Soma cube

The Soma cube is a mathematical puzzle by Piet Hein. Seven pieces made out of unit cubes must be assembled into a 3x3 cube. The pieces can also be used to make a variety of other interesting 3d shapes.

The soma cube is often regarded as the 3d equivalent of tangrams. There are interesting parity properties relating to solutions of the Soma puzzle.

Soma has been discussed in detail by the Martin Gardner and John Conway.

The seven soma pieces are all variants on the bent trimino:

The bent trimino
T: a row of three blocks with one added below the center
L: a row of three blocks with one added below the left side
S: bent trimino with block placed on outside of clockwise side
Left screw: unit cube placed on top of anticlockwise side. Chiral in 3D.
Right screw: unit cube placed on top of clockwise side. Chiral in 3D.
Branch: unit cube placed on bend. Not chiral in 3D.