# Pyraminx Crystal Edge Parity?



## some1rational (Aug 26, 2010)

Hey guys, I just got my pyraminx crystal today and am in the process of solving it.

However, as I was solving it, two edge pieces fell out and I didn't know which one went where when i put it back together (put it back together partially solved)

Now I'm at the very end and I only have two edges swapped (everything correctly oriented); I just wanted to know if this is because I put it in wrong accidentally when I put it back together or is there really a way to have just two edge pieces SWITCHED with the rest of the puzzle solved

I'm pretty sure its not possible and I just switched them accidentally when putting the puzzle back together (since I can only find commutator algorithms that do 3-cycles of edges) but I just want to make sure here


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## hawkmp4 (Aug 27, 2010)

If the puzzle has 12 colours (which I'm pretty sure it does) then no, it is because it popped and you assembled it incorrectly.


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## Forte (Aug 27, 2010)

Just so you know why, since any turn does 3 5cycles (edges, edges, corners), it cannot change the permutation parity.

EDIT: looooooooool thanks TMOY >_>


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## TMOY (Aug 27, 2010)

Actually it does 5-cycles, not 3-cycles, but otherwise you're right.


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## mrCage (Aug 27, 2010)

TMOY said:


> Actually it does 5-cycles, not 3-cycles, but otherwise you're right.


 
He did not say 3-cycles. He said 3 distinct 5-cycles. Learn to read

Per


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## Forte (Aug 27, 2010)

mrCage said:


> TMOY said:
> 
> 
> > Actually it does 5-cycles, not 3-cycles, but otherwise you're right.
> ...



I edited


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## mrCage (Aug 27, 2010)

Forte said:


> mrCage said:
> 
> 
> > TMOY said:
> ...


 
Ok. I'll learn to be quiet


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## Stefan (Aug 27, 2010)

Forte said:


> Just so you know why, since any turn does 3 5cycles (edges, edges, corners), it cannot change the permutation parity.



A middle layer turn does *four* 5-cycles.


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## some1rational (Aug 27, 2010)

haha thanks guys,

I wasn't confident enough in my own intuition and logic to gauge whether or not it was actually possible haha, good thing because I wasn't able to figure out a move that could do it

EDIT: wait, can someone explain why it does FOUR 5-cycles? I can see that there are '2' sets of 5 edges and one set of 5 corners...so wouldn't that be three 5-cycles for one turn? and what exactly is a middle layer turn in this case? it seems there's only one way to turn the pyraminx crystal

also, (one more question, haha) can someone briefly explain why it cannot change the parity given the number of 5-cycles? sorry just got into the whole puzzle craze but I'm enjoying it lol


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## Paul87 (Aug 27, 2010)

some1rational said:


> Hey guys, I just got my pyraminx crystal today and am in the process of solving it.



Just wondering... where did you order it? It's out of stock on mefferts.com and I can't find it anywhere else.


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## Forte (Aug 28, 2010)

some1rational said:


> EDIT: wait, can someone explain why it does FOUR 5-cycles? I can see that there are '2' sets of 5 edges and one set of 5 corners...so wouldn't that be three 5-cycles for one turn? and what exactly is a middle layer turn in this case? it seems there's only one way to turn the pyraminx crystal



Yeah I'm confused about this too (probably because I don't have a pyra crystal >_>)



some1rational said:


> also, (one more question, haha) can someone briefly explain why it cannot change the parity given the number of 5-cycles? sorry just got into the whole puzzle craze but I'm enjoying it lol



It actually doesn't really matter how many 5-cycles there are 
It just matters that all 5-cycles are even permutations (it's like swapping pairs of edges 4 times, which is an even number of swaps)


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## Stefan (Aug 28, 2010)

Forte said:


> Yeah I'm confused about this too (probably because I don't have a pyra crystal >_>)



Check out the one on the right, you can clearly see the two horizontal turning planes separating the top, middle and bottom layers:
http://media.photobucket.com/image/...zzles/Dutch Cube Day 2008 puzzles/all3750.jpg


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## Forte (Aug 28, 2010)

StefanPochmann said:


> Forte said:
> 
> 
> > Yeah I'm confused about this too (probably because I don't have a pyra crystal >_>)
> ...



Oh I see it now 
I dunno why I couldn't see it before


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## some1rational (Aug 29, 2010)

Paul87 said:


> some1rational said:
> 
> 
> > Hey guys, I just got my pyraminx crystal today and am in the process of solving it.
> ...



I got it on amazon 

http://www.amazon.com/Mefferts-Chal...e=UTF8&s=toys-and-games&qid=1283068113&sr=8-1

seems like its still pretty available


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