From BRYAN@wvnvm.wvnet.edu Tue May 9 18:17:13 1995 Return-Path: Received: from WVNVM.WVNET.EDU by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA15460; Tue, 9 May 95 18:17:13 EDT Received: from WVNVM.WVNET.EDU by WVNVM.WVNET.EDU (IBM VM SMTP V2R2) with BSMTP id 7466; Tue, 09 May 95 15:32:53 EDT Received: from WVNVM.WVNET.EDU (NJE origin BRYAN@WVNVM) by WVNVM.WVNET.EDU (LMail V1.2a/1.8a) with BSMTP id 7823; Tue, 9 May 1995 15:31:34 -0400 Message-Id: Date: Tue, 9 May 1995 15:31:32 -0400 (EDT) From: "Jerry Bryan" To: "Cube Lovers List" Subject: Re: more on the slice group In-Reply-To: Message of 04/14/95 at 16:03:31 from mreid@ptc.com On 04/14/95 at 16:03:31 mreid@ptc.com said: >i also calculated for the other slice metric. in this metric, >neighbors can have the same distance from start, so a "strong" >local maximum is a position all of whose neighbors are strictly >closer to start. a "weak" local maximum is a position none of >whose neighbors are further from start. I might prefer an alternative set of definitions: 1) a local maximum is a position none of whose neighbors are further from Start, 2) a strong local maximum is a position all of whose neighbors are strictly closer to Start, and 3) a weak local maximum is a local maximum which is not a strong local maximum. But in the table which follows, I adopt Mike's definition. > 90 or 180 degree number of number of strong number of weak > slice turns positions local maxima local maxima > 0 1 0 0 > 1 9 0 0 > 2 51 0 0 > 3 247 0 7 > 4 428 0 212 > 5 32 8 32 >the strict local maxima are all equivalent under symmetries of >the cube. they are the composition of pons asinorum with any >of the eight positions called "six dots". Under M-conjugacy, we have 90 or 180 degree number of number of strong number of weak slice turns positions local maxima local maxima 0 1 0 0 1 2 0 0 2 4 0 0 3 15 0 2 4 25 0 16 5 3 1 3 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) (304) 293-5192 Associate Director, WVNET (304) 293-5540 fax 837 Chestnut Ridge Road BRYAN@WVNVM Morgantown, WV 26505 BRYAN@WVNVM.WVNET.EDU