From mark.longridge@canrem.com Wed Feb 7 03:00:03 1996 Return-Path: Received: from itchy.crso.com (itchy.canrem.com) by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA13843; Wed, 7 Feb 96 03:00:03 EST Received: by canrem.com (PCB-UUCP 1.1f) id 20A151; Wed, 7 Feb 96 02:54:24 -0500 To: cube-lovers@life.ai.mit.edu Reply-To: CRSO.Cube@canrem.com Sender: CRSO.Cube@canrem.com Subject: < U, F, R > group From: mark.longridge@canrem.com (Mark Longridge) Message-Id: <60.1288.5834.0C20A151@canrem.com> Date: Wed, 7 Feb 96 02:47:00 -0500 Organization: CRS Online (Toronto, Ontario) > there was never any response to this, but i'll give my solution anyway. I am working on an engine to search optimal paths for < U, F, R > but it's not done yet. It's certainly within the bounds of computibility: Size (u_f_r) = 170,659,735,142,400 (hmmm, 170 trillion maybe not!) > let X = U2 F R' F2 R F2 R F2 R' F U2 . > > then X produces two two-cycles of corner-edge pairs. the commutator > [ X , C_UFR ] produces "cube in a cube" in 22 face / 32 quarter turns > and only turns the faces U, F and R. > > the notation C_UFR refers to a rotation of the whole cube, and > [ a, b ] denotes the commutator a b a^-1 b^-1 . > > mike Brilliant. Although harder to remember, X + ( X * C_UFR) will do. U2 F1 R3 F2 R1 F2 R1 F2 R3 F1 U2 F2 R1 U3 R2 U1 R2 U1 R2 U3 R1 F2 (22 f, 32 q) -> Mark <-