Date: 31 March 1982 22:26-EST
From: David C. Plummer <DCP at MIT-MC>
Sender: DCP0 at MIT-MC
Subject: 4**3,5**3
To: CUBE-LOVERS at MIT-MC

NO, NO, NO !!!!  You CANNOT treat 1 of the center slices of a
4x4x4 as a center of a 3x3x3.  Suppose you did this for one axis,
and for the other two axes you treated both "centers" as a unit
(and therefore the center slice of a 3x3x3).  Now take one of the
axes with a double width center, and rotate an outer slice 180
degrees.  Suppose the front face looked like this:

	+####+####+####+####+
	#    #    #    |    #
	#    #    #    |    #
	+####+####+####+####+
	#    #    #    |    #
	#    #    #    |    #
	+----+----+----+----+
	#    #    #    |    #
	#    #    #    |    #
	+####+####+####+####+
	#    #    #    |    #
	#    #    #    |    #
	+####+####+####+####+

You rotate the top slice and the front face now looks like:

	+####+####+####+####+
	#    |    #    #    #
	#    |    #    #    #
	+####+####+####+####+
	#    #    #    |    #
	#    #    #    |    #
	+----+----+----+----+
	#    #    #    |    #
	#    #    #    |    #
	+####+####+####+####+
	#    #    #    |    #
	#    #    #    |    #
	+####+####+####+####+

Notice that the top layer does not go very well with the bottom 3
layers.  The 5x5x5 has similar problems.  

I think the right way to solve both the 4x4x4 and 5x5x5 at first
is to use mono-flips.  Once conceptually understood, they are
very powerful and easy to visualize.