Message #220

From: Roice Nelson <>
Subject: Re: [MC4D] My gallery!
Date: Fri, 17 Mar 2006 01:24:58 -0600

Excellent point about us only needing to do 90 degree rotations. I spaced
out on that 5D cube applet for a while and I agree it doesn’t help much,
especially since the rotations aren’t restricted to 90 degrees. I think
MagicCube5D cube will require 2 kinds of 4D rotations, those that change the
view only and those that perform certain face twists. Note that 4D view
rotations will be required because in Remi’s pictures, portions of each
4-cube face are not visible. So these rotations would be required to bring
those portions of the faces into or out of view.

Perhaps the 4D view (and the 90 degree 5D view) rotations could both use the
control-click method. It doesn’t seem we would need to have
control-shift-clicking for most 5D view rotations (more on this below)

Twisting, both 3D and 4D twists, could all be handled by single clicks as in
MagicCube4D. A click on a 4D stickers not in the center of the 4-cube would
result in a 4D twist. Single clicks in the center 3-cube of the 4-cube face
would do 3D twist rotations just as in MagicCube4D. I have no idea if this
is making sense. This new puzzle is difficult to talk about :)

Remi’s cross-form idea has grown on me too. In the spirit of MagicCube4D,
there could just be 3 hidden faces (the ones he has moved off to the
sides). I guess that would be a lot of non-visible items to keep track of
though. In regards to the 4-cubes that don’t seem to have a place, perhaps
this is where a shift-control-click could come in. It could be used to
rotate the puzzle such that these hidden faces move to the center and hence
into the view. Say shift-control-left does one and shift-control-right does
the other (the 3rd hidden face would behave more like the hidden face in the
4D puzzle).

One thing I do not like about this projection however is that both the 4D
and the 5D portions are being centrally projected, kind of like the
attached image of a 5D cube. Since 2 dimensions are being projected along
the same axis, information gets lost. This could be part of the trouble of
fitting all the faces in. Maybe things could be improved if only the 5D
axis was centrally projected, and the 4D axis was projected along another
line. This sort of necessitates a 4D visualization portion with overlapping
parts though, not as in MagicCube4D, so maybe having 4D and 5D both
centrally projected is still the best despite the downsides. In any case,
since space is such an issue, a couple of possible thoughts to help "make
more space"…

(1) Drawing in wireframe.
(2) Drawing only colored dots at the centers of stickers - downside is that
it won’t look cubelike.
(3) Using alpha blending for translucency - I think that would be the most

I have a few more thoughts on this puzzle, which I will mention in a
response to Remi’s last email. But I hear you on volunteering for the code
development, and the solving of this puzzle if it ever materialized. I sort
of drew the line at the 4^4 and never tried the 5^4. I think it will be the
same with the 3^5. At some point, it just gets a little ridiculous! I
think we’ve all already safely secured super-geek status for ourselves
anyway :)


On 3/15/06, Melinda Green < > wrote:
> 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:
> 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
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