A Science to Big Cube Commutators

Those who were at US Nat'ls probably heard Chris Hardwick speak of the upcoming BH Method.

With the unexpected EARLY release of v-cubes, we have decided to hold back on our publication of our current endeavors, to bring you a complete system, for everything up to the 7x7!

Truly, everything you can learn from the 5x5 is applicable to the other orbits found in the 6x6 and 7x7.

While communicating over the phone and through emails, Chris and I have developed some terminology and vocabulary. I think that there needs to be some set standard, that we will use to define pieces, or locations on a big cube.

Only pieces in the same orbital can be cycled with one another and the other, yet to define one of the oblique centers as

U2b3l would be rediculous and Tedious, confusing even.

First and foremost, lets begin with the basic 3x3. With commutators you are directly solving pieces. So it is important whether you cycle to the F or the L sticker of the FL.

To cycle to the F sticker of the FL you would designate this piece in the cycle as FL. Likewise to cycle to the L sticker of the FL you would notate the piece in the cycle as LF.

A corners position is notated by the Target sticker first, then from there, going counter-clockwise around that corner.

It is not the BRU. If you start at the U, and go counter-clockwise, it would then be U -> R -> B. The order of the pieces is commutative. URB = RBU = BUR, you just start at a different sticker location.

The 8 "Oriented" Corner locations are as follows:
URB, UBL, ULF, UFR
DFL, DRF, DBR, DLB

I think that perhaps knowing the definitions of the 8 "Oriented" Locations will help in defining all of the other pieces on the cube.

Now beyond the 3x3, there are 2 t-center orbitals, 2 wing orbitals, 2 x-center orbitals, and 2 oblique orbitals.

Now on the 5x5, Chris and I define a t-center's location by capitalizing the Face that the T is on, and lowercasing the slice it is on.

The Df for example is on the D face and f slice.

For the 7x7 there is another orbital of Ts. Ul is easy enough to type in reference to the 5x5. On a 7x7 the U2l is the same as the 5x5s Ul. Notice how the 2 is ommited for the 5x5. Perhaps we could come to a standard that we can define a piece with ommitence of the "numbers". Rather if we could define the orbit ONCE per cycle, then then ommit which inner and outter slice you are on, the definition of a piece could be very easy.

With a few letters and symbols and you can define whatever orbit you are talking about, and then the given cycle in less than 10 characters.

Lets pick a few characters to help define the piece type.
"x, w, t, +/-" should suffice.

Continuing:
I said before that there are the inner 3x3s Edges and Corners.
Each piece type has 2 orbits:
Obliques, t-centers, wings, and x-centers.

Ts, wings, and Xs all have inner and outter orbits. We can ommit "orbit notation" and with using the proper casing, it will be understood as the outer orbit of this piece type.

Ts format for a location definition two characters. The first is upper case for the face, and lower case for the slice. As said before such as the Df.

Wings format has three characters. Two upper case, denoting the this wing as that edge's extension. The third character is lower case denoting the slice the wing is on. The definition of a wing's location must follow the definition of both the edge and the corner.
Example: Lets pick an edge, say the BR. Now there is only one BR wing, because the other wing on the other side of the BR edge is actually the RB wing. Is it the BRu or the BRd?

The corners were defined earlier in the first post. URB and DBR So starting with the B then the R, it goes BRd.

X-centers have the format of 3 characters, the first is uppercase with the next two lowercase. The upper notates the Face and the lowers denote the slices, following the definition of a Corner.

Fld (Not the Fdl) for example is an x-center.

It is easy to see whether a wing is in the inner or outter orbit likewise for a t-center. The key to seeing the orbitals on the obliques and x-centers is what is crucial.

Let it be understood that ommission of special character means the outer orbit is being referred to.
NOTE: For clarity though, captialized letters can be used to indicate outter orbitals. However, ommitence is a good practice, just like ommitence of pronouns is used in some languages, such as Spanish.

So for inner wings

The cycle UR3b -> FL3d -> RD3b could be notated as

w*URb -> FLd -> RDb,
*to emphasize with the ommitence of the 'w' it would be understood as the outter wing orbit.

The obliques are very similar to the x-center orbitals, but there is no inner and outter. So lets define them as clockwise and counter-clockwise orbitals. Starting with the Outter x-center touching the oblique determine if you are going clockwise or counter-clockwise to reach the specified oblique, and that will define your orbital.

So from a birds eye view of the U face, the

Urb and its inner and oblique extentions are as follows

22-X
22x+
3344
3344

For the Ulf and its inner and oblique extentions you would see
2211
2211
+x44
X-44

Per actually has given a picture of the 4 orbitals on a 6x6, the inner, outter and oblique x-centers:
http://www.epcrc.org/vcube6_centers.png

Examples
URB is a corner,
FLd is an outter wing
+Ruf is actually the R2u3f, and is clockwise oblique.
LF is an edge location, the target sticker is actually the L sticker.
tUf -> tBd -> tRb; is a redundant statement cycle of inner Ts.
tUf -> Bd -> Rb; is the same cycle above compacted.
XUbl -> Lfu -> Bur; is a cycle of outter Xs, and the X is there for for emphasis but isn't required, as it can be seen by the format, that its and x-center type cycle.