle20131213_flat_pieces.stl and just the box as diepuzzle20131213_flat_box.stl . Hint: I find the puzzle is easier to solve by building the three layers separately, stacking them as the final step. Despite having only 9 pieces, it is not an easy puzzle to solve, and can deliver hours of painful frustration. ;-)
Note that this size puzzle contains parts that could be a choking hazard, so it isn't for toddlers. Trust me... they wouldn't enjoy it anyway. My 12-year-old daughter is generally very fast with such puzzles, and she likes it, but it still took her something like 20 minutes to solve it.
As for the box added in the 20131213 version, there is also a little trick to open the sliding door. When you slide the door closed, a little oval bump on it will gently click against the front edge of the box, locking it closed. The door is printed top-down on our M2's glass bed, so it's smooth enough to give no grip when closed. To open it, quickly turn the loaded box so that the die inside gently lands on the sliding door, popping the oval's edge from against the inside of the lip and letting the door slide open freely. If you close the box with nothing inside, it will be a lot harder to open.... The latch might also stick somewhat if your printer isn't as precise as our M2.