Message #755

From: Melinda Green <melinda@superliminal.com>
Subject: Re: [MC4D] Chronicles of a Rubik junkie’s experience with the {5}x{5}
Date: Mon, 02 Nov 2009 00:25:14 -0800

Whoa, hold it right there! [Insert the sound of a vinyl LP scratching to
a halt here.] Did anybody not notice that buried in Chris’ message is
the announcement that he solved the dodecahedral prism?!?! That’s
amazing! Way to go Chris! Check out the last entry in the wiki
hall-of-fame <http://wiki.superliminal.com/wiki/MC4D_Records>. This is a
hyper prism made up of two dodecahedral end caps, connected by twelve
pentagonal 3D prisms. Bring it up in MC4D and marvel at it’s beauty.
Then shift-drag to roll it around in 4D and behold it’s construction.
Then hit Scramble > Full and notice how the two dodecahedra only share
stickers with each other while the other faces turn into a jumble of
confetti.

FYI, if you create a custom 14 color line in facecolors.txt that puts
black and white at the end, they will be assigned to the two
docecahedra. Scrambling that makes them look like holstein polyhedra!
:-) See the attached screen shot to see what I mean. There are obviously
some amazing "checkerboard-like" patterns that can be created here.
Creating these will be much easier than solving the full puzzles, so
maybe some of you sitting on the sidelines might like to try your had at
such 4D art.

Also note the second screen shot is of a {20}x{20} 3 with a single twist
applied. It really shows off the toruses well. And you should see the
wild animation involved in that single twist! Amazing to me is the fact
that all of the faces of this figure are shown in most 4D orientations.
I’d been getting used to there always being invisible faces, so this
came as a nice surprise to me. The third image shows it in another
orientation where five faces are hidden. Notice the same single twist in
this new orientation. There is some really beautiful stuff to discover
in here even if you never try to solve a single random twist. Please
feel free to upload screen shots of any lovely gems that you discover,
and then talk them up here. We probably need an image gallery on the
wiki. In fact, I think we need something like that before our first
public launch so that we can make sure people can marvel at the lovely
pictures. We might capture some passionate new users that way as there
are whole new ways to participate in the fun without taking these
monsters head-on. Please help if you have any interest in this sort of
stuff.

More ramblings below…

Chris Locke wrote:
> It was pretty easy for me to notice the torus locking stickers for me
> because of my custom color scheme. For instance, here is the longest list I
> have for 14 colors:
>
> black, white, red, green, blue, yellow, magenta, teal, grey, brown, pink,
> turquoise, dark green, peach
>
> So you can see, the first torus was basically all primary/secondary colors,
> and the second torus was all the more complicated tertiary colors, so the
> pattern REALLY jumped out at me. The reason for this, is that unlike the
> 3^4 case, where every facet can be turned by a quarter turn in any axis, the
> duoprisms are limited by geometry to only allow quarter turns within the
> respective torus. And yeah, it seems that 4^3 is unique in this regard.
> What about naming conventions though? How do you decide what to use to
> notate the standard hypercube, {4}x{4} or {4,3,3}? I’m not sure if there
> are other degeneracies in naming conventions, so it’s possible this is the
> only case like this.
>

There is also the fact that {m}x{n} duoprisms are the same as {n}x{m}
except for their initial orientation.
I’m not sure how best to make that clear on the records page but we
certainly can’t allow competing records on identical puzzles that only
differ by being created using different notations.

> I have a question too: how do we decide which puzzles will be recorded on
> the wiki record page? Since it’s a wiki, are we going to allow any puzzle?
> I only ask because I realized that there are an infinity of duoprisms
> possible to solve by using the "invent my own" feature, limited only by the
> solver’s patience (and possibly computer specs :P). Couple this with the
> fact that as you go higher, I don’t think the puzzles get fundamentally more
> difficult, just much longer. I suspect that the algorithms can be
> generalized for the duoprisms of higher order, much like how if you can
> solve 3^4, 4^4, and 5^4, you should be able to adapt the algorithms to solve
> any n^4 hypercube with enough time. Nevertheless, it is still quite a feat
> to be able to solve these higher order puzzles, and I would not be opposed
> to allowing such higher order records to stand.

As Roice already commented, this is problematic for some of the figures,
especially ones with triangular figures. The "officially" supported
puzzles are the ones listed in the puzzle menu. Ones that simply add
more faces or more slices to other duoprisms are safe as well but
everything else at this time is "on thin ice", as you so eloquently put it.

> Also, will the next release
> allow all possible twists for length 2 puzzles? What will happen to the
> records of these puzzles set with the more limited twists?

Again, Roice answered this well. The only thing I’ll add is the fact
that I’ve hated the 2^4 from the beginning, so I’m not going to put much
effort into supporting them or their newborn kin. Not everything that
can be done, should be done. It’s really up to Roice and Don to support
whatever they want in that regard.

> And yes, I
> realize both of these questions put 3 of my 4 firsts on thin ice, which was
> actual part of my motivation for going for the dodecahedral prism this
> weekend, since that should be a permanent one :D. I need a break for a bit
> now from all that cubing over the weekend (^_^’)
>

Well you deserve a good break! At this point I bet you’re starting do
dream about these beasts! Your early record grabbing in this latest gold
rush reminds me very much about the last time this sort of thing
happened in the "shortests" categories. At that time, Remi was
dominating the leaderboard for a long time. He still holds a bunch of
checkerboard records but is down to only one shortest full solve. And
then before him, Noel Chalmers was king of the hill for a while but now
all of his shortest records have been bested. I find it interesting how
history repeats itself in new situations.

> And yeah, the {5}x{5} 5 is one monster. If I still had my notes from when I
> solved 5^4, I might be able to adapt the algorithms to solve some of the
> interior pieces, but upon inspection, there are also MANY kinds of interior
> pieces, all which will probably need separate, and again probably unique,
> algorithms to solve. Beastly indeed.
>

Yes, this plumb may remain unpicked for a fair while, but after seeing
the 120 cell fall, I’m not going to bet on how long that will be!

And I should mention that poor Noel is not completely forgotten because
he holds the records for the first 4^5 and 5^5 solutions. And speaking
of 5D puzzles: Roice, even if you don’t take the {5}x{5} 5 prize, maybe
there’s still a 5D {5}x{5} 5 out there? That’d be very cool but I have
no idea since I’m stopping at 4D. I’ll leave the even higher dimensional
puzzles for a future generation of hypernauts. :-)

> 2009/11/2 Roice Nelson <roice3@gmail.com>
>
>> My thanks to Chris for the cool insights about the duoprisms! And thanks
>> to Melinda for the picture, dramatically showing the way stickers are slaved
>> to their respective tori. I hadn’t mentally put some of this together as
>> cleanly as in these emails, even after solving the {5}x{5}-3. Great stuff
>> :D
>>
>> One thing that was neat for me was to think about while reading was how the
>> {4}x{4} fit into it all. Since it has only one type of 2C piece, there
>> seems to be a succession of symmetry breaking that happens with the
>> progression of puzzles - {4}x{4} is more symmetrical than general {n}x{n},
>> which in turn is more symmetrical than general {n}x{m}.
>>
>> In some ways, it’s hard to say which puzzles are more difficult. The
>> {4}x{4} might take less sequences, but it’s stickers can move amongst both
>> tori, so the scrambling result is more complicated (it wouldn’t produce a
>> neat picture of dual tori like the {6}x{6} did for Melinda). But even if
>> there is somewhat of a conservation-of-difficulty effect with the tradeoff
>> between number of piece types and scrambling capacity, I guess it still
>> feels like difficulty rises more quickly as the duoprisms become more
>> general. Chris could say better of course.
>>
>> As an aside: the {3}x{3} (which we aren’t officially supporting yet because
>> we’re still considering how the twisting works on it) also only has 1 type
>> of 2C piece, but it is degenerate when it comes to 2C pieces around the
>> "rings". And so unlike the flexible {4}x{4}, it’s pieces are again slaved
>> to their respective tori. I always knew the 4^3 was special :)
>>
>> Chris, congrats to you as well on all the firsts your snagging :) And much
>> thanks for all the issue updates and feedback along the way!
>>
>> All the best,
>> Roice
>>
>> P.S. I agree with Melinda about the {5}x{5}-5 being a big prize. Not sure
>> I’ll ever tackle it, but that had been my favorite from very early on.