Message #1007

From: Andrey <andreyastrelin@yahoo.com>
Subject: Magic Tiles
Date: Thu, 15 Jul 2010 23:01:10 -0000

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!
For heptagons, 24 colors I used the method that I developed for 120 cell first: to select some set of centers, put in place all pieces between them (call these centers "solved"), then select some center adjacent to others and put in place all pieces between it and solved centers. Just don’t rotate solved centers in this method (only in "macros") and be careful to keep area of unsolved ceneters connected. When one face remained I just used operations from 3^3 (it’s not most effective, but I didn’t need to think).
Nice puzzle!
What do we know about finite factor-lattices of dodecahedral honeycomb?

Andrey