Message #1508

From: Roice Nelson <roice3@gmail.com>
Subject: new hemi-cube and hemi-dodecahedron puzzles
Date: Sun, 06 Mar 2011 14:46:17 -0600

Greetings,

I added two new sets of puzzles to MagicTile, the first non-orientable
puzzles which appear so visually in the program.

The hemi-cube puzzles are combinatorially the same as the 3-colored puzzles,
which Andrey has pointed out. At first I thought the even-length ones might
be different, but those end up behaving like odd-length puzzles anyway.

The 6-color hemi-dodecahedron puzzles are something new to investigate. If
you discover unusual behaviors during a solve, please do share :) I have
the feeling the length-3 puzzle will turn out to be a favorite for me.

These both have the topology of the real projective
plane<http://en.wikipedia.org/wiki/Real_projective_plane>,
so now we just need a Boy’s
surface<http://en.wikipedia.org/wiki/Boy%27s_surface>display of them
:D

I think with the right mechanism, these puzzles might be candidates for
actual physical variants. Perhaps I should write experts like Oskar or Bram
about this.

At the same time, I went ahead and fixed the loading/saving to persist out
the "slicing expansion" setting, so that people can record their progress
with deep-cut puzzles. Disclaimer: I know making the circles too big can
produce unintended weirdness, so it will be up to you to decide if the
setting you’ve chosen has produced a valid puzzle. I still want to make
this setting less experimental in the next version.

Enjoy!
Roice

Some Fine Print… To get hemi-puzzles to work right, I needed to fix the
twisting behavior on Rubik’s Cube/Megaminx for the faces inverted by the
projection (which Matt Galla suggested I do early on). The new behavior is
better, but it has the downside of breaking any log files that were
generated for these puzzles. I rev’d the version number in the log files to
mark this, but things aren’t backward compatible for loading. I’ll keep
around the last version, so people will be able load those if necessary.