From mreid@ptc.com Thu Jan 19 18:30:05 1995 Return-Path: Received: from ptc.com (poster.ptc.com) by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA09088; Thu, 19 Jan 95 18:30:05 EST Received: from ducie.ptc.com by ptc.com (5.0/SMI-SVR4-NN) id AA15016; Thu, 19 Jan 95 18:28:35 EST Received: by ducie.ptc.com (1.38.193.4/sendmail.28-May-87) id AA09110; Thu, 19 Jan 1995 18:41:47 -0500 Date: Thu, 19 Jan 1995 18:41:47 -0500 From: mreid@ptc.com (michael reid) Message-Id: <9501192341.AA09110@ducie.ptc.com> To: cube-lovers@ai.mit.edu Subject: symmetric maneuvers Content-Length: 1504 mark writes > p = R3 U2 B1 L3 F1 U3 B1 D1 F1 U1 D3 (12 q) > > Then p + (p * Sm) = Superflip > > This is Mike's process slightly patched, with the last two (commuting) > cube turns swapped in position. i'm surprised this hasn't been pointed out previously. however, i would write the above as (R3 U2 B1 L3 F1 U3 B1 D1 F1 U1 D3 C_X)^2 where i use C_X for central reflection. this fits in with mark's idea of "cyclic decomposition". i've noticed that a number of minimal (or presumed to be minimal) maneuvers for pretty patterns have some symmetry. here i'll use commutator notation: [ A , B ] refers to A B A' B' also i'll use bandelow's notation for rotations of the whole cube: C_U , C_RF , C_URF , denote rotation about a face-face axis, edge-edge axis, corner-corner axis, respectively. now some patterns: anaconda: B1 R1 D3 R3 F1 B3 D1 F3 U1 D3 L1 F1 L3 U3 = [ B1 R1 D3 R3 F1 B3 D1 , C_UB ] python: D2 F3 U3 L1 F3 B1 D3 B1 U1 D3 R3 F1 U1 B2 = [ D2 F3 U3 L1 F3 B1 D3 , C_UF ] 6 x's (order 3): R2 L3 D1 F2 R3 D3 F1 B3 U1 D3 F1 L1 D2 F3 R1 L2 = [ R2 L3 D1 F2 R3 D3 F1 B3 , C_UB ] my favorite example is four twisted peaks: U3 D1 B1 R3 F1 R1 B3 L3 F3 B1 L1 F1 R3 B3 R1 F3 U3 D1 = [ U3 D1 B1 R3 F1 R1 B3 L3 F3 , C_R2 ] i'd hoped to find maneuvers for "cube within a cube" and "cube within a cube within a cube", but no such luck. mike