Message #4222

From: Roice Nelson <>
Subject: Re: [MC4D] Minimal number of pieces affected via a slice move in n-dimensions
Date: Thu, 26 Sep 2019 14:00:10 -0500

Hi Paul,

You could make a puzzle with twisting like you describe, and I’ve seen one
in the past by Nate Berglund supporting that mode (it makes the puzzle
easier to solve). It breaks the analogy to the classic 3x3x3 in the sense
that such twists don’t move all stickers on the face of a puzzle. A twist
like you describe would be somewhat like allowing a twist on Rubik’s cube
that only affected edge pieces on a single face… "somewhat like" because
3-dimensions don’t allow that without self-intersections, whereas
4-dimensions have enough space to "twist" only 2C+3C stickers on a single
face without overlap.

If you stick to the idea that a twist should affect all face stickers,
there will be no twists like you describe in any dimension… any twist
will always move pieces of every type, including corners (I’m considering
center-slice twists as twists of two faces here). MC4D and MC5D strictly
follow the analogy in this sense and don’t support the twists you mention.

Of course, this can be debated. Here’s quite an old thread, from 2005, that
discusses both approaches:


On Thu, Sep 26, 2019 at 8:22 AM [4D_Cubing] <> wrote:

> My question relates to three divisions per side.
> Is it possible to move just eight "pieces" in 4D? It looks like this
> should be possible by moving four 3-coloured cubies and four 2-coloured
> cubies (using either the smaller cube jnside or the larger outside cube).
> Slice move only so no 4-coloured pieces affected.
> Although this option is not implemented in the MC4D model ? But perhaps my
> understanding is flawed. Please can someone illuminate - I am particularly
> interested in higher than four dimensions also i.e. could one always move a
> layer just affecting eight pieces in isolation (ignoring the piece that
> exposed no stickers)
> Paul
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