Parity on higher order puzzles.

[mrCage]

The higher order cubes and even the mosaic cube has parity. So is this always the case for "higher order" puzzles. Proof or counterexample anyone???

Per

 

[vcuber13]

the mosaic cube parity is a centre twist right?

 

[Tao Yu]

Gigaminx has no parity http://www.speedsolving.com/forum/showthread.php?15861-Gigaminx-Parity

Not fully sure if teraminx has parity. Searching for "teraminx Parity" didn't return any threads specifically on that subject

 

[StachuK1992]

Sq1? Void cube?
A list of these would be nice here.


I'm thinking my interpretation of this thread may be off?

 

[Kirjava]

Not sure how you're defining "higher order puzzle" and "parity" here.

Anyway, the 1x2x17 doesn't have parity.

 

[Escher]

Not sure how you're defining "higher order puzzle" and "parity" here.

Ya the question is a little ambiguous...

 

[mrCage]

By higher order i mean a puzzle with more layers than the base puzzle. The 4x4x4 is a higher order 3x3x3 (or 2x2x2) and the gigaminx is higher order megaminx. A 1x2x17 is not really higher order with my interporetation. It has to be extended in all 3 dimensions. A 2x2x17 might be considered a higher order 1x1x16. Hard to define precisely. I think the gigaminx is good couterexample already...

Let us compile a list of higher order puzzles with and without parity.

Per

 

[Kirjava]

Define "base puzzle".

 

[mrCage]

Define "base puzzle".

I think my post gave a "definition by example"

Parity is kind of a nightmare to define though. Apparent swap would do for now ...

Per

 

[Kirjava]

I know, but I don't know why you gave 3x3x3 as an example of a base puzzle when 2x2x2 has a lower order than it.

 

[mrCage]

I know, but I don't know why you gave 3x3x3 as an example of a base puzzle when 2x2x2 has a lower order than it.

Maybe because it's a more common puzzle?? Ok, then 2x2x2 is a lower order 3x3x3

Per

And i believe the 3x3x3 was invented before 2x2x2 right?? Or at least was released before it

 

[JonnyWhoopes]

Not trying to be facetious, but then how do we determine what the base puzzle is? Is the megaminx just a lower order gigaminx?

 

[mrCage]

Not trying to be facetious, but then how do we determine what the base puzzle is? Is the megaminx just a lower order gigaminx?

Correct! Teraminx is higher order gigaminx (or megaminx). Petaminx is higher order teraminx (or etc ...)

Per

Then what is flowerminx?? ...

 

[Kirjava]

Maybe because it's a more common puzzle??

And i believe the 3x3x3 was invented before 2x2x2 right?? Or at least was released before it

These are both very silly reasons.

Your definition of "base puzzle" and "higher order puzzle" is arbitrary. Nothing wrong with this, it just makes it somewhat meaningless.

 

[JonnyWhoopes]

Correct! Teraminx is higher order gigaminx (or megaminx). Petaminx is higher order teraminx (or etc ...)

Per

Then what is flowerminx?? ...

So, you're pretty much just asking "what puzzles have parity" right? If we have no definition of a base puzzle, or what higher order means, then this is what it comes down to.

 

[Kirjava]

2x2x2 and 3x3x3 are small cubes or "lower order cubes".

Why?

A flowerminx is a 2x2x2 dodecahedron. The creator decided not to use the mathematical term I guess. The real name for it would be "whatever comes before mega" and minx.

Kilominx is something else.

 

[uberCuber]

OLL edge parity: Only even numbered cubes
PLL parity: Only even numbered cubes.
OLL corner parity: Uh... only pops?
Edge paring parity: All big cubes that involve edge pairing. (This means "cubes" not other twistypuzzles like dodecahedrons).

These are assuming reduction method, though, which not everybody uses. Because PLL parity isn't parity at all, and what you are referring to as "OLL edge pairty" and "edge pairing parity" become the same thing.

 

[qqwref]

A pretty good rule of thumb is that any turn of 1/(2n+1) of a full rotation can't cause parity (whereas turns of 1/(2n) can). So, any higher-order Pyraminx, Megaminx, Dino Cube, Skewb, and so on can't have parity, in the sense of being able to do a pure 2-cycle without affecting any other pieces.

 

[TMOY]

I think you mean any other pieces of the same orbit, or else the corners+centers parity of the 4^3 for example wouldn't qualify as a parity.

 

[mrCage]

These are both very silly reasons.

Your definition of "base puzzle" and "higher order puzzle" is arbitrary. Nothing wrong with this, it just makes it somewhat meaningless.

Then how about this: 3x3x3 is the base cube puzzle because it's the lowest order of it's kind with all the various types of pieces. 2x2x2 is not the base because it has no center pieces. Same goes with flowerminx versus megaminx. We have always used higher order term without a proper definition so it's about time we define it now. This forum is the right place to discuss this

Per