From cube-lovers-errors@mc.lcs.mit.edu Fri Apr 3 19:32:23 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.1/mc) with SMTP id TAA16989; Fri, 3 Apr 1998 19:32:23 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From cube-lovers-request@life.ai.mit.edu Sun Mar 29 19:35:16 1998 Date: Sun, 29 Mar 1998 19:35:43 -0400 (EDT) From: Jerry Bryan Subject: Re: partial isoglyphs In-Reply-To: <199708210441.AAA22489@life.ai.mit.edu> To: Cube-Lovers Message-Id: On Thu, 21 Aug 1997, michael reid wrote: > dan recently introduced the concept of "partial isoglyphs", in which > some faces are solid, and the others are glyphs of the same pattern. > i looked into this a little and didn't find much. only the case > of two opposite solid faces seems to have many possible glyph types, > although some of these possible types may have many solutions. > > here's what i found Note that all the glyph types which Mike lists (01, 02, 0D, 04, and 03 in Dan's taxonomy) fix the corners. Thus, his note below points out that in order to have anything other than two solid faces opposite to each other, you must fix the corners. The correspondence between Dan's taxonomy and my charts is 01=BF, 02=AF, 03=A7, 04=A5, and 0D=BD. As I said earlier, the identfication numbers on my charts are not a taxonomy. Rather, they provide a unique identification for each of the 2^8 glyphs. > > 6 solid faces: start > 5 solid faces: no possibilities > 4 solid faces: > other two faces opposite: types 02, 0D and 04 are possible All three possibilities do occur in my chart. > other two faces adjacent: type 0D is possible This possibility does occur in my chart. > 3 solid faces: > mutually adjacent: type 02 is possible This possibility does occur in my chart. > not mutually adjacent: types 01 and 0D are possible Both possibilities do occur in my chart. > 2 solid faces: > adjacent: types 01, 02, 0D and 03 are possible All four possibilities do occur in my chart. > opposite: many possible types Indeed! > 1 solid face: types 01, 02 and 0D are possible > All three possibilities do occur in my chart. In addition, I found three partial isoglyphs of type 03 with one solid face. = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) jbryan@pstcc.cc.tn.us Pellissippi State (423) 539-7198 10915 Hardin Valley Road (423) 694-6435 (fax) P.O. Box 22990 Knoxville, TN 37933-0990