From @mail.uunet.ca:mark.longridge@canrem.com Mon Sep 12 01:05:56 1994 Return-Path: <@mail.uunet.ca:mark.longridge@canrem.com> Received: from seraph.uunet.ca (uunet.ca) by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA24942; Mon, 12 Sep 94 01:05:56 EDT Received: from portnoy.canrem.com ([198.133.42.251]) by mail.uunet.ca with SMTP id <101743-2>; Mon, 12 Sep 1994 01:05:58 -0400 Received: from canrem.com by portnoy.canrem.com (4.1/SMI-4.1) id AA20552; Mon, 12 Sep 94 01:03:01 EDT Received: by canrem.com (PCB-UUCP 1.1f) id 1AF26D; Mon, 12 Sep 94 00:48:46 -0400 To: cube-lovers@life.ai.mit.edu Reply-To: CRSO.Cube@canrem.com Sender: CRSO.Cube@canrem.com Subject: More UR Stuff! From: mark.longridge@canrem.com (Mark Longridge) Message-Id: <60.799.5834.0C1AF26D@canrem.com> Date: Mon, 12 Sep 1994 00:28:00 -0400 Organization: CRS Online (Toronto, Ontario) Notes on the UR Group --------------------- Well, some small news about the < U, R > group. Previously I believed that my 3-cycle of edges: UR1 = U3 R3 U2 R1 U1 R3 U1 R1 U1 R1 U2 R3 U3 R1 U3 R3 = 18 q, 16 h ...discovered by hand was minimal. My newly created < U, R > solver (now being at the point of churning out correct results) as happily proven me wrong! UR2 = U3 R1 U2 R1 U1 R1 U1 R2 U3 R3 U3 R2 U1 = 16 q, 13 h Also I found 6 "UR-Reflective" processes altogether. This is all there are up to and including 12 q turns: U3 R1 U1 R1 (U2) R3 U3 R3 U1 = R3 U1 R1 U1 (R2) U3 R3 U3 R1 (10) U1 R3 U3 R3 (U2) R1 U1 R1 U3 = R1 U3 R3 U3 (R2) U1 R1 U1 R3 (10) ( U2 R2 ) ^ 3 = ( R2 U2 ) ^ 3 (12) U1 R1 U2 R3 U2 R3 U2 R1 U1 = R1 U1 R2 U3 R2 U3 R2 U1 R1 (12) ( U1 R1 U3 R3 ) ^3 = ( R1 U1 R3 U3 ) ^3 (12) ( U3 R3 U1 R1 ) ^3 = ( R3 U3 R1 U1 ) ^3 (12) The program is still a sluggish beast, but I think with further refinements it should eventually find other interesting results like antipodes and pure twists, etc. -> Mark <- Email: mark.longridge@canrem.com