Ok, I still consider myself an amateur woodworker at best so I didn't want to try to make the tetrahedron shape. Therefore, I took the easy route and 3D printed this part. I pocketed it out to save weight (cost) but this also made it easier to grab and manipulate which took away a little bit of the puzzle challenge (not a good thing). I've provided dimensions for a solid version that hopefully a woodworker with more talent than me can produce :).

Note that the tetrahedron size is arbitrary. However, you must size the cage opening to get the correct fit. You can either work the geometry (Pythagorean Theorem) by hand or refer to table for other sizes. For the table, the tetra size (L) for this build is 2.5". This requires a square opening on the top of 1.768" (L/2^0.5). I added 0.025" to this dimension under the "recommended box opening" column to guarantee fit.

Note that the exact dimensions shown for the tetrahedron are slightly too big for my cage opening (Step 5). You have a few options:

Round the edges/points of the tetrahedron by ~ .010" Increase the cage opening (hypotenuse) to ~ 2.55" (Step 5) Reduce the tetra sides down to 2.4"

My 3D print came in small so I was good. If I made it from wood, rounding the edges would have been the optimum choice for me. Note that with use, the vertices will get rounded very quickly anyway.