Message #2461

From: Eduard Baumann <>
Subject: Re: [MC4D] MagicTile Solving
Date: Mon, 05 Nov 2012 09:11:21 +0100

Thanks very much for these comments. I learn a lot.

—– Original Message —–
From: Roice Nelson
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.,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.


On Sat, Nov 3, 2012 at 7:29 AM, Eduard Baumann <> wrote:

Color graphs of MagigTile puzzes.

I inspected now also the MT infrastructure of MT irp &#123;4,5&#125; 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.<br>
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
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 &#123;4,5&#125; a30 F 0&#58;0&#58;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.


  On 11/2/2012 2&#58;05 PM, Eduard Baumann wrote&#58;


    The similar puzzle I mentioned is <br>
    MT irp &#123;4,5&#125; a30 F 0&#58;0&#58;1<br>
    MT irp &#123;4,6&#125; 12 F 0&#58;0&#58;1

    I will attack <br>
    MT irp &#123;4,5&#125; a30 F 0&#58;0&#58;1<br>
    next time but I wanted study before he color topology of a30 and b30.


      ----- Original Message ----- <br>
      From&#58; Melinda Green <br>
      To&#58; 4D&#95; <br>
      Sent&#58; Friday, November 02, 2012 9&#58;53 PM<br>
      Subject&#58; Re&#58; &#91;MC4D&#93; 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?


On 11/2/2012 11:17 AM, Eduard wrote:

Solving of MT irp {4,5} b30 F 0:0:1 —– || 11/02/2012 || 2393

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 !!).