Well done Oskar, and I much appreciate the tribute to my puzzle!
Regarding viewing the insides of the puzzle, I've made a few images to help understand the internal geometry (minus any complications from an actual mechanism). Here's the puzzle with all exterior pieces transparent. The yellow pieces are all axles that are attached to the core of the puzzle. Note that the three exterior axle pieces (the curved triangle faces) are yellow too, but I've also made them transparent so you can see past them. The core is red:
rototribute geometry.jpg [ 69.05 KiB | Viewed 1704 times ]
Next, I've removed one turning layer, including the outer curved triangular axle:
rototribute geometry turning layer removed.jpg [ 64.67 KiB | Viewed 1704 times ]
Then I've removed all of the remaining orbiting pieces (the corners and flat top and bottom triangle faces):
rototribute geometry orbiting pieces removed.jpg [ 54.54 KiB | Viewed 1704 times ]
Next I have taken away the remaining two outer axles, leaving the core and the six inner axle pieces:
rototribute geometry outer axles removed.jpg [ 46.95 KiB | Viewed 1704 times ]
Finally, I've removed all of the axle pieces to reveal the core of the puzzle (Does anyone recognize this shape?):
rototribute geometry all axles removed.jpg [ 35.62 KiB | Viewed 1704 times ]
As you can see from this series of images, Rototribute is indeed a shallow-cut puzzle with nine axes of rotation. I'll be posting a similar set of images for the original RotoPrism 2 in the Deeper-than-Origin thread
in a few minutes.