Message #1510

From: Andrey <andreyastrelin@yahoo.com>
Subject: Re: new hemi-cube and hemi-dodecahedron puzzles
Date: Sun, 06 Mar 2011 22:27:21 -0000

Roice, thank you!
Hemi-dodecahedron is hard enough. I’ve selected the simplest way -
solve 2C (from "infinite line" down to the center), and then solved 3C by commutator (FRF’R’)^3. But at the end I had to twist two corners and it was very difficult to find space for it.
Result is 452 twists (3 layers).

Andrey

— In 4D_Cubing@yahoogroups.com, Roice Nelson <roice3@…> wrote:
>
> 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.
>