From @mail.uunet.ca:mark.longridge@canrem.com Thu Jan 19 01:02:38 1995 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 AA10634; Thu, 19 Jan 95 01:02:38 EST Received: from portnoy.canrem.com ([198.133.42.17]) by mail.uunet.ca with SMTP id <159428-2>; Thu, 19 Jan 1995 00:35:27 -0500 Received: from canrem.com by portnoy.canrem.com (4.1/SMI-4.1) id AA00872; Thu, 19 Jan 95 00:21:59 EST Received: by canrem.com (PCB-UUCP 1.1f) id 1CA56D; Thu, 19 Jan 95 00:11:23 -0500 To: cube-lovers@life.ai.mit.edu Reply-To: CRSO.Cube@canrem.com Sender: CRSO.Cube@canrem.com Subject: Shift Invariance Recap From: mark.longridge@canrem.com (Mark Longridge) Message-Id: <60.1003.5834.0C1CA56D@canrem.com> Date: Thu, 19 Jan 1995 00:08:00 -0500 Organization: CRS Online (Toronto, Ontario) Shift Invariance the Final Chapter?? ------------------------------------ 2 x Order 2 (the diagonal square element) Subgroup , order = 2 D2 F2 T2 F2 B2 T2 F2 T2 2 Swap (the single square element) Subgroup , order = 2 D2 R2 D2 R2 D2 R2 2 H (the edge square element) Subgroup , order = 2 L2 R2 B2 L2 R2 F2 12 flip (the central element) Subgroup , order = 2 R1 L1 D2 B3 L2 F2 R2 U3 D1 R3 D2 F3 B3 D3 F2 D3 R2 U3 F2 D3 Special Property: Effects all edges the same 6 Counterclockwise twist (the odd element) Subgroup , order = 3 U2 R1 U1 R1 U1 R3 U1 R3 U1 R3 U2 R1 U1 R1 U1 R3 U1 R3 U1 R3 Special Property: Effects all corners the same Martin's message about the SuperSkewb having a non-trivial centre reminded me that the SuperCube should have 3 more positions which are also shift invariant: 3x3x3 cube with 6 centre pieces rotated 90, 180 and 270 degrees, with orders 4, 2 and 4 respectively. This time all the centres are effected the same! Naturally there are 3 more positions in SG's as well. A pity there is no "Centre All-Twist" process in any of the cube literature. -> Mark <- I'll leave a superflip process for the Magic Dodecahedron as a 'exercise for the reader' ;-)