# Message #797

From: Chris Locke <project.eutopia@gmail.com>

Subject: Re: [MC4D] Records: Now with moar images!

Date: Thu, 26 Nov 2009 01:07:44 +0900

Hello everyone!

I would’ve sent an email off after finishing the length 5 {5}x{4} duoprism,

but it was like 3am my time, so I chose sleep over email. I hope you can

all understand ^^

First, I was asked to give an update on how my solution to the length 2

{6}x{6} duoprism, especially since the program now has the ability to do all

possible twists of these length 2 puzzles, so there are some more

complications that can arise. The main thing I noticed was that you now

need to keep track of the relative orientation of the colors of each torus.

If you put the 2c pieces into place without considering this and you get it

reversed, then you won’t be able to solve. I carelessly neglected this, and

ended up chosing the wrong orientation along the way. I was too lazy to

restart and just fixed the problem there. Luckily it wasn’t too hard to

just flip the colors of one torus, and then fix the damage. Saved me time,

but not twists :P

Now, the big one is the length 5 duoprism {5}x{4}. I totally didn’t expect

to attempt this puzzle, but I was playing around a bit after solving the

{6}x{6} 2, and got toying with the length 5 puzzles, and decided to see if I

am able to fix some 1c centers in them. This quickly turned into a a desire

to go for a full solve. When picking which to do, I settled on the {5}x{4}

over the {5}x{5}. While it’s true that the {5}x{5} has less move sequences

you need to learn because the two torii are the same shape, the pentagonal

shaped toruses always seem more awkward to work with. Basically, I felt

more comfortable working with the nice cube shaped faces :P. My adversion

to the pentagonal torii seemed to be justified a little though. I had a bit

more trouble finding macros for fixing the centers, faces, and edges of the

pentagonal torus.

By the way, one notational convention I used in my notes and macro names is

the following. We all know and use 1c, 2c, 3c… to describe pieces. In

these duoprisms though, I pointed out previously, there are different kinds

of pieces depending on their locations. For instance, among 2c pieces in

the {5}x{4}, there are 2c pieces between two pentagonal facets, 2c pieces

between a pentagonal and square facet, and 2c pieces between two square

facets (facet is just the term for a hyperface - so in 4D that is a 3D

hyperface which are the ‘faces’ you twist). I label these different pieces

2c(5,5), 2c(5,4), 2c(4,4). Similarly you can have 1c(5), 1c(4), 3c(5,5,4),

3c(5,4,4).

Because I felt less comfortable with the pentagonal facets, I always made an

effort to fix those blocks first (I also distinguish between ‘fixing’ pieces

as putting the blocks together, and solving them by putting them in the

correct relative location). I was able to fix all the 1c pieces without any

macros thankfully. Then, I worked my way from there, and developed macros

along the way for each of the kinds of blocks present that needed fixing.

One thing that is nice about fixing blocks over placing them, is that you

can freely rotate the blocks into any arbitrary position you want before

applying a macro, and since you aren’t yet solving them, you don’t need to

be careful about undoing the sequence afterwards (conjugation). This meant

that I was able to use my 3swap algorithms to almost invariably place 2

pieces in the correct block and orientation. When I got to actually solving

though, sometimes the move sequences to put everything in place to solve 2

pieces is too long to remember how to undo, so I usually settled for less

moves to get one piece in, and as such could cut down that part of the solve

a fair bit.

Oh yeah, I also ran into a problem I had before with the solution to the

reduced {5}x{4} 3 puzzle. In this length 3 puzzle, you can have a case

where you think all your 2c pieces are placed nicely, then end up with a

case where you have to swap just two 2c pieces, which seems at first to be

an impossibility. I found out how to fix this before, and again since I

didn’t remember how I fixed it, had to come up with it again, by examining

the effects of each kind of twist. By looking at all the twists, and

determining whether it is an even or odd permutation of 2c pieces, you can

find that by doing a single twist of a square facet, you are doing a 4cycle

of 2c(5,4) pieces, which is odd. So you can basically fix this problem by

using your 3swap algorithm to rotate the 2c(5,4) pieces a quarter-turn, then

you will be left in a case that is more directly solvable. This same

problem can arise in any case where there are odd permutation twists

(therefore, it can also happen in the hexagonal duoprisms).

Anyway, this last step of solving I was able to do actually in less then

half the moves of my first time solving the {5}x{4} 3 due to being more

comfortable with these newer puzzles now. It was quite a marathon of

working a fair bit every night for 3 nights, but it’s over now and was worth

it. I’m actually now able to solve my 5^3 cube without having to resort to

any memorized algorithms now because of my experiences with this and other

puzzles. Very cool.

It’s late here again, so I’ll finish with that. The biggest advice I can

give is that while these bigger puzzles seem intimidating, if you have

patience and some experience with other bigger puzzles (like 4^4 and 5^4)

then even these monsters are conquerable!

Chris

2009/11/25 Melinda Green <melinda@superliminal.com>

>

>

> Dear Cubists,

>

> I had been thinking that we really needed to sex-up the records and puzzle

> pages with images, so I took some screen shots of the {5}x{4} in several

> lengths, uploaded them to the wiki, and inserted the appropriate one into

> each length section of the {5}x{4} puzzle page<http://wiki.superliminal.com/wiki/Pentagonal_Duoprism>and one example into the records

> page <http://wiki.superliminal.com/wiki/MC4D_Records>. I think that this

> turned out quite well and would like to propose that we do this in general.

> I would be very grateful if someone would do this for the rest of the

> puzzles. This would be a great way for a non-programmer/non-solver to make a

> valuable contribution to this project. I’ll be happy to offer suggestions on

> how to capture, edit, upload, and format images if anyone has questions.

>

> In related news, notice that the {5}x{4} records now includes the first

> length-5 solution by Christopher Locke<http://wiki.superliminal.com/wiki/User:Vega12#vega12-5_4_2PentagonalDuoprism.281316.29>.

> Well done Christopher!!

>

> -Melinda

>

>