Message #218

From: Melinda Green <melinda@superliminal.com>
Subject: Re: [MC4D] My gallery!
Date: Tue, 14 Mar 2006 22:01:45 -0800

I totally agree with everything you say about the problems of
representation, etc. Adjacent 4-cubes would "meet" at a common 3-cube,
and not just at their 2D faces but at every point in the 3-cube. I like
Remi’s idea of unfolding the 5-cube into a cross form. In such an
interface I am imagining that only the one (currently) central 4-cube
would be the workable one that you would interact with, but even with
allowing for overlapping 3-cubes we would need to recognize that the
central 3-cube in that central 4-cube would still need to be shown
somehow overlapping with a couple of other 4-cubes and I would have no
idea where to put them.

Regarding your comment about playing with the rotations of a simple
5-cube in order to understand the problem better, there is something
that looks like that here:
http://home.att.net/~numericana/answer/polyhedra.htm#polytopes but I
don’t see how that helps much. I mean that we’re not really looking for
a way to rotate a 5-cube but just a way to rotate one of its 4D
hyperfaces, right? Well MC4D already implements a way to rotate the 4D
cube by control-clicking a 3D hyperface to rotate it to the center. It
seems to me that this should be enough of an interface to specify a
twist in 5D. That would only allow 90 degree twists but some combination
of these should be enough to specify any legal twist of a face of a
5-cube. Now imagine operating on the central 4-cube in one of Remi’s
cross arrangements. The only other thing I expect would be needed to
solve the 5D cube would be some way to rotate other 4-cubes into the
center. The natural extension to the 4D puzzle would perhaps be to
shift-control-click on a 4-cube adjacent to the central one in order to
"rotate" that one into the center. Of course I still haven’t solved the
problem of where to place the missing couple of 4-cubes from the
previous paragraph, nor am I volunteering to do any of the development
of such a beast but I suspect it might just be possible. Good luck
solving it though!!

-Melinda