From BRYAN@wvnvm.wvnet.edu Mon Nov 14 15:28:55 1994 Return-Path: Received: from WVNVM.WVNET.EDU by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA00620; Mon, 14 Nov 94 15:28:55 EST Message-Id: <9411142028.AA00620@life.ai.mit.edu> Received: from WVNVM.WVNET.EDU by WVNVM.WVNET.EDU (IBM VM SMTP V2R2) with BSMTP id 1855; Mon, 14 Nov 94 15:05:14 EST Received: from WVNVM.WVNET.EDU (NJE origin BRYAN@WVNVM) by WVNVM.WVNET.EDU (LMail V1.2a/1.8a) with BSMTP id 9387; Mon, 14 Nov 1994 15:05:13 -0500 X-Acknowledge-To: Date: Mon, 14 Nov 1994 15:05:12 -0500 (EST) From: "Jerry Bryan" To: Subject: Re: Antipode! In-Reply-To: Message of 11/14/94 at 11:59:00 from mark.longridge@canrem.com Of the 54 antipodes under Q+H processing, only 16 are unique up to W-conjugacy, with all 16 antipodes being 20 q+h moves from Start. Also, there is only one cube position which is both one of the 27 antipodes under Q (25 moves from Start) and also one of the 16 antipodes under Q+H (20 moves from Start). Just for completeness, here are the 16 Q+H antipodes. BBR BBB BBL BBB BBB BBB FBU LBD RBU RUR BUB BUR UUU UUU UUU RUU RUU DUF DLU FFL FRB ULU FFL FRR DLR FFR URB LLL FFF RRR LLL FFF RRR LLL FFF RRR LLL FFU LRD LLL FFD FRU LLL FFL URU DDB DDR DDF DDD DDD DDD DDB DDR DDB ---------------------------------------------------- BBD BBU BBR BBB BBB BBB LBR LBR RBB UUF UUB UUL UUU UUU UUU BUR BUR LUR FLL UFU FRD FLL UFD BRU BLF UFF DRU LLL FFF RRR LLL FFF RRR LLL FFF RRR LLL FFR URB LLL FFR DRF LLL FFU RRD DDB DDF DDF DDD DDD DDD DDR DDR DDB ---------------------------------------------------- BBL BBR BBU BBB BBB BBB RBR LBU FBB BUU BUR RUR UUU UUU UUU LUB LUF FUR DLF UFU RRF ULF UFR URB DLU LFU FRD LLL FFF RRR LLL FFF RRR LLL FFF RRR LLL FFD FRU LLL FFD FRD LLL FFL BRR DDR DDR DDU DDD DDD DDD DDB DDB DDB ---------------------------------------------------- BBF BFU BRB BBF BBD BBU FBR LBR BBR LUU UUD UFB UUU UUB DUU UUR LUF UBF ULB LFB URF FBU BLD RRB LRL FRR ULU LLL FFB RRR LLL FFU RRR LLL FFU BRF LLL FFR BRD LLL FFR FRR LLL FFF RRR DDD DDU DDD DDD DDF DDU DDR DDB DDD ---------------------------------------------------- BRL BRB BFB BBU BBU BBU DBF FBF FBD FFR RDR RUB DUU FUU UUF DBR UBB FDU RRB RRB URU DRL FRL URU DLU LRF RRR LLL FFU BRF LLL FFU FRB LLL FFB RRR LLL FFU LLF LLL FFR ULR LLL FFU LBU DDB DDB DDB DDU DDU DDU DDU DDD DDR --------------------------------------------------------- BFF BBU UBB LUU UUF BDR BLR DRF DRR LLL FFB RRR LLL FFU RBU DDF DDU DDL = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 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 If you don't have time to do it right today, what makes you think you are going to have time to do it over again tomorrow?