From cube-lovers-errors@mc.lcs.mit.edu Mon Feb 23 17:21:17 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.1/mc) with SMTP id RAA27553; Mon, 23 Feb 1998 17:21:14 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From cube-lovers-request@life.ai.mit.edu Mon Feb 23 11:00:45 1998 Date: Mon, 23 Feb 1998 10:59:54 -0500 (Eastern Standard Time) From: Jerry Bryan Subject: Re: Strong Local Maxima 9f from Start In-Reply-To: To: Cube-Lovers Message-Id: On Sun, 15 Feb 1998, Jerry Bryan wrote: > #1. D2 F2 L2 D' U L2 F2 D' U' > #2. U D B2 R2 U D' L2 B2 U2 > > These positions "look" very symmetric, especially #2, .... The reason #2 "looks" so symmetric is that it is an isoglyph. That is, each face contains only two colors and the pattern of colors is the same on all six faces. If I am reading Dan Hoey's glyph table correctly, the glyph is of type 20. The glyph looks like the following, and the glyph itself is fairly symmetric. XOX OXO OOO On a lark, I asked Herbert Kociemba's Cube Explorer 1.5 program to find all isoglyphs which can be built with this glyph. Any such isoglyph is likely to be pretty. Up to symmetry, it found four isoglyphs (one of which is #2, which is a strong local maximum in the face turn metric). The other three are as follows: F2 U2 L' R D2 F2 L' R 8f F2 U2 B2 L2 U' B2 U' B2 L2 D2 L2 U R2 U' 14f U' L2 D' L2 D B2 F2 L2 R2 D F2 U' F2 U' 14f Cube Explorer 1.5 was able to show that the 8f maneuver is minimal. This position is not a strong local maximum, because the shortest strong local maxima are 9f. Cube Explorer 1.5 was not able to show that the 14f maneuvers are minimal in the time I gave it (six hours each on a Pentium 166). But I suspect that 14f is in fact minimal. Also, I do not know if the 14f maneuvers are strong local maxima because my search for strong local maxima extended only through 9f from Start. = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 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