Cube Lovers: Re: <U, R> Antipode!

Date: Mon, 14 Nov 94 15:05:12 -0500

From: Jerry Bryan <BRYAN@wvnvm.wvnet.edu >

Subject: Re: <U, R> Antipode!

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
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