From dik@cwi.nl  Thu Aug 22 20:44:41 1991
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Date: Fri, 23 Aug 91 02:37:50 +0200
From: dik@cwi.nl
Message-Id: <9108230037.AA00481@paring.cwi.nl>
To: Cube-Lovers@life.ai.mit.edu, dn1l+@andrew.cmu.edu
Subject: Re:  New "CUBE"

 > I found a fun new cube, sorta.
 > It is called Square 1.
 > it rotates in WIERD ways.
Yes, it is also on sale in Europe.
 > 
 > it is a challenge to return to the state of being a cube, much less to
 > solve it.
True.  To solve it when it is a cube, knowledge of the magic domino is
sufficient.  But it might even be that restoring it to cube form is not
much more dificult than the magic domino.  I do not know yet.  When my
cube got in disorder, by some magical moves it was restored to cube form;
not by me, but by my 8 year old daughter, I still do not know how.
 > 
 > My friend calls it "unfriendly."
That is uncalled for.
 > 
 > the way it is set up, it is a cube, with a center band that has one
 > split.  the two faces on either side of it that are split into the
 > normal three on a side, but the pieces meet at the center, i.e.: the
 > side ones are wedges, and the corners are almost-squares with the point
 > not on the outside being the center.
Something is missing from this description.  I think it can best be
explained based on the MagiBall that came some years ago from Austria.
The MagiBall consists of two halves that can be rotated with respect to each
other.  But only rotates of 180 degrees make sense.  Further it has four bands
of moving pieces.  Movement of the bands is perpendicular to the rotations
of the halves.  Each band has 8 pieces.  When the halves are rotated with
respect to each other, the "left" half of an upper band is connected to the
"right" half of a lower band.  This creates two puzzles, each with 16 pieces.
Now consider that ball; remove the inner two bands (leaving only the uppermost
and lowermost band).  Next go through the bands clockwards when you look from
above.  Alternatingly glue two pieces in a band together and skip a piece.
This will leave you in each band with four double size pieces.  Ignoring
the middle layer of the new cube, this is the new cube (but the middle layer
is easily dealt with).  Now what was missing from the description is that the
centre angle of a cornerpiece is exactly twice the center angle of a wedge.

I have some algorithms to do cycles on three corner pieces and also for
three wedge pieces.  The latter are fairly long however.  And they all only
work if the puzzle is already in cube form.
 > 
 > it is fun.
 > 
 > I was told it will be out at christmas, but I bought it in a store
 > called Games Unlimited in Squirrel Hill, a neighborhood of Pittsburgh. 
 > Buy one from someone, and fry your brain.
 > 
 > Enjoy.
 > 
 > Dale
 >