# Message #1518

From: Melinda Green <melinda@superliminal.com>

Subject: Re: [MC4D] Re: MagicTile Extension in Superliminal/Wiki

Date: Mon, 07 Mar 2011 12:19:53 -0800

On 3/5/2011 4:58 PM, Roice Nelson wrote:

> On Sat, Mar 5, 2011 at 6:27 AM, Andrey wrote:

>

> What is interesting - to fing group that is generated by these

> permutations. It’s easy, that spots are numbers from Z/23Z with

> "infinity" number, so that rotation of circle works like +1 or -1.

> Swapping is some fraction like P(x)/x (or P(x)/Q(x), where

> Q(0)=0), and I’m trying to find it. Their hint says that it may be

> about some object in 5 dimensions, but I don’t see it now.

>

>

> I didn’t fully follow this, but the puzzle permutations are based on

> the Mathieu group <http://en.wikipedia.org/wiki/Mathieu_group_M24> M24

> (as described in the Scientific American article about this puzzle).

> Is that what you were trying to uncover? Or maybe you are trying to

> find a polytope representation of the group structure? It was

> surprising to learn just now that M24 can be constructed starting from

> the symmetries of the Klein Quartic, then augmenting by one additional

> permutation, as described here

> <http://en.wikipedia.org/wiki/Mathieu_group_M24#Polyhedral_symmetries>.

>

This is fascinating! Within the Wikipedia section you referenced is a

link for "coloring the triangles" that gives this tiling

<http://homepages.wmich.edu/%7Edrichter/images/mathieu/hypercolors.jpg>.

I’ve been trying to construct a physical {3,7} using Polydron but I

haven’t yet figured out the color mapping.

-Melinda