The Soma cube is a solid dissection puzzle invented by Danish polymath Piet Hein in 1933 during a lecture on quantum mechanics conducted by Werner Heisenberg.
Seven pieces made out of unit cubes must be assembled into a 3×3×3 cube. The pieces can also be used to make a variety of other 3D shapes.
The pieces of the Soma cube consist of all possible combinations of three or four unit cubes, joined at their faces, such that at least one inside corner is formed. There is one combination of three cubes that satisfies this condition, and six combinations of four cubes that satisfy this condition, of which two are mirror images of each other. Thus, 3 + (6 × 4) is 27, which is exactly the number of cells in a 3×3×3 cube.
In addition to constructing a cube, the SOMA manual provides assorted figures to construct with the seven pieces.