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Friday, December 12, 2008

Friday December 12, 2008

Filed under: General,Geometry — m759 @ 3:09 PM
On the Symmetric Group S8

Wikipedia on Rubik's 2×2×2 "Pocket Cube"–
 

http://www.log24.com/log/pix08A/081212-PocketCube.jpg
 

"Any permutation of the 8 corner cubies is possible (8! positions)."

Some pages related to this claim–

Simple Groups at Play

Analyzing Rubik's Cube with GAP

Online JavaScript Pocket Cube.

The claim is of course trivially true for the unconnected subcubes of Froebel's Third Gift:
 

Froebel's third gift, the eightfold cube
© 2005 The Institute for Figuring

 

Photo by Norman Brosterman
fom the Inventing Kindergarten
exhibit at The Institute for Figuring
(co-founded by Margaret Wertheim)

See also:

MoMA Goes to Kindergarten,

Tea Privileges
,

and

"Ad Reinhardt and Tony Smith:
A Dialogue,"
an exhibition opening today
at Pace Wildenstein.

For a different sort
of dialogue, click on the
artists' names above.

For a different
approach to S8,
see Symmetries.

"With humor, my dear Zilkov.
Always with a little humor."

-- The Manchurian Candidate

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