# Message #1052

From: Andrey <andreyastrelin@yahoo.com>

Subject: Re: [MC4D] Magic Tile again

Date: Tue, 20 Jul 2010 18:59:22 -0000

Roice,

I’ve missed the "double pyraminx" because it should give "planar" tile - {6,3}, 8 colors. But now I see that it’s an excellent opportunity to check my theory - and this theory doesn’t work! We cannot "upgrade" 4-colored {6,3} to 8 colors, but easily design 12-colored tile. So it’s some "triple pyraminx" but with only double size of face.

I’m investigating {9,3} patterns now. And sometimes I fill that there exists 12-color tile (and 16-color) and sometimes not. It’s difficult to understand hyperbolic transitions of plane, but very interesting…

Andrey

>I am

> curious to hear more of why you suspect this nonagonal possibility (did you

> also suspect an 8-color "double pyraminx" as possible? why or why not?).

> There is an entry in the table implying there could be a 36 color nonagonal

> puzzle.

>

> From the size of the table, one can see that there a *huge* number of

> potential puzzles that are possible if one removes the restriction of 3

> polygons meeting at a vertex.

>

> I’ll close with something unique about the 12 colored octagonal, which may

> or may not lead to further insight (I don’t know if it is significant). But

> it is the only hyperbolic puzzle in the MagicTile list where copied cells

> are generated by an odd number of reflections (3 reflections). Find a cell,

> and check the shortest path to one of its repeats to see what I mean, and

> compare this with other puzzles.

>

> Cheers,

> Roice

>