Message #1009

From: Roice Nelson <roice3@gmail.com>
Subject: Re: [MC4D] Magic Tiles
Date: Thu, 15 Jul 2010 20:26:42 -0500

Andrey wrote:

> I’ve started to play with Magic Tiles from octagon, 6 colors and nonagons,
> 4 colors. I can says that it’s a very nice joke! Thank you for it, Roice!

You’re welcome, and I’m glad you are liking it :)

Btw, I’ve been watching the MC7D adventure unfold with my jaw dropped. I’ve
played with it some, and both the program and your solution are highly
impressive. So thank you! My 4 year old memories of slogging through a 3^5
solution are still fresh enough to keep me from attempting a full solve of
anything higher, but it is great fun to be a spectator.

Melinda wrote:

> I’m not sure what you mean by "finite factor-lattices of dodecahedral
> honeycomb". That sounds to me like simply the 120-cell.

I was wondering what Andrey meant by this as well. I thought maybe he was
asking about a hyperbolic dodecahedral
honeycomb<http://en.wikipedia.org/wiki/Order-4_dodecahedral_honeycomb>,
and whether you could cover the entire infinite space by coloring the cells
in a repeating manner using a finite number of colors. I haven’t seen any
info on whether this is possible (and what the corresponding topologies
might be), but I’d love to be pointed to it.

Roice