Message #2868

From: Melinda Green <>
Subject: Re: [MC4D] RE: MPUltimate 1.5
Date: Tue, 24 Dec 2013 21:23:07 -0800

On 12/24/2013 2:42 PM, wrote:
> —In 4D_Cubing@{{emailDomain}}, <melinda@…> wrote:
> >>Hey, I just had a thought. What if clicking anywhere on a cell
> caused it to completely invert? IOW, reflect through its center. That
> won’t work for all puzzles, but it should work for a lot. Maybe most.
> Do you mean (x, y, z) -> (-x, -y, -z)? That would be an interesting
> subgroup of reflections. There’s only one move for each cell. And
> there are only 8 moves on the whole 3^4 because there are only 8
> cells. Sounds fun. I hope it’s not trivial to solve.

Yes, 3 reflections is one way to look at it, but that’s just for the
cube. The more general way to think about it is to take every point on
the face and move it through the cell center and then the same distance
beyond. So dodecahedral cells would work too, but not tetrahedral.

I hope that it’s just barely not trivial, being one reasonable way to
extrapolate from MC2D.

> >> I’d also like to suggest that that reflectable puzzles not require
> modifier keys and not include rotations, or at least that those
> puzzles be distinct from ones that include multiple move types.
> You know, two reflections is always a rotation. For example, although
> Puzzle A allows reflections with respect to the orthogonal planes and
> 180-deg rotations, the rotations can be derived from the reflections.
> So essentially Puzzle A only allows those reflection moves. Puzzle B
> essentially allows all types of reflections on a cube and the
> rotations derived from it. It’s only a convenience to have some ways
> to perform rotation.

Good point. I suppose the difference is the way that moves are counted.
Also, the inconvenience can be part of the charm, similar to a no-macro
solution when that shouldn’t matter either. Or like move counts, except
when that’s the challenge.