# Message #1505

From: Roice Nelson <roice3@gmail.com>

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

Date: Sat, 05 Mar 2011 18:58:07 -0600

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>

.

Roice