Knuth's packing puzzle

In case you found the Hoffman packing puzzle to easy, here is the Knuth version.
In 1978 Hoffman proposed that a if you take cuboids with size AxBxC, you can always pack 27 into a cube that has edges of length A+B+C.
In 2003 Knuth showed that for a special subset you can fit 28 cuboids into a cube. As you can see in the pictures the short side of the cuboids fits 4 times into the cube. Therefor design falls into this subset and should therefor be solvable for 28 pieces instead of the typical 27. Good luck.

Warning, this is a really hard puzzle. There are solutions to be found online though. Or you can throw away one piece and solve it like a Hoffman puzzle (which it technically is not).
Very similar easier puzzle: https://www.thingiverse.com/thing:4751947

All parts have 0.2 mm play in the design. I would not recommend to scale it down. A parametric fusion file is included, if you want a smaller version use the "scale" parameter from the list.

You need to print the cube, the