From cube-lovers-errors@mc.lcs.mit.edu Wed Aug 6 19:25:21 1997
Return-Path:
Received: from sun30.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.1/mc) with SMTP
id TAA04684; Wed, 6 Aug 1997 19:25:21 -0400 (EDT)
Precedence: bulk
Errors-To: cube-lovers-errors@mc.lcs.mit.edu
Mail-from: From Hoey@AIC.NRL.Navy.Mil Wed Aug 6 19:23:53 1997
Date: Wed, 6 Aug 1997 19:10:30 -0400
Message-Id: <199708062310.TAA17135@sun30.aic.nrl.navy.mil>
From: Dan Hoey
To: Cube-lovers@ai.mit.edu
Subject: Reassembled patterns (was Glyph patterns)
I wrote:
> When every cubie of a continuous glyph pattern has either all "figure"
> facets or all "ground" facets, we call the pattern a "reassembled"
> glyph pattern. In this case, we can envision the cube having been cut
> apart into figure and ground cubies and put back together in a
> different orientation....
On second thought, I prefer the definition that a (2-part) reassembled
pattern is one that can be partitioned into two sets of cubies, where
the cubies of each set are in agreement with each other. This
definition differs from the previous in two ways. Reassembled
patterns need not be continuous--"laughter" is a noncontinuous glyph
pattern. And not all continous glyph patterns with figure/ground
cubies meet this definition--e.g. flip the LF and RD edge cubies.
We may also speak of 3-part reassembled patterns, though they are not
necessarily glyph patterns. Are there any particularly nice ones?
Cube-in-a-cube-in-a-cube comes to mind.
Call an "N-part" pattern one that requires cutting into at least N
parts for reassembly. Surely every position can be reassembled from
at most 21 parts, since that's all the pieces there are. Is this
achievable? We could restrict the reorientation of the parts to C,
but in some cases (e.g. pons asinorum) we can manage with fewer parts
if we allow reorienting some of the edges by M. Is there a 20-part
pattern that would require 21 parts if the orientations were
restricted to C?
In the supergroup, can we manage a 24-part position? A 23-part
position that requires 24 parts for C-reorientation?
Dan Hoey
Hoey@AIC.NRL.Navy.Mil