*Simple observations:* A regular tetrahedron can be cut into 2 mutually congruent pieces (in 3 obvious ways which are all basically the same way, giving one and same pair of congruent pieces). The regular tet can be cut into 3 mutually congruent pieces (infinitely many sets of 3 resultant pieces) and into 6 pieces (1 obvious set of resultant pieces). It also allows congruent partition into 4 pieces (only one obvious set of pieces) and also into 12 pieces (infinitely many different sets of pieces based on first cutting into 4), 8 pieces (1 obvious set of pieces) and 24 pieces (1 obvious set).

- Is there any tetrahedron (regular or otherwise) that can be cut into n mutually congruent connected pieces (no other constraint on the pieces, not even convexity) for any other value of n, say, 16 or 20...?

mightjust have some non-trivial congruent partitions of the tet for n values like perhaps 16 or 20. $\endgroup$