Message #2042

From: Eduard Baumann <baumann@mcnet.ch>
Subject: Re: [MC4D] 4D-interactive puzzles in MagicTile
Date: Mon, 05 Mar 2012 09:49:39 +0100

Thanks Roice.

An other point:
in http://www.superliminal.com/cube/halloffame.htm
there is a link to my home page (clicking my name). Please change this link as follows.

The old adress is
http://private.mcnet.ch/baumann/
and is valable only to end juin 2012

Please change the link to
http://www.baumanneduard.ch/

Kind regards
Ed

—– Original Message —–
From: Roice Nelson
To: 4D_Cubing@yahoogroups.com
Sent: Monday, March 05, 2012 7:24 AM
Subject: Re: [MC4D] 4D-interactive puzzles in MagicTile

Hi Ed,

It is 4D, in that the puzzle only fits together in a truly regular way in 4 dimensions. But the puzzle faces are still 2D (the {4,4|4} has 16 2D faces). This is unlike MC4D, which has 3D faces fitting together in 4D. Still, you can see how some of the square faces of the {4,4|4} are being warped due to the 4D -> 3D projection. As in MC4D, shift+left drag to do some 4D rotations that will affect this warping.

None of the 16 faces are getting hidden. Whereas in MC4D, a 3D face can be "back facing" or "front facing" relative to a 4D camera, these 2D faces have no such orientation. How come? Use dimensional analogy to think of a set of 1D edges embedded in 3D. Although a 2D polygon can be back facing or front facing in 3D (relative to a 3D camera), a 1D segment can not - a polygon will have a normal that can only point in two directions, but a segment has an infinite number of normal directions. Similarly for a 2D polygon living in 4-space. Hope that made sense, but in short, there is not a way to hide the 2D puzzle faces based on their location in 4D.

However, I should mention that skew polyhedra divide space into two halves (the IRPs divide 3D space in two, the 4D skews divide the hypersphere surface into two 3D partitions). It is therefore possible to consider one of these halves the "inside" and the other the "outside". If we then interpreted the puzzle as a solid 3D object which was the inside half, we could hide faces based on that. I chose not to do this though, in keeping with the MagicTile abstraction of representing puzzles as 2D surfaces alone. In MagicTile, the Rubik’s Cube is not a solid cube, only a tiling of squares on a 2D surface.

Hope this helps clarify some.

All the best,
Roice

On Sun, Mar 4, 2012 at 2:20 PM, Eduard Baumann <baumann@mcnet.ch> wrote:

Awesome !!!

I like the new forms.

Question&#58; <br>
example &#123; 4 4&#124;4 &#125;<br>
Is this 3D or 4D. I see only 4 cells.<br>
If 4D&#58; are there hidden cells (as in tesseract the exterior 8th cell)?

Kind regards<br>
Ed