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Date: Mon, 5 Feb 1996 16:31:26 -0500
From: michael reid <mreid@ptc.com>
To: cube-lovers@ai.mit.edu
Subject: cube in a cube

recently i wrote

> back in the days before i did computer-cubing, i found an interesting
> maneuver for "cube in a cube" that only turns three faces.  what's the
> shortest such maneuver that you know?

there was never any response to this, but i'll give my solution anyway.

let  X  =  U2 F R' F2 R F2 R F2 R' F U2 .

then  X  produces two two-cycles of corner-edge pairs.  the commutator
[ X , C_UFR ]  produces "cube in a cube" in 22 face / 32 quarter turns
and only turns the faces  U, F  and  R.

the notation  C_UFR  refers to a rotation of the whole cube, and
[ a, b ]  denotes the commutator  a b a^-1 b^-1 .

mike