Message #2974

From: Melinda Green <>
Subject: Re: [MC4D] RE: 120Z solved!!!
Date: Sat, 08 Mar 2014 14:52:56 -0800

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, 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?
> Nan