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