Soma cube

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The Soma cube is a solid dissection puzzle created by Piet Hein during a lecture on quantum mechanics by Werner Heisenberg.

Related Topics:
Solid dissection puzzle - Piet Hein - Quantum mechanics - Werner Heisenberg

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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.

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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 3 blocks. Of course, if the puzzle actually consisted of only, and all, possible 4 block pieces, then it wouldn't be solvable.

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The soma cube is often regarded as the 3D equivalent of tangrams.

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There are interesting parity properties relating to solutions of the Soma puzzle.

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

Related Topics:
Soma - Aldous Huxley - Brave New World

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

Related Topics:
Martin Gardner - John Conway

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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.

Related Topics:
Winning Ways for your Mathematical Plays - Up to - Backtracking search - Eight queens puzzle

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The seven soma pieces are:

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• The bent triomino

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

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• 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.
 
Soma cube: See also ►