Message #217

From: Roice Nelson <roice@gravitation3d.com>
Subject: Re: [MC4D] My gallery!
Date: Tue, 14 Mar 2006 22:12:50 -0600

cool :)

I think your pics under the category "Roice’s Solution" would be useful
explanation tools. I have a 3D cube I’ve pulled the corners off of that I
use to help people ignore these pieces when I’m teaching them to solve
edges. If you were interested, we could try to incorporate your pictures
into the hypercube solution.

Your emails have had me thinking about the n^5 some more the past couple
days. Unfortunately, I’ve sort of come to the same conclusion I have in the
past, which is that there is not an elegant way to present it. Working by
analogy, I try to find a clean way to draw a 4D cube in 2D space, which
although this is what MagicCube4D in fact does, to make the analogy right, I
have to think of doing it cleanly as a 2D being, stuck in the 2D space of
the screen and viewing from there. So the limitations are more strict, and
we don’t have the luxury as in MagicCube4D of looking at our projection from
off the page. It feels like the only reasonable way to present an n^5
cube may be to paste a bunch of hyperfaces all over the screen as you’ve
done. Given this limitation, I think I would prefer your layout below the
best.

http://genezis.station76.pl/Hypercubes/2x2x2x2x2/slides/10x2^4.html<http://genezis.station76.pl/Hypercubes/2x2x2x2x2/slides/10x2%5E4.html>

The other options I think confuse things more because they make connections
in certain places and leave them out in others. Another concept that is
left out of these drawings are the fact that since faces of a 5D cube are
now hypercubes, the connection points between faces are joined volumes (vs.
joined areas in MagicCube4D vs. joined lines in the Rubik’s Cube). So the
correct projection analogy really needs to be drawing 3D volumes of certain
colors on top of 3D volumes of other colors, or at least making a better
association between connected faces, which of course will be a mess.

I guess I haven’t given up completely though. As you say, somebody has to
try ;) If there is a way, I think we’d need to nail down how the 4D
rotations would take place to twist faces, which has been discussed some in
the past. The fact that there are 192 possibilities and there is the extra
complication of certain rotations being "orthogonal and inertial" to each
other (reference ‘Physical models of Rubik’s Cube’ thread in April 2005) is
daunting though.

I think a first step towards a better understanding would be a 5D cube
program (not permutation puzzle, just cube) that would let us play with the
3D, 4D, and maybe a limited subset of the 5D rotations.

Roice

On 3/14/06, Remigiusz Durka <thesamer@interia.pl> wrote:
>
> I made a gallery with pictures of hypercubes so I invite everyone to:
>
> http://genezis.station76.pl/Hypercubes/
>
> I hope you will like it :)
>
>
>
>
>
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