Stacked Tritans

Since there are only 10 Tritans, we have a good chance to find solutions for some figures by hand. But a computer program is helpful to check, if a construction is possible at all.

Boxes with sides parallel to the grid aren't possible with the whole set, because the piece #7 needs 2 units in x and y direction and the piece #10 need 3 units in z direction. Otherwise factorizing the whole volume yields 15=1*3*5. Boxes with sides parallel to the diagonals of the grid aren't possible either, because the bottom area must be even.

Using only some of the pieces you can get some boxes: 1s*2s*3, 1h*2h*3 or 1h*3h*2.

But there are prisms with height=3, bottom area=5 and a prism with height=5, bottom area=3 which can be built. For the cross section of the prisms shapes with one or two axes of symmetry or rotational symmetry are possible. Some prisms and other symmetric figures are shown below.

After some playing around with the pieces you might get a solution for each of the above figures in about 10 to 15 minutes.

The pieces were easily cut from MDF and glued, but I think choosing a thicker board would have been better.