From mreid@ptc.com Tue May 30 15:39:31 1995 Return-Path: Received: from ptc.com (poster.ptc.com) by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA25072; Tue, 30 May 95 15:39:31 EDT Received: from ducie by ptc.com (5.0/SMI-SVR4-NN) id AA11138; Tue, 30 May 95 15:37:29 EDT Received: by ducie (1.38.193.4/sendmail.28-May-87) id AA15624; Tue, 30 May 1995 12:29:29 -0400 Date: Tue, 30 May 1995 12:29:29 -0400 From: mreid@ptc.com (michael reid) Message-Id: <9505301629.AA15624@ducie> To: cube-lovers@ai.mit.edu Subject: Re: AntiSlice Under M-conjugacy (and a problem with slice) Content-Length: 1649 jerry writes [ ... ] > >> >> Level Positions Strong Weak Total > >> >> Local Max Local Max Local Max > >> >> > >> >> 6 184 1 35 36 > >> > >> >beg the obvious question: what is that strong local maximum, > >> >which is unique up to symmetry? [ ... ] > Try instead, (L2R2)(U2D2)(F'B')(U2D2)(L2R2)(F'B'). > > This is a very pretty pattern which may well have a name, but I > don't know what the name is. Also, it is its own inverse. > > Is the length 12h in ? Is it a local maximum (strong or otherwise) > in ? Is the length 20q in ? Is it a local maximum in ? no, yes (otherwise), no, and yes, respectively. we have seen this pattern several times recently. this is one of those positions with 16 symmetries. i called it "four pluses" in my message of may 11 (although i gave it in a different orientation) ) four pluses ( R2 F2 R2 U'D F2 R2 F2 UD' ) in fact, this maneuver is minimal in both the quarter turn and the face turn metrics, so its length is 16q, 10f. it is a weak local maximum in the face turn metric; one can check that no minimal maneuver ends with the face turn R. however, using the 16 symmetries which preserve the U-D axis, and inversion, we can give minimal maneuvers which end with turns of any of the six faces. this shows that it's a weak local maximum in the face turn metric. local maximality in the quarter turn metric follows in a similar manner. also, mark pointed out on april 16 that this position lies in the center of the antislice group. mike