From @mail.uunet.ca:mark.longridge@canrem.com Mon Jul 3 14:15:29 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 AA06658; Mon, 3 Jul 95 14:15:29 EDT Received: from portnoy.canrem.com ([198.133.42.17]) by mail.uunet.ca with SMTP id <181839-4>; Mon, 3 Jul 1995 14:16:59 -0400 Received: from canrem.com by portnoy.canrem.com (4.1/SMI-4.1) id AA20583; Mon, 3 Jul 95 14:11:12 EDT Received: by canrem.com (PCB-UUCP 1.1f) id 1E9C06; Mon, 3 Jul 95 14:04:58 -0500 To: cube-lovers@life.ai.mit.edu Reply-To: CRSO.Cube@canrem.com Sender: CRSO.Cube@canrem.com Subject: Crazy Corner Pattern Revisited From: mark.longridge@canrem.com (Mark Longridge) Message-Id: <60.1182.5834.0C1E9C06@canrem.com> Date: Mon, 3 Jul 1995 14:59:00 -0400 Organization: CRS Online (Toronto, Ontario) Jerry writes: > In their position, the UFL and RBD corners are >in place, and the other three pairs are swapped. The "girdle" >includes the three pairs that are swapped. Hence, there >is an axis of symmetry along the UFL-RBD axis. The odd number of >swaps is compensated by an odd number in the edges. The compensation >is not required for corners only. > > R D D > U U D > U U B > > D L L F F D L L F L F F > R L L F F B L R R B B F > R R B R B B U R R B B U > > U U L > U D D > F D D Much is explained! (And this is all the way back in file "cube01" in the archives, Date: 14 December 1980 1916-EST). What does the 1916- mean in front of EST??? If we put the edges in place in Jerry's (and Dan's) position then we have a position M-conjugate to the one I posted. (re-posted below). F U U U U U D U L R L B R F B D R R B B D L L L F F F R R R B B B U L L F F U L R F L B F D D B D D D R D U Jerry Continues: >...there is an axis of symmetry along the UFL-RBD axis. The odd >number of swaps is compensated by an odd number in the edges. >The compensation is not required for corners only. Great! We both concur that this pattern is in the swap orbit. There is another position with M-class 4 in the twist orbit, but that one is *utterly* impossible unless one corner twists on it's own (perhaps due to desperate cube turning?) There are 2 other types of position with M-class 4, and that is pinwheels and pinwheels + pons asinorum. -> Mark <- (I must be cubing too much, 1916-EST has to be 7:16 pm Eastern Standard Time).