Message #1021

From: Andrey <>
Subject: Magic Tile again
Date: Sat, 17 Jul 2010 16:19:58 -0000

I’ve took a closer look to Magic Tile set of puzzles and found a strange thing.
Of 11 puzzles from "hyperbolic" part of set there are only 5 mathematically different ones and two of them are already listed in "spherical" section: all 6-colors are equivalent to Rubik’s cube, all 4-colors are alternative implementations of pyraminx, and 3-colors are equivalent to 3-colored Rubik’s cube - non-oriented polyhedron with one vertex, 3 edges and 3 digonal faces :) (are they the same as "digonal" puzzle? No, there is not enough 1C pieces in the latter). Two others - 24-color Klein’s quartic and 12-colors {8,3} puzzle (double cube?) are really hyperbolic. This {8,3} looks very interesting - and I have to understand how it works. Like we cut a hole in center of paper cube, dupicated the rest and interconnented copies so that when you pass some of edges you go to another cube… May be not. And it looks like there could be 12-colored {9,3} (triple pyraminx) and 18-colored {12,3} - triple cube or double {6,3}*9 colors.
3 colors, 7 layers took some time to understand and solve it - most algorithms from N^3 didn’t work. Luckily there is only small set of colors distribution, and simplest commutators did the trick :)))
Thanks again, Roice!