Message #3030

From: Roice Nelson <roice3@gmail.com>
Subject: Re: [MC4D] Swapping two adjacent corners on the 4d cube.
Date: Mon, 08 Sep 2014 23:50:54 -0500

Hi Allen,

I think what you are asking for is impossible because of parity
restrictions. 4C corner positions can not have odd parity because a 90
degree twist results in two 4-cycles of corner positions (even parity). An
algorithm that produced a single 2-cycle would produce odd parity.

On the 3D cube, you can swap just two corners, but only if you also swap
two edges! In 4D, you can do something similar with 2C and 3C pieces, but
you are out of luck with 4C corners. It should be possible to make a
sequence that swaps two sets of two corner pieces though. To dig deeper, I
recommend the 2009 thread on this group titled "Parity on MC m^n".

https://groups.yahoo.com/neo/groups/4D_Cubing/conversations/messages/624

Also related, but not exactly what you want… You can twirl (in place)
two corners connected by an edge. See the sequence at the bottom of this
page.

http://www.superliminal.com/cube/solution/pages/series_hints.htm

Cheers,
Roice

On Sun, Sep 7, 2014 at 8:56 PM, ohara_allen@yahoo.com [4D_Cubing] <
4D_Cubing@yahoogroups.com> wrote:

>
>
> Does any one have an algorithm for swapping two corners pieces on the 4d
> cube that are connected by an edge? I don’t need it to preserve the edges
> or faces. It doesn’t matter what the orientations of the corners are, so
> long as those two corner pieces are the only corner pieces that swap.
>
>
> Has anyone encountered this situation before? It should be possible, I
> just can’t seem to deduce such an algorithm.
>
>
>
>