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 Post subject: easy pure 3 cycle on the bauhinia (10 moves)
PostPosted: Tue Jan 07, 2014 5:49 pm 
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Hello! I just found an easy 3 cycle for the bauhinia dodecahedron! It's very easy and only 10 moves!!!!! on the solving post there was said that 12 moves was the lowest pure 3-cycle, now 10 its the real lowest?

video:
https://www.youtube.com/watch?v=mRcJiJR ... ata_player


Attachments:
20140107_234817.jpg
20140107_234817.jpg [ 1.95 MiB | Viewed 984 times ]

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Last edited by Elias Acrich on Tue Jan 07, 2014 7:25 pm, edited 1 time in total.
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 Post subject: Re: easy pure 3 cycle on the bauhinia (10 moves)
PostPosted: Tue Jan 07, 2014 6:32 pm 
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Eliasthecollector93 wrote:
Hello! I just found an easy 3 cycle for the bauhinia dodecahedron! It's very easy and only 10 moves!!!!! on the solving post there was said that 12 moves was the lowest pure 3-cycle, now 10 its the real lowest?

maybe I'll post a video or something!!

Please do. Without jumbling 12 moves is definitely the lowest pure commutator length. Also, you should check to see if all 10 moves are really required. A 10-move commutator is of the form [[1,1],1] (I suppose jumbling could violate this rule though) but you might be able to do it in [[1:1],1] which is only 8 moves.

When I get home I'll work on jumbling commutators for it too.

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 Post subject: Re: easy pure 3 cycle on the bauhinia (10 moves)
PostPosted: Tue Jan 07, 2014 6:41 pm 
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originally was 12 moves but as you said I skipped 2 moves!

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 Post subject: Re: easy pure 3 cycle on the bauhinia (10 moves)
PostPosted: Tue Jan 07, 2014 7:07 pm 
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Can you give us the algorithm you used and the notation (as far as I know there is no definite notation)? If so, I could test it out and see if it works.

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 Post subject: Re: easy pure 3 cycle on the bauhinia (10 moves)
PostPosted: Tue Jan 07, 2014 7:22 pm 
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Well, all my 3-cycles are 12 steps. These also apply to Eitan's Star and the Radiolarian 3. If there is a 10 step 3-cycle on the Bauhinia, it could take advantage of the fact that five of the points on each face are the same colour (so not exactly pure). Here is my nomenclature:
Attachment:
Nomenclature.PNG
Nomenclature.PNG [ 516.65 KiB | Viewed 927 times ]

Here is one of the 3-cycles from my Bauhinia notes (inherited from Eitan's Star):
Attachment:
3-cycle illustration.PNG
3-cycle illustration.PNG [ 191.65 KiB | Viewed 927 times ]

I'd love to see a pure 3-cycle that is shorter than 12 steps!

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Last edited by Pete the Geek on Tue Jan 07, 2014 7:25 pm, edited 2 times in total.

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 Post subject: Re: easy pure 3 cycle on the bauhinia (10 moves)
PostPosted: Tue Jan 07, 2014 7:24 pm 
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edited the post with a video!! Pete mine is 10, but uses jumbling!

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 Post subject: Re: easy pure 3 cycle on the bauhinia (10 moves)
PostPosted: Tue Jan 07, 2014 7:36 pm 
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Eliasthecollector93 wrote:
edited the post with a video!! Pete mine is 10, but uses jumbling!


Un-private the video :D


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 Post subject: Re: easy pure 3 cycle on the bauhinia (10 moves)
PostPosted: Tue Jan 07, 2014 7:44 pm 
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ups sorry! now should work

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 Post subject: Re: easy pure 3 cycle on the bauhinia (10 moves)
PostPosted: Tue Jan 07, 2014 11:47 pm 
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Eliasthecollector93 wrote:
edited the post with a video!! Pete mine is 10, but uses jumbling!

Interesting. Your sequence isn't a commutator.

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 Post subject: Re: easy pure 3 cycle on the bauhinia (10 moves)
PostPosted: Wed Jan 08, 2014 9:40 am 
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Very interesting, how did you come up with it?

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 Post subject: Re: easy pure 3 cycle on the bauhinia (10 moves)
PostPosted: Wed Jan 08, 2014 10:33 am 
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It's really amazing! 10 moves! Somehow it's a little like commutator, which has a 5 step setup at first, but after that the algorithm doesn't undo the setup in a normal way but still can reverse the setup! Really brilliant one!

And you know what? I try this algorithm on my Eitan's Star immediately, and the result is......
Attachment:
File comment: 3 cycle on Eitan's Star
IMG_20140108_232325.jpg
IMG_20140108_232325.jpg [ 1.59 MiB | Viewed 767 times ]


Work!


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 Post subject: Re: easy pure 3 cycle on the bauhinia (10 moves)
PostPosted: Wed Jan 08, 2014 12:41 pm 
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Thanks Otischeng! glad it is helping!

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 Post subject: Re: easy pure 3 cycle on the bauhinia (10 moves)
PostPosted: Thu Jan 09, 2014 9:19 pm 
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Elias, that is amazing! You do have a 10 move 3-cycle, and I agree it is an easy algorithm. In the notation I use this would be:

FR UFR UFL' UFR' FR' J(MBR) J(UFR') UFL 2UFR' J(MBR)

Of course, I don't have jumbling algorithms, so I may have to tweak the jumbling notation a bit. Visually, it is easy to follow.

When I first looked at the Bauhinia, I didn't see the jumbling as doing anything that couldn't be done through regular turns. The idea to use jumbling to shorten algorithms has tremendous potential and I can see a lot of complex puzzles being revisited.

When I think if applying this to Eitan's Star, it is very exciting. The sixty two-colour corner points (as I call them) have unique placement and it generally takes me more than sixty 3-cycles to place all of the corner points. Shortening each of those sixty-plus algorithm applications from 12 to 10 moves will have a huge impact on this part of the solve.

So, I'm curious to know how you developed this algorithm. Trial-and-error?

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 Post subject: Re: easy pure 3 cycle on the bauhinia (10 moves)
PostPosted: Fri Jan 10, 2014 7:58 am 
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:) before scramblng that beast, I tried to apply some algorithims, I started with the typical 3 petal cycle from the rex cube and worked, so I began trying things and one of them was to first break a petal ( first move of the secuence) and then typical rex swap, as a result I ended up with a little triangle isolated and I realized that swaping 3 big petals would create what I wanted and the only way through was by jumbling! I have aplied the same concept on the rex cube and the result is also a 10 move 3-cycle!

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