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@ruuddotorg argh, I think you have to divide the 24 orientations for (2) by some symmetry factor. I'm guessing in half but need to double-check...
EDIT: yeah, I think it's 12. you can generate them uniquely by starting with 2 pancakes (3 options) and then choosing one of the four corners in in the plane of their orientation to swap between the two pancakes. 3 * 4 = 12.
if this is right, that's 12+3+1 = 16 disconnected tetracube decompositions.
@ruuddotorg if you allow disconnected tetracubes you get 28 more possibilities, I think, made by three disconnected-tetracube-within-2x2-cube shapes:
(1) a 2 cube line and another parallel 2 cube line diagonally opposite it. 3 orientations (one per axis).
(2) three cubes in an L shape plus a disconnected cube diagonally opposite the corner of the L. 8 (choices of corner) * 3 (orientations of L) = 24 orientations, I think.
(3) four disconnected cubes. 1 orientation, I think.
