Message #828

From: Roice Nelson <roice3@gmail.com>
Subject: Introducing "MagicTile"
Date: Sat, 30 Jan 2010 21:04:50 -0600

Thanks to everyone for the thoughtful feedback on my question this week. I
appreciate it, and it was good to get your perspectives.

I think I’m ready enough to share a first pass of the new Rubik analogue I
started playing with before the MC4D 4.0 fun, which I mentioned the
possibility of here<http://games.groups.yahoo.com/group/4D_Cubing/message/541>some
time ago. While you might observe it doesn’t quite fall into the
category of hyperpuzzles, it does in at least once sense mentioned below :D
Here is the page with the download, pictures, and a
video<http://www.gravitation3d.com/magictile>.
To describe the analogue idea, I’ll just quote the beginning of the
explanation on that page:

> This program aims to support twisty puzzles based on regular polygonal
> tilings <http://en.wikipedia.org/wiki/Regular_tessellation> having Schlafli
> symbols <http://en.wikipedia.org/wiki/Schlafli_symbol> of the form {p,3}
> for any p>=2. That is, all regular tilings of polygons with two or more
> sides, where three tiles (puzzle faces) meet at a vertex. The Rubik’s cube
> is the special case where faces are squares (p=4). The other familiar
> special cases are the Megaminx (p=5) and the Pyraminx (p=3), although you’ll
> discover the last takes a slightly different form under this abstraction
> (akin to Jing’s Pyraminx <http://www.youtube.com/watch?v=FuD3YwQTW2c>).
> All the other puzzles are new as far as I know, and some may be surprising,
> e.g. the puzzles based on digons <http://en.wikipedia.org/wiki/Digon>
> (p=2).

> Each 2D tiling admits a particular constant curvature (homogenous)
> geometry. The geometry is Spherical for p=2 to p=5, Euclidean (flat) for
> p=6, and Hyperbolic for p>=7. Since you can’t "isometrically embed" the
> entire hyperbolic plane in 3-space<http://www.math.cornell.edu/~dwh/papers/crochet/crochet.html>,
> I have a connection to hyperpuzzling<http://games.groups.yahoo.com/group/4D_Cubing/> even
> though I’m talking about 2D tilings!

…

I’ve actually only solved the 3x3x3 on it so far, and I wonder if it may be
more fun to watch than play! I’ve been calling it MagicTile, though perhaps
there could be something better? As with everything, it is a known work in
progress (the length of the task list has grown to scary proportions). I
have no plans for further development at the moment, though I’ll happily fix
any glaring bugs.

Enjoy!
Roice

P.S. This is the only "twisty puzzle" group I’m active in, so if any of you
are also members of other groups and think they would be interested to hear
about these new puzzles, I’ll appreciate the exposure :)