My original problem is:
1) Let $XYZT.X'Y'Z'T'$ be a cube. Given $A\in XYY'X',B\in XYZT,C\in Y'Z'$ and $D\in TT'$. Is there a way to dissect the cube into Trirectangular Tetrahedra and $ABCD$?
I have no had a clear approach for this problem, just trying to answer easier questions.
2) Can a cube be dissected into trirectangular tetrahedra? I know it cannot be dissected into 6 such ones Equidecomposability of a Cube into 6 Trirectangular Tetrahedra. But I wanna generalize the question a little bit here. Clearly if $ZXY'T'$ can be dissected into trirectangular tetrahedra, the question is solved.
3) Can a 3-dimensional figure be dissected into cubes?
Those are my current questions and approaches, I hope u can help. Thank you