Parity issues of 6x6 v-cube

[Termite]

are there other parity cases on a 6x6x6 v-cube than on a 4x4x4 / 5x5x5 cube?
I think there are many ways to combine pieces on a 6x6 cube to reduce it to a 3x3 or 4x4 or 5x5 cube. Are they equally good or bad?

cheers
Michael

 

[mrCage]

are there other parity cases on a 6x6x6 v-cube than on a 4x4x4 / 5x5x5 cube?
I think there are many ways to combine pieces on a 6x6 cube to reduce it to a 3x3 or 4x4 or 5x5 cube. Are they equally good or bad?

cheers
Michael

Hi

Yes the 6x6x6 has one more parity (parody ) than 4x4x4. How this can be i leave it to you to figure it out yourself
Reduction to other size cube is possible - but not very feasible. I cannot think of ANY easy (!!!) way to reduce to for example a 3x3x3 cube.

- Per

 

[AvGalen]

I have never attempted a 6x6x6 solve, but my logic says that only the same KIND of parities (OLL/PLL) as on 4x4x4 are possible when using reduction. That kind of parity should be fixable the same way as on 4x4x4 although the actual layer/slice you perform the algorithm on will be different.

I hope to receive my V-Cubes this week so I can test this theory

 

[MTGjumper]

If you pair up the centre edges, then the outside centre edges (like you would on a 5x5x5) you can end up with both 5x5x5 OLL parity and 4x4x4 OLL parity. That takes a while to sort out by using both of the parity algorithms used on a 4x4x4 and a 5x5x5.

And also, you can get a PLL parity.

 

[cpt.Justice]

On a 6x6 you can get parity during edgepairing, OLL parity and PLL parity. The two latter ones can be solved using expansions of the 4x4 P-algs, and the edgepairing can be solved using the same algs and some intuition

If you pair up the centre edges, then the outside centre edges (like you would on a 5x5x5) you can end up with both 5x5x5 OLL parity and 4x4x4 OLL parity. That takes a while to sort out by using both of the parity algorithms used on a 4x4x4 and a 5x5x5.

And also, you can get a PLL parity.

What is 5x5 OLL parity?!

 

[AvGalen]

Isn't (5x5x5) edge-pairing parity the same as (4x4x4) OLL parity?

 

[Termite]

reducing to 3x3

hmm, one could also combine the corners with their edges and inner single-colour-thingies and then the middle edges. This gives a perfect symmetrical big 3x3 cube made of 2x2 cubes

 

[AvGalen]

hmm, one could also combine the corners with their edges and inner single-colour-thingies and then the middle edges. This gives a perfect symmetrical big 3x3 cube made of 2x2 cubes

That idea has been tried for 4x4x4 (reducing it to a 2x2x2 cube), but it was way to slow. For reducing a 6x6x6 to a 3x3x3 it would be even worse.

However, it is fun to do and might be a nice way to create fake scrambles

 

[cpt.Justice]

Isn't (5x5x5) edge-pairing parity the same as (4x4x4) OLL parity?

It's not the same, even though you can use the same alg's to solve it. And what I meant earlier is this: 5x5 edge-pairing parity shouldnt be referred to as 5x5 OLL parity. Simply because it is not Orienting the Last Layer. Unless you wait with the parity until after the F2L

 

[AvGalen]

Isn't (5x5x5) edge-pairing parity the same as (4x4x4) OLL parity?

It's not the same, even though you can use the same alg's to solve it. And what I meant earlier is this: 5x5 edge-pairing parity shouldnt be referred to as 5x5 OLL parity. Simply because it is not Orienting the Last Layer. Unless you wait with the parity until after the F2L

I disagree about the first part. It is the same! It is just that on a 4x4x4 (or other even cubes) it's hard to recognise untill you reach the last layer.

I agree that OLL-parity and PLL-parity are bad names (OLL-parity can be solved during the center-stage with 1 quarter-turn). But what would be good alternative names?
Edge-Parity and Corner-Parity?

 

[cpt.Justice]

I disagree about the first part. It is the same! It is just that on a 4x4x4 (or other even cubes) it's hard to recognise untill you reach the last layer.

Well, when you put it like that

I agree that OLL-parity and PLL-parity are bad names (OLL-parity can be solved during the center-stage with 1 quarter-turn). But what would be good alternative names?
Edge-Parity and Corner-Parity?

No ideas about good names, but Permutation-parity and Orientation-parity is better than OLL- and PLL-parity

Solving OLL parity with a quarter turn isnt exactly widely used in reduction, is it? How would one do that? Counting all the oriented edges seems pretty timeconsuming

 

[AvGalen]

I disagree about the first part. It is the same! It is just that on a 4x4x4 (or other even cubes) it's hard to recognise untill you reach the last layer.

Well, when you put it like that

I agree that OLL-parity and PLL-parity are bad names (OLL-parity can be solved during the center-stage with 1 quarter-turn). But what would be good alternative names?
Edge-Parity and Corner-Parity?

No ideas about good names, but Permutation-parity and Orientation-parity is better than OLL- and PLL-parity

Solving OLL parity with a quarter turn isnt exactly widely used in reduction, is it? How would one do that? Counting all the oriented edges seems pretty timeconsuming

The quarter turn fix is not (yet) doable for a speedsolve. Analyzing cycles (odd=parity, even=no parity), using an even number of quarterturns if the cycles were even and an odd number of quarterturns otherwise for solving centers works.
Lars and I tried counting oriented/misoriented edges (not cycles) which works in theory, but has problems during execution.
So basically this is only doable for 4x4x4 FMC

 

[rjohnson_8ball]

I agree that OLL-parity and PLL-parity are bad names (OLL-parity can be solved during the center-stage with 1 quarter-turn). But what would be good alternative names?
Edge-Parity and Corner-Parity?

I think of them as "flipped cubies in a super edge" in place of OLL parity and "swapped super edges" in place of PLL parity. On big "even x even" cubes it is tough to distinquish which are flipped wrong/right, so I wait until F2L is done. On big "odd x odd" cubes, the middle cubie of the super edge indicates which way the cubies should be flipped, so I can fix it before F2L.

 

[Ton]

are there other parity cases on a 6x6x6 v-cube than on a 4x4x4 / 5x5x5 cube?
I think there are many ways to combine pieces on a 6x6 cube to reduce it to a 3x3 or 4x4 or 5x5 cube. Are they equally good or bad?

cheers
Michael

No, is you reduce first the two middle edges you have a 5x5 so you can have a 5x5 parity case, and solving the edges as a 5x5 make the 3x3 part you end with the same parities as a 4x4.

I can not think of a fast way to combine these parties.