Message #44

From: Melinda Green <melinda@superliminal.com>
Subject: Re: [MC4D] Orientations of the centre cubes …
Date: Thu, 11 Sep 2003 17:04:47 -0700

mahdeltaphi wrote:

> David’s comment:
> […] So there are two levels at which one
> >may "ignore" orientations.
>
> Yes, there are two types of orientation, which could be classed
> as "visible" and "invisible" (on a uniformly coloured tesseract).

i don’t know if you included this but i suspect there may be a 3rd type
of ambiguity found in puzzles with more than 3 cubies along an edge. for
example when there is more than one "middle" cubie along an edge they
can all be correctly oriented yet placed in interchangeable positions.
this would also show up with a 4^3 picture cube, or more generally, an
N^D textured cube for all N > 3. so even positions can be ambiguous, not
just orientations. this should apply to more than just edge pieces too
and in fact should apply to all cubies that are not corners or face
center-center (0 colored) cubies when N is odd.

-melinda