Message #3187

From: Roice Nelson <roice3@gmail.com>
Subject: Re: [MC4D] Re: 120Cell question
Date: Tue, 20 Oct 2015 14:29:18 -0500

There will be no problem. On the 120-cell puzzle, you can swap (or
reorient) two 2C pieces in isolation. See David Smith’s writeup about the
number of permutations for more details:

http://www.gravitation3d.com/magic120cell/Hyperminx_number_of_positions.txt

Also see the historical topics here on parity. A thread started by Levi
titled "Parity on MC m^n" has lots of great discussion:

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

One last comment. Even if 2C pieces were tied to 3C pieces, you still
probably wouldn’t have a problem on the torus-colored puzzle because there
are multiple pieces with the same sticker colors and many pieces with all
stickers the same color. These could be exchanged or reoriented without
being visually different (to overcome parity constraints), and Magic120Cell
would still consider the puzzle solved.

Roice

On Mon, Oct 19, 2015 at 10:33 PM, llamaonacid@gmail.com [4D_Cubing] <
4D_Cubing@yahoogroups.com> wrote:

>
>
> I am not sure how to explain this. In the Rubik’s Cube if you swap two 2c
> you also affect two 3c. I was wondering if swapping pieces in 120Cell would
> make it so that you wont be able to get all the greens in a tori and all
> the reds in the other.
>
>
>