Soma cube: Difference between revisions

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The [[Soma cube]] is a [[mathematical game|mathematical puzzle]] by [[Piet Hein]].
The [[Soma cube]] is a [[mathematical game|mathematical puzzle]] by [[Piet Hein]].

:''This text is from the 'Tetromino' article, and is being edited''

Counting rotations in [[2d|two dimensions]] as equivalent, there are seven possible shapes:
<ul>
<li>[[image:tetris-i.png]] I (also called "stick", "straight"): four blocks in a straight line</li>
<li>[[image:tetris-o.png]] Square (also called "O", "package", "block"): four blocks in a 2x2 square</li>
<li>[[image:tetris-t.png]] T: a row of three blocks with one added below the center
<br>A common move with the T piece is to spin it in place to fill a line.</li>
<li>[[image:tetris-l.png]] L: a row of three blocks with one added below the left side</li>
<li>[[image:tetris-j.png]] J (also called "inverted L", "[[Gamma]]"): a row of three blocks with one added below the right side
<br>This piece is a reflection of L but cannot be rotated into L in two dimensions; this is an example of [[chirality]].
However, in [[3d|three dimensions]], this piece is identical to L.)</li>
<li>[[image:tetris-s.png]] S: bent trimino with block placed on outside of clockwise side</li>
<li>[[image:tetris-z.png]] Z: bent trimino with block added on outside of anticlockwise side
<br>Reflection to S. See "J", above.</li>
</ul>

When added the third dimension, there are three more patterns, all created by placing a unit cube on the bent trimino:
<ul>
<li>[[image:tetris-lscrew.png]] Left screw: unit cube placed on top of anticlockwise side. Chiral in 3D.</li>
<li>[[image:tetris-rscrew.png]] Right screw: unit cube placed on top of clockwise side. Chiral in 3D.</li>
<li>[[image:tetris-branch.png]] Branch: unit cube placed on bend. Not chiral in 3D.</li>
</ul>



See also:
See also:

Revision as of 00:01, 27 January 2002

The Soma cube is a mathematical puzzle by Piet Hein.

This text is from the 'Tetromino' article, and is being edited

Counting rotations in two dimensions as equivalent, there are seven possible shapes:

  • I (also called "stick", "straight"): four blocks in a straight line
  • Square (also called "O", "package", "block"): four blocks in a 2x2 square
  • T: a row of three blocks with one added below the center
    A common move with the T piece is to spin it in place to fill a line.
  • L: a row of three blocks with one added below the left side
  • J (also called "inverted L", "Gamma"): a row of three blocks with one added below the right side
    This piece is a reflection of L but cannot be rotated into L in two dimensions; this is an example of chirality. However, in three dimensions, this piece is identical to L.)
  • S: bent trimino with block placed on outside of clockwise side
  • Z: bent trimino with block added on outside of anticlockwise side
    Reflection to S. See "J", above.

When added the third dimension, there are three more patterns, all created by placing a unit cube on the bent trimino:

  • 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.


See also: