The dissection of the cube into 6 half-couplers is easy to show with Cube-It! from the Huntar Company. I purchased my copy years ago at Math 'n Stuff in Seattle. The half-couplers further disintegrate into 4 MITEs (MInimum TEtrahedra) in Fuller's concentric hierarchy.
Most middle schoolers received no instruction in these concepts for over 30 years after their publication, despite their obvious relevance and simplicity.
For further reading: [1][2][3][4]
