Thread: "5D Cube"

Hello everybody...

I have to say, that I'm really impressed about the realisation of the 5D
Cube... Very nice, I like it. :-) I hope, that soon twists will be
possible... I'd really like to twist this thing... :-) It's somehow a
little bit crazy, but I like it very much!
So far for the 5D cube... In the last days I thought a little bit about
the 4D Cube and a strange idea came to my mind... We all look at the
computer and the 3-dimensional projection of this 4D-Object... And like
everyone knows, it is not really 3D... So the idea came to my mind...
Would it be possible to create something, that looks like the projection
of the 4D Cube in real space... I think in a first step one can create
something that only looks like the 4D cube and that one can rotate the
whole object like in 4D (inside-out-effect)... That should be
possible... Also with the spacings between the stickers... I think that
is not the problem... But the next step would be nice to realize, to
make twists possible... :-) I only thought about it and I'm not shure if
this is possible in anyway. Please tell me, if you ever thought about
something like this or if something like this was ever discussed... :-)
Would be nice!

Thanks

Denny



Melinda Green wrote:

>Wow, Roice presents yet another tour de force!!
>Here is my random feedback:
>* I love how you've insisted on a single set of projection parameters
>thereby maintaining a "faithful" spatial representation. I'm not opposed
>to using unfolded or other logical representations if that makes the
>puzzle more solvable but if it can be operated and solved this way,
>that's much preferable. In fact it's for exactly this reason that we
>felt motivated to building the 4D version in the first place.
>* The wireframe representation does help one to see the structure though
>it may be harder to select stickers. BTW, the 4D stickers look *very*
>cool! With a wireframe design I'd personally prefer side-by-side
>cross-eyed stereo views otherwise you can only make out the structure
>while rotating it, but I know that is not for everyone.
>* The 3D drag rotations clearly applies all of one axis rotation before
>the other which makes it different to predict what will happen. I
>suggest that you use the quaternion code that I use in the Java version
>which makes it so that each drag increment always does what you
>naturally expect.
>* Instead of axis drop-downs for 5D rotations I would suggest a
>lower-triangular grid of 15 small rotate buttons.
>* I suggest that toggling of individual faces should operate on their
>rotated logical positions rather than on their colors. IOW, like MC4D
>does with the outside face.
>* I understand that you wrote this mostly as a GUI feasibility study but
>I encourage you to give some serious consideration to working out a UI
>and implementation of a twist. I know that will be a huge task, and that
>once you do that you'll be all but compelled to turn it into a workable
>puzzle and then compelled to solve it but it would still be way cool to
>see some twists regardless of whether you ever take it further.
>
>I'd been dismissing 5D cubes out-of-hand as hopeless the same way that
>most people would dismiss 4D cubes. Thanks for building this and sharing
>it with us. It's making me rethink my assumptions.
>-Melinda
>
>Roice Nelson wrote:
>
>
>
>>Well I must eat my words, or at least admit to being a little
>>ridiculous because Remi's enthusiasm gave me the bug again. I've
>>relapsed slightly into my obsessive compulsive rubik's disorder by
>>doing some hobby programming this past week to create a MagicCube5D
>>proof of concept. This will allow 2^5 through 5^5, has some options
>>to play with in terms of projections, and allows overall cube (view)
>>rotations. There is no twisting yet, but it makes me believe such a
>>puzzle is plenty possible. I'm not sure yet if I want to do any more
>>than this, but I did want to share what is here with you guys.
>>
>>I posted a couple screen shots and an install here if you are interested:
>>
>>http://www.gravitation3d.com/magiccube5d/
>>
>>
>>A couple quick comments on it...
>>
>>Left mouse dragging will rotate the view and right mouse dragging will
>>zoom (3D transformations only).
>>
>>The full view rotations are done by selecting 2 axes and then pressing
>>a button. Using 2 axes is the proper extension to higher dimensions,
>>and the way to think about it is that a rotation transforms a set of
>>points in a plane. So for example, if this were a 3D puzzle and you
>>wanted to do the rotation you typically think of as about the z axis,
>>you would select x and y as your 2 axes to define the rotation plane.
>>You could think of the rotation axis as being the rotation plane
>>normal vector, but in the case of a 5D cube, there are 3 normal
>>vectors to a given rotation plane.
>>
>>I made the projection distance for 4D and 5D separately changeable to
>>avoid direct face overlapping problems if that is desired. Some of
>>the other options were just made in the effort to try and find out how
>>to make enough space for this puzzle.
>>
>>Enjoy :)
>>
>>Roice
>>
>>
>>
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>
>Yahoo! Groups Links
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Hey Denny,

There was some discussion about this very early on, I think before the yaho=
o
group existed. Two ideas I remember were:

(1) A physical cube you could hold, but which had electronic lights that
would change appropriately as you manipulated it. I'm not sure real twists
could be done with this, since some of the faces warp and change shape with
certain twists. So it might be limited to button pressing for twisting.

(2) Stereo vision and virtual reality. This might be the next best thing
to holding a real one. I mentioned the eDimensional glasses in my last pos=
t
(www.eDimensional.com). If you also had a virtual reality glove, you could
perhaps get a decent feeling of manipulating the puzzle like a real Rubik's
cube.

Roice


On 3/31/06, Denny wrote:
>
> Hello everybody...
>
> I have to say, that I'm really impressed about the realisation of the 5D
> Cube... Very nice, I like it. :-) I hope, that soon twists will be
> possible... I'd really like to twist this thing... :-) It's somehow a
> little bit crazy, but I like it very much!
> So far for the 5D cube... In the last days I thought a little bit about
> the 4D Cube and a strange idea came to my mind... We all look at the
> computer and the 3-dimensional projection of this 4D-Object... And like
> everyone knows, it is not really 3D... So the idea came to my mind...
> Would it be possible to create something, that looks like the projection
> of the 4D Cube in real space... I think in a first step one can create
> something that only looks like the 4D cube and that one can rotate the
> whole object like in 4D (inside-out-effect)... That should be
> possible... Also with the spacings between the stickers... I think that
> is not the problem... But the next step would be nice to realize, to
> make twists possible... :-) I only thought about it and I'm not shure if
> this is possible in anyway. Please tell me, if you ever thought about
> something like this or if something like this was ever discussed... :-)
> Would be nice!
>
> Thanks
>
> Denny
>

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