Message #1452

From: Brandon Enright <bmenrigh@ucsd.edu>
Subject: Re: [MC4D] slicing up MagicTile puzzles without triangle vertex figures
Date: Fri, 25 Feb 2011 03:45:25 +0000

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On Tue, 22 Feb 2011 22:18:57 -0600
Roice Nelson <roice3@gmail.com> wrote:

> Hi all,
>
> I made a toy to help study the problem of how to slice up (face
> turning) MagicTile puzzles that do not have triangle vertex figures,
> and wanted to share. Honestly, my initial impression is that I wish
> the slicing turned out to be more elegant in the general case.
> Instead, there seem to be a huge number of possible puzzles for
> tilings like the {3,7}, none of them which feel particularly natural
> to me. You can play with the study tool directly in a web browser if
> you have Silverlight installed (or are willing to install it). I
> seem to be overtaxing the Silverlight drawing a bit, and some of the
> spherical puzzles aren’t perfect due to things projecting to
> infinity, but it serves the purpose I wanted pretty well.
>
> www.gravitation3d.com/magictile/slicing_study.html
>
> Here are a few thoughts I had, but I’d really love other opinions on
> what would be the best puzzles for the next iteration of MagicTile.
>
> - Starting with a small circle size and increasing, the transition
> between puzzle types happens at points where new intersections begin
> between sets of two or more slicing circles (it reminds me of Venn
> diagrams). All the possible ways in which this can happen are very
> complicated. As you increase the circle size, there can be *a lot*
> of puzzle "phase transitions".
[…]

Hey Roice,

I rarely have easy access to a Windows box so I don’t have
Silver light (I’m looking forward to getting Moonlight+Mono working
though).

Based on what you are describing in words, I think you might be
interested in some similar work done by Carl Hoff.

Here is an animation of varying the cut depth for a face turning
dodecahedron:
http://twistypuzzles.com/forum/viewtopic.php?p=179381&#p179381

As you can see that puzzle stays pretty simple.

Carl also did a similar animation for edge-turning cuts:
http://twistypuzzles.com/forum/viewtopic.php?p=189458#p189458

As you can see, certain depths cause a huge number of tiny pieces to
spring in an out of existence ("phase transition").

As for solving experience, I prefer semi-deep cuts with no more than
two different types of tiny pieces. I think Schuma (Nan) likes crazy
challenges with tons of hard-to-isolate tiny pieces.

This weekend I’ll find a Windows machine and play with your slicing
study.

Best,

Brandon

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