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]