From cube-lovers-errors@mc.lcs.mit.edu Tue Feb 2 17:56:32 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA19088 for ; Tue, 2 Feb 1999 17:56:32 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Mon, 1 Feb 1999 17:16:54 -0500 From: michael reid Message-Id: <199902012216.RAA07304@chern.math.brown.edu> To: cube-lovers@ai.mit.edu Subject: Re: Query on Octagon Cube Edge Parity Problem Cc: hansker@yahoo.com > I ran into an unusual scenario with the Octagon cube recently where > only ONE edge piece was flipped and all the other pieces were > positioned and oriented properly. This is bizarre of course, because > with a Rubik's cube, this is an impossible scenario; there must be a > minimum of TWO edge pieces flipped. the "octagon" puzzle has some "edges" with only one visible face. namely, these are the U-D layer edges on a cube, which were shaved when the cube was modified in shape. these edges have no visible orientation, so flip one of these along with the edge that's definitely in the wrong orientation. in a similar way, it's possible to get positions that appear to have the wrong permutation parity. there are four vertical columns of two corners and an edge each. these do not have any fixed "home" location, so that any permutation of these also constitutes a "solved" state. (well, at least most people would consider it to be solved.) but swapping two of these columns creates an odd permutation parity. thus you can swap two columns, and also swap a pair of edges or corners, which gives the impression of incorrect parity. for a simple example, do R2 F2 R2 from the solved position. the edges UF and DF have been swapped, and it looks like nothing else has happened. in fact, the FL column has been swapped with the BR column as well. mike [Moderator's note: I hadn't noticed that this had such an obvious answer. Thanks also to Jon Ferro, Steve LoBasso, der Mouse, Guy N. Hurst, Michael Ehrt, and Christ van Willegen for also providing the answer. I've selected Mike Reid's, since he points out the other notable ambiguity of the Octagon. What wasn't noted is that the Spratt wrench can be used to flip the noted edge along with three of the ambiguous edges. --Dan]