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From: Andy Latto <andyl@harlequin.com>
Date: Tue, 7 Dec 1993 10:37:37 -0500
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To: Alan@lcs.mit.edu
Cc: BRYAN@wvnvm.bitnet, Cube-Lovers@ai.mit.edu
In-Reply-To: Alan Bawden's message of Mon, 6 Dec 93 20:16:26 -0500 <6Dec1993.195513.Alan@LCS.MIT.EDU>
Subject: Unique Antipodal of the 3x3x3 Edges

   Date: Mon, 6 Dec 93 20:16:26 -0500
   From: Alan Bawden <Alan@lcs.mit.edu>
   Sender: Alan@lcs.mit.edu

      Date:      Mon, 6 Dec 1993 18:32:15 EST
      From: Jerry Bryan <BRYAN%WVNVM.BITNET@mitvma.mit.edu>
      ...  It is really quite extraordinary and wonderful.  I already knew
      that there were only four equivalence classes with 24 elements.  Well,
      two of them are Start itself and its antipodal.  Without further ado:...

   This is very interesting indeed!  
   So the next natural question would seem to be: What are the -other- two?

Switch each edge with its antipode, with or without flipping all twelve edges.