Message #3396

From: Roice Nelson <>
Subject: Re: [MC4D] 3^4 parity?
Date: Mon, 27 Jun 2016 22:28:08 -0500


I think someone must have popped your puzzle apart, put it back together in
a different orbit, and is playing a trick on you! But seriously, as far as
I understand, you can’t have two swapped edge (3-colored) pieces on the 3^4
in isolation. See this message
the archives (and the entire thread really, for tons of discussion about

If you had only two unsolved 3C pieces, they would necessarily be in the
correct position, but wrong orientation. If that’s the case, you can
leverage the 3rd sequence on this page
<> to correct
the orientations. That sequence twirls a 3C and two 4C pieces. If you
build a commutator with it and a middle slice move that permutes that 3C
piece but not the 4C pieces, you’ll end up twirling two 3C pieces, that is

3rd sequence
reverse of 3rd sequence
reverse of move

Or maybe your situation is different than I’ve inferred here (say two
*flipped* edge pieces like here
<>). Let us
know more specifics if so. Hope this helps.


On Mon, Jun 27, 2016 at 6:51 PM, [4D_Cubing] <> wrote:

> My first four solves, I got the better side of a coin flip and didn’t get
> any parity. But ever since I had completed my second solve, it occurred to
> me that I probably should be encountering some sort of parity issues; maybe
> flipped/swapped 3c/4c pieces … and now on my fifth solve I have two
> swapped edge pieces. I’m not really sure what to do now. I’ve been thinking
> about this for most of the day, and I understand 100% *why* this happens,
> but I don’t entirely know how to fix it. I have a vague idea to rotate one
> face 90° and "get away with it" (i.e. reposition the 1c/2c pieces of the
> middle slice of that face back to where they started, while keeping an even
> number of 90° rotations of the center) but I’m not really sure how to
> accomplish that, because I can’t do a four-cycle of 2c pieces.
> I am not looking for a solution to this parity; I am looking for an
> explanation of how to go about creating one. If an example solution is
> necessary to do that, that’s fine. Thanks. :)