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soma cube

Wikipedia soma cube
The pieces of a Soma cube (with extra coloring)Enlarge The pieces of a
Soma cube (with extra coloring) The same puzzle, assembled into a cubeEnlarge
The same puzzle, assembled into a cube

The Soma cube is a solid dissection puzzle created 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 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 simple recursive backtracking 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:

* image:tetris-t.png T: a row of three blocks with one added below
the center

* image:tetris-l.png L: a row of three blocks with one added below
the left side

* image:tetris-s.png S: bent triomino with block placed on outside
of clockwise side

* image:tetris-lscrew.png Left screw: unit cube placed on top of
anticlockwise side. Chiral in 3D.

* image:tetris-rscrew.png Right screw: unit cube placed on top of
clockwise side. Chiral in 3D.

* image:tetris-branch.png 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.mathematik.uni-bielefeld.de/~sillke/POLYCUBE/SOMA/cube-secrets

* Soma Cube -- from MathWorld (http://mathworld.wolfram.com/SomaCube.html)



This entry is from Wikipedia, the leading user-contributed
encyclopedia. It may not have been reviewed by professional editors
(see full disclaimer)

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Best of the Web

Some good "soma cube" pages on the web:


Math
mathworld.wolfram.com

Mentioned In soma cube is mentioned in the following topics:

Piet Hein (Danish scientist and poet)

List of terms based on the word cube

Winning Ways for your Mathematical Plays

polyform

John Conway

List of puzzle topics

polycube puzzle

Soma (disambiguation)

tetromino

mathematical game

More>


Copyrights:



Wikipedia information about soma cube
This article is licensed under the GNU Free Documentation License. It
uses material from the Wikipedia article "Soma cube". More from
Wikipedia








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