Message #1518

From: Melinda Green <>
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 <> 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
> <>.

This is fascinating! Within the Wikipedia section you referenced is a
link for "coloring the triangles" that gives this tiling
I’ve been trying to construct a physical {3,7} using Polydron but I
haven’t yet figured out the color mapping.