Message #132

From: Melinda Green <>
Subject: Re: [MC4D] "Physical models" of Rubik’s Cube (tesseract, hypercube, etc.)
Date: Mon, 18 Apr 2005 13:21:23 -0700

hello nathanael,

welcome to the MC4D group!!

you will be interested to know that don and i originally had a
protracted debate about the "best" 4D generalization of the 3D puzzle.
my initial feeling was that it was all about 90 degree rotations and
that the proper generalization would only allow twists about hyperface
axies passing through center/center cubies. don’s position was that all
rotations about hyperface cubies should be allowed, if only because you
can get to any of these through some, possibly painful, sequence of 90
rotations anyway. eventually i convince myself that his ui does make
perfect sense if we look at the N dimensional puzzle by defining a twist
like this: 1) detach the face to be twisted from the rest of the model.
(note that this includes some stickers from other faces.) 2) apply any
rotation of that face that results in its original orientation. 3)
replace the face. with this definition, a twist on a 3D cube detaches a
3x3 slice of cubies which can only be turned into 4 unique positions.
the fact that these are all rotations about a single axis is just a
coincidence that happens in the special case of 3 dimensions. in 4D, the
way to think of the analogous process is is to take a 3x3x3 face of
stickers along with the slice of stickers on each adjoining face, and
pull the entire cubic assembly out of an imaginary box. you should then
be allowed to rotate this 3D cube into any orientation that fits back
into that box, and then slide it back in. this definition generalizes
into N dimensions even if the program’s UI does not. i have no idea how
to create a similarly holistic 5D puzzle interface that a human could
reasonably solve.


Nathanael Berglund wrote:

>A few years back I thought of a possible "physical model"
>for higher dimensional Rubik’s Cubes.