Message #2981

From: Eduard Baumann <>
Subject: Re: [MC4D] RE: 120Z solved!!!
Date: Tue, 11 Mar 2014 13:42:01 +0100

Very very interesting indeed! Thanks a lot for the link.

—– Original Message —–
Sent: Tuesday, March 11, 2014 6:09 AM
Subject: Re: [MC4D] RE: 120Z solved!!!

I always think the solving the orbit parity is like a Lights Out game. These days I did some research and found some Lights Out puzzles on Jaap’s puzzle page. First I found this Orbix puzzle:

It has the shape of a dodecahedron. The type-1 version is a simple and neat Lights Out on a dodecahedron.

Jaap made a very powerful game, Lights Out on a Graph.

One can draw any graph and thus defines a Lights Out puzzle. Players can also share the puzzle definitions by uploading and downloading. There are a lot of predefined puzzles already. And of course there isn’t one that’s equivalent to 3C of 120 cell. That’s too crazy… But there is a hypercube in the folder "Les". I could spend a lot of time on this game.

Melinda asked me what’s next for me. I was playing 120-cell Mirror Z on my commute. Today I played Candy Crush. It was not easy…


—In, <melinda@…> wrote :

Nan and Andrey,

Perhaps a 3C-only 24-cell will be more difficult without the 2C pieces to help get the 3C pieces into the correct parity? I’m wondering if we can find a puzzle that preserves the most difficult part of the 120Z but in a much smaller puzzle. I’m particularly interested in whether this can be done in 3D. The nature of the Z puzzles would make it hard to imagine how to produce physical versions, but it would be ideal to find the lowest dimension in which this puzzle can exist. Thoughts?

As an aside, I’ve been meaning to ask Andrey what he would think of renaming the Z puzzles to X. I’m proposing this because the shape of the letter ‘X’ looks like a map of how all parts of a cell transform through the cell center, ending up at their antipodes. I know it’s a little late in the game for this but I keep thinking of it so I thought I’d throw it out there. No pressure, though. I like ‘Z’ as well because I have a Nissan 350Z. :-)


On 3/8/2014 11:26 AM, mananself@… wrote:

  Melinda and Andrey, Thanks.

As I posted earlier here, when I solved 24Z, I solved 2C first. There, 2C orbits do have a complicated orbit parity situation. But because there are less orbits and less pieces, the parity can be solved intuitively. After solving 2C, 3C orbits are all evenly permuted. So no drama for 3C in 24Z, unlike in 120Z. Maybe it’s because an octahedron has 6 (even number) pairs of edges, but a dodecahedron has 15 (odd number) pairs of edges.

3^4 Z is even cuter. I looked up my note, and I solved 3^4 Z with the order of 4C, 2C, 3C. It’s because 4C pieces are in a unusual group. And there are parity situation in each step. But they are not very difficult. It’s hard to compare that puzzle to 24Z and 120Z.

Andrey, you mentioned that you would like to try vertex turning 24-cell and 16-cell. Are they just equivalent to cell-turning 24-cell and 8-cell due to duality?