Message #1456

From: Roice Nelson <roice3@gmail.com>
Subject: Re: [MC4D] slicing up MagicTile puzzles without triangle vertex figures
Date: Sat, 26 Feb 2011 11:52:32 -0600

Hi Brandon,

That’s really cool, thanks for sharing. You’re right, Carl’s animations are
similar to this study, and his edge turning animation reminds me of some of
the puzzles I lamented being so complicated at times. His face turning
animation made me realize I should allow the circles to get bigger for the
spherical puzzles (so I’ve extended the range possible).

Of course, the twistypuzzles thread has further intriguing aspects to it
(impressive job on solving the multidodecahedron using the applets!).
Carl’s scaling of the dodecahedron he used to move through the various
puzzles has a definite "4D feel" to it, as Nan hinted at in one post. The
central projection of a dodecahedron being moved through a 4th dimension
towards a camera would change size like that, and the resulting hypervolume
the dodecahedron moves through is a dodecahedral prism. So this
multidodecahedron discussion made me wonder if there are some unique
slicings possible for our prism puzzles which we haven’t yet considered.
This Type II guy leads me to believe you can slice up the dodecahedral prism
so that the two dodecahedra at the two ends of the prism would get sliced
differently (say one looking like a Megaminx and the other like a Pyraminx
Crystal). The slicing planes would no longer be perpendicular to the cells,
and the big thing you’d give up is that after a twist, the shape of the
puzzle would change! It would no longer be a dodecahedral prism, since some
of the stickers on the two ends would be interchanged, and those swapped
stickers will have different shapes. Maybe it’s not really possible to
scramble it much though. I’d need to think more about it (thinking of the
3D analogue of a pentagonal prism puzzle is helpful).

I suppose I should have considered shape-changing 4D puzzles before now, as
I’m sure they are inevitable in the evolution of things. (Maybe I haven’t
because I’ve never really liked these puzzles very much myself.) Anyway,
cool links! And thanks too for the feedback of the characteristics of
puzzles you prefer.

Take Care,
Roice

On Thu, Feb 24, 2011 at 9:45 PM, Brandon Enright <bmenrigh@ucsd.edu> wrote:

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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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