New Puzzle: Nine Bed Nightmare

The Nine Bed Nightmare, a new box packing puzzle by George Bell. You can now purchase a copy for a limited time from

The nine puzzle pieces:

Note that all pieces are 3D, none of them are planar!
Volume of front row: 6, 8, 10, 12 units (total 36 units).
Volume of middle row: 12, 15, 18 units (total 45 units).
Volume of top row: 20, 24 units (total 44 units).
Total volume of all pieces: 125 units.

Another way to sort the shapes:

All nine pieces can be used to build:

A 5x5x5 cube (hard, solution is unique). Or ...

A 5x4x4 brick and a 5x3x3 brick (easy, solution is unique). Or ...

A "big bed". The volume of this bed is 126 units, so there is one hole somewhere (not visible in this photo). There are two solutions with different hole locations.

Using a subset of the pieces, we can also build:

A 5x5x4 brick (medium, 2 solutions both using the same pieces). Or ...

A 4x4x4 cube (easy, 6 solutions all using the same pieces).

Finally, it is possible to add three larger "beds" of analogous shape and build a 7x7x7 cube with a unique solution. This is the "twelve bed nightmare".