Message #2468

From: Melinda Green <melinda@superliminal.com>
Subject: Re: [MC4D] MagicTile Solving
Date: Mon, 05 Nov 2012 14:14:25 -0800

It’s even harder to find a four holed doughnut. (Mmmmm, doughnut)

I’m probably repeating myself, but all of the IRP’s are "angular" wrl
(VRML) models. Using just a single cell and bending things around to
create a finite high-genus model seems a bit of a contortion whereas the
IRP versions of the same uncontorted (tiled) models seems like the
natural way to model them.

-Melinda

On 11/5/2012 4:56 AM, Eduard Baumann wrote:
>
>
> You wrote:
> "So both of your face adjacency graphs will naturally live on the
> surface of a 4-torus (four holed donut)."
> What a dream :
> _A 4-torus (four holed donut) having the coloring of a30 and b30_
> It is not easy to find beautyfull pictures of genus 4 manifolds (many
> are only genus 3) :
> http://wiki.superliminal.com/wiki/File:Genus_4_1.PNG
> _http://wiki.superliminal.com/wiki/File:Genus_4_2.PNG_
> http://wiki.superliminal.com/wiki/File:Genus_4_3.PNG
> http://wiki.superliminal.com/wiki/File:Genus_4_4.PNG
> http://wiki.superliminal.com/wiki/File:Genus_4_5.PNG
> Have you better ones ?
> Make angular wrl samples ?
> Ed
>
> —– Original Message —–
> *From:* Roice Nelson <mailto:roice3@gmail.com>
> *To:* 4D_Cubing@yahoogroups.com <mailto:4D_Cubing@yahoogroups.com>
> *Sent:* Monday, November 05, 2012 4:54 AM
> *Subject:* Re: [MC4D] MagicTile Solving
>
> Hi Ed,
>
>
> I like your study and posts on these topics. I was surprised to
> see that although these two IRPs look quite different, their
> element counts and genus are identical.
>
> Faces: 30
> Edges: 60
> Vertices: 24
> Euler Characteristic: -6
> Genus: 4
>
> So both of your face adjacency graphs will naturally live on the
> surface of a 4-torus (four holed donut).
>
> You asked for comments on the edgesets in these files. You are
> right that edgesets are how MagicTile encodes the coloring, so
> they are indirectly responsible for the resulting face adjacency
> graphs. But it would not really be possible to directly relate
> one to the other, as there are lots of interim calculations done.
> An analogy that pops to mind is to think of edgesets as an
> organism’s DNA and the adjacency graphs as the organism’s visible
> traits.
>
> An "edgeset" is the set of CCW 0-indexed edges to reflect across
> to go from the central white tile to an identified copy. As an
> example, here is a picture showing how the "3:3:3" edgeset in the
> {7,3} config tells the program to go from the central white tile
> to copies.
>
> http://www.gravitation3d.com/magictile/pics/73/%7B7,3%7D_reflections.png
>
> (By default, reflections are done across all the initial edges, so
> "3:3:3" actually represents 4 reflections, applied in each of the
> 7 directions, encoding 7 copies). There are further nuances to
> the config. I tried to make it a useful/compact description,
> though it’s surely imperfect. If there was enough interest, I
> could try to write up a better description of all the details.
>
> seeya,
> Roice
>
>
>
> On Sat, Nov 3, 2012 at 7:29 AM, Eduard Baumann <baumann@mcnet.ch
> <mailto:baumann@mcnet.ch>> wrote:
>
>
>
> Color graphs of MagigTile puzzes.
> I inspected now also the MT infrastructure of MT irp {4,5}
> x30, x=a or b.
> For the _geometry_ there is an ._wrl_ file. I can view it with
> cortona3D. But I can also look at with an editor. a30 is shown
> with 4 colors and b30 with 5 colors.
> For the _puzzle_ there is an ._xml_ configuration file. For
> the color definitions I see only very small information in 6
> _edgesets_.
> The connection with an adjacency list of the corresponding
> color graph ist not easy to see.
> Interesting matter! Roice please comment.
>
> —– Original Message —–
> *From:* Melinda Green <mailto:melinda@superliminal.com>
> *To:* 4D_Cubing@yahoogroups.com
> <mailto:4D_Cubing@yahoogroups.com>
> *Sent:* Friday, November 02, 2012 11:52 PM
> *Subject:* Re: [MC4D] MagicTile Solving
>
> Ah, I missed the ‘6’, thank you for the correction. This
> is one of the 3 IRPs that are as perfectly symmetric as
> the Platonic solids in every way. It is also the IRP twin
> of the original Rubik’s cube. I would still like to know
> why Nan’s solution is so much shorter.
>
> I also do not understand why you see the IRP 4-5 b30 f001
> as a warm-up exercise to the IRP {4,5} a30 F 0:0:1. True
> they both have 30 colors and genus 4, but they have
> different symmetries which I would guess would make the
> ‘a’ puzzle the simpler of the two.
>
> -Melinda
>
> On 11/2/2012 2:05 PM, Eduard Baumann wrote:
>> Wait.
>> The similar puzzle I mentioned is
>> NOT
>> MT irp {4,5} a30 F 0:0:1
>> BUT
>> MT irp {4,6} 12 F 0:0:1
>> I will attack
>> MT irp {4,5} a30 F 0:0:1
>> next time but I wanted study before he color topology of
>> a30 and b30.
>> Ed
>>
>> —– Original Message —–
>> *From:* Melinda Green <mailto:melinda@superliminal.com>
>> *To:* 4D_Cubing@yahoogroups.com
>> <mailto:4D_Cubing@yahoogroups.com>
>> *Sent:* Friday, November 02, 2012 9:53 PM
>> *Subject:* Re: [MC4D] MagicTile Solving
>>
>> {4,5} a30 is one of my favorite IRPs. I find it to be quite beautiful and symmetric. It is the one that I showcase on themain geometry page <http://superliminal.com/geometry/geometry.htm> to introduce the subject. (Third image down.) The ‘b’ puzzle that surprised you is less symmetric but is still a fascinating structure. It looks very much like an apartment complex. I would like to know why Nan was able to solve it with such a smaller number of twists. Unless your macros are extremely long, it doesn’t seem like that can be the only difference. What do you think, Nan?
>>
>> -Melinda
>>
>> On 11/2/2012 11:17 AM, Eduard wrote:
>>> Solving of MT irp {4,5} b30 F 0:0:1 —– || 11/02/2012 || 2393
>>>
>>> Remark:
>>> Over 2000 twists. I worked without macros this time. Not low hanging fruit. Here 30 colors. In the similar puzzle "irp 4-6 12 f001" with 12 colors I worked with macros and needed 21’000 twists (Nan only 400 !!).
>>
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