Soma cube

The Soma cube is a mathematical puzzle by Piet Hein. Seven pieces made out of unit cubes must be assembled into a 3x3x3 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.

It is unclear whether the puzzle is named after the fictitious drug 'soma' in Aldous Huxley's novel Brave New World.

Soma has been discussed in detail by Martin Gardner and John Conway, and the book Winning Ways for your Mathematical Plays contains a detailed analysis of the soma cube problem. There are 240 distinct solutions of the soma cube puzzle, up to rotations and reflections: these are easily generated by a recursive search computer program similar to that used for the eight queens puzzle.

The seven soma pieces are:

• The bent triomino

and six tetrominoes, all made from the bent triomino with one added cube:

• 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 triomino 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.

Note the lack of a 2x2x1 square and a 4x1x1 line, and addition of a right-angle piece of only 3 blocks. Of course, if the puzzle actually consisted of only, and all, possible 4 block pieces, then it wouldn't be solvable.

See also:

• Triomino
• Tetromino
• Bedlam cube

External links

• http://www.fam-bundgaard.dk/SOMA/SOMA.HTM
• http://www.geocities.com/dnehen/soma/soma.htm
• http://www.la.unm.edu/~mbrettin/algorithms/somacube.html
• http://www.mathematik.uni-bielefeld.de/~sillke/POLYCUBE/SOMA/cube-secrets