Message #2456
From: Eduard Baumann <baumann@mcnet.ch>
Subject: Re: [MC4D] MagicTile Solving
Date: Sat, 03 Nov 2012 18:35:58 +0100
Results of my color graph study for MT irp {4,5} 30.
First the adjacency list of b30:
1 2 3 4 5
2 1 6 7 8
3 1 7 9 10
4 1 7 11 12
5 1 7 13 14
6 2 9 9 15
7 2 3 4 5
8 2 13 13 16
9 3 6 6 17
10 3 11 11 18
11 4 10 10 19
12 4 14 14 20
13 5 8 8 21
14 5 12 12 22
15 6 24 23 25
16 8 26 27 28
17 9 23 25 29
18 10 26 27 29
19 11 24 26 27
20 12 23 25 28
21 13 26 27 30
22 14 23 25 30
23 15 17 20 22
24 15 19 30 30
25 15 17 20 22
26 16 18 19 21
27 16 18 19 21
28 16 20 29 29
29 17 18 28 28
30 21 22 24 24
It is interesting that here we have 12 vertices which have doubled neighbours (6, 8-14,24 and 28-30). Then also we have two pairs of vertices which have same neighbours (1+7) and (26+27).
The adjacency list of a30 had none of these specialities.
My try to embed a30 gave the following. I hope the uploaded pictures to wiki are linkable.
http://wiki.superliminal.com/wiki/File:Color_graph_a30_manual.PNG
And now Mathematica helping me:
http://wiki.superliminal.com/wiki/File:Color_graph_ab30_Mtica.PNG
The spring embedding procedure is certainly performant but the graphs to be shown are complex and not very regular.
Regards
Ed
—– Original Message —–
From: Melinda Green
To: 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 <br>
NOT<br>
MT irp {4,5} a30 F 0:0:1<br>
BUT<br>
MT irp {4,6} 12 F 0:0:1
I will attack <br>
MT irp {4,5} a30 F 0:0:1<br>
next time but I wanted study before he color topology of a30 and b30.
Ed
----- Original Message ----- <br>
From: Melinda Green <br>
To: 4D_Cubing@yahoogroups.com <br>
Sent: Friday, November 02, 2012 9:53 PM<br>
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 the main geometry page 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 !!).