Rose Tricylinder Puzzle

This is a "work in progress" as I'm not entirely satisfied with it. Three pieces assemble into a tricylinder, the solid obtained by intersecting 3 cylinders at right angles. Also known as a "Steinmetz solid". https://en.wikipedia.org/wiki/Steinmetz_solid

Stephen Chin invented this puzzle in 2014 as a rhombic dodecahedron. He made the wood copies in the photos. It turns out a tricylinder is equivalent to a rhombic dodecahedron with curved faces and edges. On the inside, both versions are the same. If this puzzle is made with exact, rigid pieces it cannot be assembled. Some clever modification of the pieces is required in order to get it to go together.

This puzzle is trickier to assemble than you might think. Do not simply jam the pieces together and push hard! This will require significant force and can damage the puzzle. In addition, if you force the pieces together you may not be able to get them apart! Note the piece orientation, if you get a piece backwards and force things you can assemble the puzzle incorrectly. See if you can find the way to assemble the puzzle correctly, with no force. Taking it apart is easy when assembled correctly.

You need three copies of the basic piece. I include a file for the piece which makes a rhombic dodecahedron as well. The diameter of the puzzle is around 6 cm.

WARNING: One of the images shows how the puzzle got its name but is also a spoiler!