[math-fun] cubic thirds

There are some interesting possibilities for dissecting a cube into three congruent pieces. Select a triagonal, and split the cube in half with a plane perp-bisecting the triagonal. The two pieces have regular triangle symmetry, and each can be cut into thirds using 120deg wedges with the triagonal as the spine. The starting wedge angular position is arbitrary, so the two halves of the cube can have different cutting positions. Wedges from the two halves can be glued for a rather peculiar looking congruent trisection. I believe one of Gardner's columns was about dissections, and said the square-into-5-congruent- pieces problem had only the trivial solution, and that a proof existed. Rich