From andyl@harlequin.com  Tue Dec  7 12:24:30 1993
Return-Path: <andyl@harlequin.com>
Received: from hilly.harlequin.com by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA08855; Tue, 7 Dec 93 12:24:30 EST
Received: from epcot.harlequin.com by hilly.harlequin.com; Tue, 7 Dec 1993 12:27:09 -0500
Received: from phaedrus.harlequin.com (phaedrus) by epcot.harlequin.com; Tue, 7 Dec 1993 12:29:34 -0500
From: Andy Latto <andyl@harlequin.com>
Date: Tue, 7 Dec 1993 12:29:32 -0500
Message-Id: <12292.199312071729@phaedrus.harlequin.com>
To: ccw@eql12.caltech.edu
Cc: BRYAN%WVNVM.WVNET.EDU%WVNVM.WVNET.EDU@mitvma.mit.edu,
        cube-lovers@ai.mit.edu
In-Reply-To: Chris Worrell's message of Mon, 6 Dec 93 19:13:20 PST <931206185340.20400b26@EQL12.Caltech.Edu>
Subject: Unique antipode of edges only



   Unfortunately, this is wishfull thinking.
   This antipode is 15 qtw from Home, an odd distance.
   All edges flipped is an even distance from Home in the qtw metric.

   Looking at Jerry Bryan's pictures, I see 5 two edge swaps.

   >
   >          *6*              *6*
   >          6*6              3*4
   >          *6*              *1*
   >          *2*              *5*
   >          2*2              3*4
   >          *2*              *2*
   >       *3**1**4*        *1**1**1*
   >       3*31*14*4        5*23*42*5
   >       *3**1**4*        *6**6**6*
   >          *5*              *2*
   >          5*5              3*4
   >          *5*              *5*
   >
   >         Start          Antipodal
   >

The antipodal position is an interesting one. If you take the antipodal
position, and flip all the edges, you get:

        *5*                      
        5*5                      
        *5*                      
        *1*                      
        1*1                      
        *1*                      
     *3**2**4*                   
     3*32*24*4                   
     *3**2**4*                   
        *6*                      
        6*6                      
        *6*                      

Antipodal with edges flipped.

This looks like a rotation of the solved state at first glance, since
all the faces on a given side of the cube are the same color. But
look again! This is not the solved state of the original cube, but 
of the mirror image cube. If you added in the centers or the corners,
there would be no way to add them to make this a solved state.

					Andy Latto
					andyl@harlequin.com