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 Post subject: Gigaminx algorithms "tredges"Posted: Thu Sep 10, 2009 11:51 pm

Joined: Sat Feb 03, 2007 10:03 pm
Location: Mississippi
Ok - i've searched but not found anything - can anyone help me in converting 5x5 algs to the gigaminx? In particular, I'm looking for a way to solve my edges similar to this page:

http://www.bigcubes.com/5x5x5/lastedges.html

The problem is that most of these algorithms seem to use 180 degree turns which assume the other piece is lining up in it's "opposite" side, but of course on the gigaminx it is over one...

Or, does anyone have any reliable way to avoid these situations when solving the edges?

Also - anyone come up yet with an algorithm to reverse two edges (like the 4x4 parity) - i.e. (Rr)2 B2 U2 (Ll) U2 (Rr)' U2 (Rr) U2 F2 (Rr) F2 (Ll)' B2 (Rr)2 on the page above...

Thanks!

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 Post subject: Re: Gigaminx algorithms "tredges"Posted: Fri Sep 11, 2009 12:13 am

Joined: Sat Jan 14, 2006 9:36 am
Location: Europe
Yikes, you can get parity? I've solved my gigaminx three times and never had that happen, so I was wondering if it's possible.

Try replacing the half-turns like U2 with U2 and U2' as needed. It worked for the algorithm I use to swap centre pieces.

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 Post subject: Re: Gigaminx algorithms "tredges"Posted: Fri Sep 11, 2009 12:17 am

Joined: Sat Mar 29, 2008 12:55 am
Location: WA, USA
A parity on a gigaminx is impossible from what I understand.

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 Post subject: Re: Gigaminx algorithms "tredges"Posted: Fri Sep 11, 2009 12:35 am

Joined: Sun Oct 08, 2006 1:47 pm
Location: Houston/San Antonio, Texas
Yes that's correct. There are no parities on a gigaminx. It can be proven by the fact that the rotation of a side always cycles an odd number of pieces (5) which is an even-cycle which can't have a parity. Something like that....
Anyway, you will never get a parity unless ofcourse someone tampers it, or you get creative with sticker variations I guess, but then I'm not sure if that's even called a parity....

Peace,
Matt Galla

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 Post subject: Re: Gigaminx algorithms "tredges"Posted: Fri Sep 11, 2009 12:54 am

Joined: Tue Jan 06, 2009 7:23 pm
his parity assumption is both correct and incorrect. it does seem to be *similar* to 5x5x5 parity, but can be avoided. Parity is "impossible" on the giga, but parity like situations can confuse the first time solver

i had this happen every time i soved my gigaminx (3 times now.... its much too hard to turn still). You have all but ....2 or 3 edges done.

what i am assuming you are seeing is where one wing piece is flipped with its corresponding middle edge. so if you have a blue/white middle edge and a wing paired up then the blue on the wing is touching the white on the middle edge and the white on the wing is touching the blue on the middle edge. and then there is a third piece that still needs to be paired

what you should do (assuming you are in the same situation) is put the correct wing in the position that the incorrect wing is in so blue touches blue and white touches white (in this example of course) and then do your normal pairing routine. push the pair into the top layer, and insert a solved pair, and then unpair the tredge, what you should be left with is 3 paired edges... each missing the last wing, and each other contains one of the others wing waiting to be paired. use your logic to put it into position so that when you make a tredge pair, the tredge you put in its place is the last unpaired tredge. once you do the "unpairing move" your last two tredges should get magically paired. perhaps a video is in order?

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 Post subject: Re: Gigaminx algorithms "tredges"Posted: Fri Sep 11, 2009 1:30 am

Joined: Tue Aug 11, 2009 2:44 pm
Here's a simple wing-edge 3-cycle (pardon the verbosity; we need some notation!):

Orient with a top edge facing you. (In this position the "front" face is on the upper half.) Then:

front clockwise
bottom right slice counterclockwise
front counterclockwise
top clockwise
front clockwise
bottom right slice clockwise
front counterclockwise
top counterclockwise

This permutes two edges on the top layer and one on the upper right face. I won't try to name them; try it and you'll see which ones.

Then just use conjugate moves ( X cycle X' ) to put the edges you want to permute there.

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 Post subject: Re: Gigaminx algorithms "tredges"Posted: Fri Sep 11, 2009 8:05 am

Joined: Sat Feb 03, 2007 10:03 pm
Location: Mississippi
Thanks guys - yes this "parity" you describe is what I'm running into. I'll have to digest your answers when I get off work... I think the best idea is to swap things around until you get a three cycle, but the problem is that I keep swapping the wrong way, and ending up with four, or two pieces that need to swap - again I'll have to read these responses again when I can...

 Attachments: pairty.jpg [ 13.72 KiB | Viewed 2969 times ]

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 Post subject: Re: Gigaminx algorithms "tredges"Posted: Fri Sep 11, 2009 12:39 pm

Joined: Tue Aug 11, 2009 2:44 pm
Allagem wrote:
Yes that's correct. There are no parities on a gigaminx. It can be proven by the fact that the rotation of a side always cycles an odd number of pieces (5) which is an even-cycle which can't have a parity. Something like that....

Yeah. A 5-cycle is equivalent to 4 swaps:

12345
21345
23145
23415
23451

so no number of 5-cycles can result in a single swap. This is a stronger parity restriction than on the Rubik's cube. 4-cycles are made of 3 swaps -- an odd number -- so you can combine them to get a single swap. But since each move permutes corners as well as edges, you can only swap two edges if you also swap two corners. On the Gigaminx you can't even do that.

In the "parity" pic above, some other edges must also be out of place elsewhere. Don't look for a way to swap just these two; there isn't one.

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 Post subject: Re: Gigaminx algorithms "tredges"Posted: Fri Sep 11, 2009 1:11 pm

Joined: Sat Feb 03, 2007 10:03 pm
Location: Mississippi
bhearn wrote:
Allagem wrote:
Yes that's correct. There are no parities on a gigaminx. It can be proven by the fact that the rotation of a side always cycles an odd number of pieces (5) which is an even-cycle which can't have a parity. Something like that....

Yeah. A 5-cycle is equivalent to 4 swaps:

12345
21345
23145
23415
23451

so no number of 5-cycles can result in a single swap. This is a stronger parity restriction than on the Rubik's cube. 4-cycles are made of 3 swaps -- an odd number -- so you can combine them to get a single swap. But since each move permutes corners as well as edges, you can only swap two edges if you also swap two corners. On the Gigaminx you can't even do that.

In the "parity" pic above, some other edges must also be out of place elsewhere. Don't look for a way to swap just these two; there isn't one.

AH HA! Thank you so much - I finally realized that my light yellow stickers are really hard to tell apart from the dark yellow stickers, especially when they are next to pink... LOL

 Attachments: oops.jpg [ 42.88 KiB | Viewed 2861 times ]

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 Post subject: Re: Gigaminx algorithms "tredges"Posted: Fri Sep 11, 2009 8:43 pm

Joined: Tue Jan 06, 2009 7:23 pm
jabeck wrote:
bhearn wrote:
Allagem wrote:
Yes that's correct. There are no parities on a gigaminx. It can be proven by the fact that the rotation of a side always cycles an odd number of pieces (5) which is an even-cycle which can't have a parity. Something like that....

Yeah. A 5-cycle is equivalent to 4 swaps:

12345
21345
23145
23415
23451

so no number of 5-cycles can result in a single swap. This is a stronger parity restriction than on the Rubik's cube. 4-cycles are made of 3 swaps -- an odd number -- so you can combine them to get a single swap. But since each move permutes corners as well as edges, you can only swap two edges if you also swap two corners. On the Gigaminx you can't even do that.

In the "parity" pic above, some other edges must also be out of place elsewhere. Don't look for a way to swap just these two; there isn't one.

AH HA! Thank you so much - I finally realized that my light yellow stickers are really hard to tell apart from the dark yellow stickers, especially when they are next to pink... LOL

that would explain it, and i think you need to do a little work with your stickering job, theres a little green guy over there thats about to fall off of his world.....

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 Post subject: Re: Gigaminx algorithms "tredges"Posted: Fri Sep 11, 2009 9:20 pm

Joined: Sat Feb 03, 2007 10:03 pm
Location: Mississippi
Yep - a complete resticker is in order I think - this time with Silver opposite white I think...

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 Post subject: Re: Gigaminx algorithms "tredges"Posted: Sat Sep 19, 2009 5:34 pm

Joined: Sun Feb 11, 2007 8:54 am
Location: New England
Hey guys, I don't know if you remember me, I've been quiet around here for quite a while!

I don't use a specific method for solving the Gigaminx, I just use a method I sorta put together. For the last two edges, I actually make it three edges, and then solve them all at once by doing the two edges at once. So you have all three of the unsolved edges on top. Then bring down one of the edges to solve one, then when you move it out of the "slot" put back in the third unsolved edge in a way that when you put it back, they're all solved. I'm terrible at explaining so I thought a drawing may do.

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