From cube-lovers-errors@mc.lcs.mit.edu Tue Aug 5 15:30:18 1997 Return-Path: Received: from sun30.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.1/mc) with SMTP id PAA24768; Tue, 5 Aug 1997 15:30:18 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From reid@math.brown.edu Tue Aug 5 14:31:16 1997 Message-Id: <199708051827.OAA07000@life.ai.mit.edu> Date: Tue, 5 Aug 1997 14:33:36 -0400 From: michael reid To: cube-lovers@ai.mit.edu Subject: 20f maneuvers for superfliptwist because of the historical interest in the pattern superfliptwist, i decided to find all 20f maneuvers for it. this took about 114 hours of searching, using the symmetry reductions i described in an earlier message. by "all" maneuvers, i mean that any 20 face turn sequence for superfliptwist can be transformed in to one on my list by conjugating by one of the 24 symmetries that fix superfliptwist, or by inverting the sequence and conjugating by the cube rotation C_U , and perhaps again by one of the 24 symmetries. some extra processing by hand was required to eliminate inverse pairs. hopefully i haven't made any errors here. the list of maneuvers is U R F' B U' D' F U' D F L F' L' U R D F U R L (20f, 20q) U F D L U R' F' R F U' D F U' D' F' B L U R L (20f, 20q) U R' F' U' F' R' B' D2 R' D R L' B R F B2 R' U' B D' (20f, 22q) U F L D L F R U2 F U' F' B R' F' R2 L' F D R' D' (20f, 22q) U R' U' D F' U' F2 B' U L F' R L' U B L B U F R2 (20f, 22q) U R' U' D F' U' B' R' F' R U F2 R U B L B U F R2 (20f, 22q) U F L D L F R U2 F U' F' B R' F' L' U' R' U F R2 (20f, 22q) U F R' F' L' U' R' U' D F' U F2 R U L B L U F R2 (20f, 22q) U F D L D F R L' U' L F U2 D' F' U' F' B R' F R2 (20f, 22q) U F D L D F R U2 F R U' R' D' F' U' F' B R' F R2 (20f, 22q) U R B D2 L B R' D' R' B L' D2 L B' D2 R' F B2 D' R (20f, 24q) U R' B L2 U' L2 U' B U' L2 D R B D F U2 R' L' B' R' (20f, 24q) U F B' R' U2 L U' R2 B' L' F2 U' R' D' L2 U D B D' B (20f, 24q) U R L2 F U F U F L D2 L' D' L U' D F2 B L' F R2 (20f, 24q) U R L' B' R' F R' F' B' D2 F U B L2 D R U2 B D' B2 (20f, 24q) U R' U2 D F B' R F' R' F2 R U B U B U R2 L B L2 (20f, 24q) U R' B R U' L' U2 B' R2 L' D B2 L U' B R F U B L2 (20f, 24q) U R' D2 B' U' F2 R' D' L' U2 R L B L' B R F B' D' R2 (20f, 24q) U F D L U F' R U2 B R' L2 U' F2 R' F' L U L' F R2 (20f, 24q) U F2 R' U' F' R' L2 U B U L' F B' U2 D L U' D' B R2 (20f, 24q) U F' B' L F B2 U' D L' B U B R' L2 D' B' R' D2 B R2 (20f, 24q) U R2 B L' U2 B' R' L F2 D F L2 D R' F2 D' R L' U2 B (20f, 26q) U F R' L D B R2 U2 L2 D' R' D' R L2 U' F L D2 B R2 (20f, 26q) U F2 L D B' R L2 F' R' F' L2 B2 R2 U F R' L D B R2 (20f, 26q) U F2 R' L' U F' U' D2 B2 U' B D R' L2 D2 L2 D2 F U2 B' (20f, 28q) the maneuver that herbert kociemba found is equivalent to the 28q maneuver. the two maneuvers that are 20q long can be obtained from one another by inverting the first, then cyclically shifting the antislice to the end of the maneuver, and then reorienting. the first of the 26q maneuvers is quite interesting. it can also be written as (U R2 B L' U2 B' R' L F2 D C_UF)^2 where C_UF is a cube rotation about the UF - DB edge axis (as in bandelow's book). mike