Message #2046

From: Andrey <andreyastrelin@yahoo.com>
Subject: Re: 4D-interactive puzzles in MagicTile
Date: Tue, 06 Mar 2012 16:03:52 -0000

Roice,
New puzzles are beautiful! It’s very nice to see these sceletons of our familiar 4D bodies and wander around them :)
I solved only one puzzle so far - bitruncated simplex (my favorite polytope :) ) in F:0:0:1 slicing. It was not very easy, and one of main problems is that twising rotation depends on side of face that you click: if you see one side, face twists clockwise, but if you go to the other side and make the same click, it twists counterclockwise. I think that it’s not difficult to fix.
This puzzle has a kind of "global non-orientability": if you have wrong oriented edge, you can’t reorient it by moving around the vertex, you have to make a loop around a tube. I guess that same effects will be in 5x5 and 7x7 duoprisms (that are actually just another implementations of planar tori :) )

Thank you for these puzzles!

Andrey

— In 4D_Cubing@yahoogroups.com, Roice Nelson <roice3@…> wrote:
>
> Recently, I learned that in addition to the regular skew polyhedra that are
> infinite (Melinda’s IRPs), there are regular skew polyhedra which are
> finite. They close back around on themselves in 4 dimensions. Here was an
> awesome opportunity to make MagicTile genuinely applicable to the 4D_Cubing
> group :D
>
> To start, I’ve included 4D skew polyhedra associated with some duoprisms,
> the runcinated 5-cell, and the bitruncated 5-cell, though there are additional
> possibilities <http://en.wikipedia.org/wiki/Regular_skew_polyhedron> for
> the future. These should be pleasant to solve in skew mode, and I’m sure
> many interesting observations can be made of the shapes included so far.
> For instance, check out how the surface of the {4,6|3} relates to 3
> intersecting spheres.
>
> I just uploaded some
> pics<http://groups.yahoo.com/group/4D_Cubing/photos/album/597055459/pic/list>of…
>
> - {4,4|4} duoprism, aka hypercube
> - {4,4|5} duoprism
> - {4,4|7} duoprism
> - {4,6|3} runcinated 5-cell
> - {6,4|3} bitruncated 5-cell
>
> Although the duoprisms are easily seen as having genus 1, can you figure
> out the genus of the other two? Not trivial to figure out by sight! I
> won’t give away the answer, but will say both have the same genus.
>
> I changed the 4D viewing controls slightly from MC4D, so that the 4D camera
> distance could be altered with the mouse (I didn’t want to rely on a
> slider). Things will mostly be familiar though, and details are in the
> Help menu.
>
> This feels like a great plateau, so now I’m going to take a break from
> MagicTile for real :)
>
> Enjoy! <http://www.gravitation3d.com/magictile/downloads/MagicTile_v2.zip>
> Roice
>