Message #3464
From: Roice Nelson <roice3@gmail.com>
Subject: Re: [MC4D] Re: MagicTile Solving
Date: Mon, 18 Jul 2016 13:14:52 -0500
Thanks a bunch Ed! Below are the answers I sent to Burkard. His question
#3 makes me want to attempt a superflip on the KQ and see what happens :)
Cheers,
Roice
> 1. Which puzzles do you consider the easiest to do?
>
This is something the group has discussed, and is interesting in a number
of ways. Some things that make puzzles more difficult are:
- Deeper cuts (bigger slicing circles in MagicTile) cause more
difficulty because each twist affects more material. - Puzzles with more complex vertex figures tend to have more complicated
pieces and are more difficult, e.g. icosahedral puzzles have a pentagonal
vertex figure and are generally more difficult than dodecahedral puzzles,
which have a triangle vertex figure. Well, this comment applies to face
turning puzzles anyway. A vertex-turning icosahedral puzzle behaves a lot
like a dodecahedral face turning puzzle. - Perhaps unintuitively, more colors can be easier because there is more
"space" to move pieces around. You might argue that the Megaminx is easier
than the Rubik’s cube in this sense. - More complex topology tends to be more difficult, but I think this is
less of an effect.
With that list of considerations, I’d point out the "Klein Quartic Classic"
as one of the easiest puzzles to solve. Even though it is a hyperbolic
puzzle with a genus-3 topology, the cuts are shallow, the vertex figure is
a triangle, and there is plenty of space to move pieces where you want them.
- Which are your favourite ones when it actually comes to actually solving
> them? Have you had much feedback from people highlighting features/puzzles
> that they really like playing with?
>
For me personally, I stick with the simpler ones, so I have to say the
Klein Quartic puzzle is a favorite. But I know some of the group members
find this puzzle boring in it’s difficulty. The topology gives a nice
surprise though. If you solve the Rubik’s Cube layer-by-layer, you end up
with one unsolved face at the end. If you solve this puzzle
layer-by-layer, you end up with two unsolved faces at the end!
The "{6,3} 7-Color (Szilassi polyhedron) F0.67:0:1" is an easy euclidean
puzzle for all these same reasons. The cuts are very much like on the
Rubik’s cube and the number of colors is similar too (enough to give some
space).
A feature request I got very early was macros, and it was interesting
designing them so that they can be "one click". Ed Baumann uses these in
dramatic fashion, and sometimes his macros run into the thousands of
moves! I gather from the users that this is a must have feature that they
are happy with.
I really enjoy playing with the different projections myself, especially in
the case of spherical puzzles. I’d like to add some more options there,
like Mercator, etc. I also like that the program calculates the Euler
characteristic of the surface for you and displays it at the bottom. This
was surprisingly difficult to implement.
- Which have a non-trivial center (like the superflip for the Rubik’s
> cube)?
>
I don’t know the answer to this question, and we definitely could do more
group-theoretic analysis on these than we have. We haven’t even really
done a proper dig into the Klein Quartic puzzle (calculating number of
permutations, looking at the group, it’s center, etc.). But the nice thing
about my answer is that there are a lot of open-ended problems ripe for
study!
Some similar kinds of analysis we’ve done:
- Possible checkerboard patterns on the quartic puzzle (pictures
<http://www.gravitation3d.com/magictile/checkerboards/> and thread
<https://beta.groups.yahoo.com/neo/groups/4D_Cubing/conversations/messages/1376>
). - Parity situations, which can often arise in surprising and difficult
ways, like on this torus puzzle (thread
<https://beta.groups.yahoo.com/neo/groups/4D_Cubing/conversations/messages/2631>).
I like to think of the stickers becoming "entangled particles" as they move
about the surface.
- Any superingenious aspects that set certain puzzles apart from others?
>
There are so many interesting things that pop up, all over the map. Here
are a few aspects that come to my mind.
- The topological effects like I mentioned for the quartic (where each
face has two "opposites"). - Non-orientable puzzles. You can tell which are non-orientable because
some identified stickers on the universal cover will rotate in the opposite
direction. - Some of the puzzles are not manifolds, but orbifolds, and strange in
the way they connect up (thread
<https://beta.groups.yahoo.com/neo/groups/4D_Cubing/conversations/messages/1980>
). - Surprises abound. The {8,3} 6-color puzzle turns out to be identical
to the original Rubik’s Cube from a sticker and permutation
standpoint (Andrey Astrelin discovered this). Because of the
identifications, the octagons are squares in disguise. - I like spherical "super chop" puzzles because all the cuts are along
great circles. This means they are geodesic, and therefore straight lines
when you display them in the gnomonic model. For a trippy time, pull up a
super chop puzzle, scramble it, set the gliding to 1 and the model to
gnomonic, then start it auto-solving and spin the view :)
On Sun, Jul 10, 2016 at 5:14 AM, ed.baumann@bluewin.ch [4D_Cubing] <
4D_Cubing@yahoogroups.com> wrote:
>
>
> Some MagicTile topics for Burkard Polster:
>
> 1) You get extremely accustomed to the stereographic projection in
> MagicTile. It becomes even easier than the normal perspective view.
>
> 2) Absolutely crucial is the possibility for defining and using macros.
>
> 3) The help for setup’s and their undoing is very comfortable.
>
> 4) There is an enormous variety of puzzles. All are very interesting.
>
> 5) Half solved puzzles are often very beautiful (esthetic).
>
> 6) Often parity aspects form a big challenge.
>
> 7) The exotic Klein- and Mobius-topology can naturally be integrated in
> the framwork of MagicTile.
>
> 8) MagicTile is ENDLESS FUN !
>
> Best regards
> Ed
>
>