Soma cube

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The Soma cube is a solid dissection puzzle invented by Piet Hein during a lecture on quantum mechanics by Werner Heisenberg. 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 pieces of the Soma cube consist of all possible non-regular (i.e. excluding rectangles) combinations of four or less unit cubes. Note the lack of a 2x2x1 square and a 4x1x1 line, and addition of a right-angle piece of only three blocks. Of course, if the puzzle actually consisted of only, and all, possible four-block pieces, then it wouldn't be solvable.

The soma cube is often regarded as the 3D equivalent of polyominos. 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 Horton 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 simple recursive backtracking search computer program similar to that used for the eight queens puzzle.

The seven soma pieces are all polycubes of order three or four:

• Image:Tetris-ra.png The "L" tricube
• Image:Tetris-t.png T tetracube: a row of three blocks with one added below the center
• Image:Tetris-l.png L tetracube: a row of three blocks with one added below the left side
• Image:Tetris-s.png S tetracube: bent triomino with block placed on outside of clockwise side
• Image:Tetris-lscrew.png Left screw tetracube: unit cube placed on top of anticlockwise side. Chiral in 3D.
• Image:Tetris-rscrew.png Right screw tetracube: unit cube placed on top of clockwise side. Chiral in 3D.
• Image:Tetris-branch.png Branch tetracube: unit cube placed on bend. Not chiral in 3D.

See also

• Triomino
• Tetromino
• Bedlam cube
• polyomino
• tangram

External links

• http://www.fam-bundgaard.dk/SOMA/SOMA.HTM
• http://www.geocities.com/dnehen/soma/soma.htm
• http://www.mathematik.uni-bielefeld.de/~sillke/POLYCUBE/SOMA/cube-secrets
• Soma Cube -- from MathWorld
• The puzzle can be played online at http://www.puzzles.com/Projects/MillenniumPuzzles/SomaCube.htmde:Somawürfel

es:Cubo Soma ko:소마 큐브 it:Cubo soma ja:ソーマキューブ pt:Cubo soma