BH Resource Center

[dbeyer]

Adjacent cubies have different classifications of interchangability.
Interchangable on the Slice, the Plane, or Layer, or the lack there of.
All adjacent cubies are interchangable on two layers. URB and UFR are interchangable on the U and R layers.
The URB and URF are interchangeable on the U/R layer and specifically the U plane
The URB and the FUR are interchangable on the U/R layer and specifically R slice
The URB and the RFU are interchangable on the U/R layer, but not on any slice or plane.
Again, this is where the term AnI was coined.
AnI cubies share two layers, their individual unique layers are parallel.
the URB and RFU's parallel layers are the F and B.
A quarter turn on either of the parallel layers will make the AnI pieces interchangeable opposites.
A half turn of either of the parallel layers will make the AnI pieces twisted polar opposites.

 

[dbeyer]

Lets look at an Orbit.

The Controls--
Two adjacent pieces
Turning the F layer
The UFR cubie

Let this piece be AnI to the Buffer.
URB and RUF for example.
Turn F, you have slice-orbit opposites,
Turn F2, you have twisted polar opposites.
Turn F', you have plane-orbit opposites
Turn F4, you have Adjacent non-Interchangable (AnI)

Let this piece be interchangeable on the slice-orbit
URB and FRU
Turn F, you have twisted opposites
Turn F2, you have twisted polar opposites
Turn F', you have twisted opposites
Turn F4, you have Adjacent Slice-Orbit (AsO)

Two adjacent pieces
Let this piece be interchangable on the plane-oribit
URB and UFR
turn F, you have twisted opposites
turn F2, you have parallel polar opposites
turn F', you have twisted opposites.
turn F4, you have Adjacent Plane-orbit (ApO)


The controls--
Two opposite pieces
Turning the F layer
The ULF cubie

Interchangable Opposites
URB and ULF
turn F, you have AnI
turn F2, you have interchangable opposites
turn F', you have twisted polar opposites
turn F4, you have interhchangable opposites

Twisted Opposites - On the Plane (F plane)
URB and FUL
turn F, you have AsO
turn F2, you have twisted opposites
turn F', you have twisted polar opposites
turn F4, you have twisted opposites

Twisted Opposites -- On the Slice (F slice)
URB and LFU
turn F, you have ApO
turn F2, you have twisted opposites
turn F', you have twisted polar opposites
turn F4, you have twisted opposites

Of course if you were to turn the L layer, and use the ULF cubie, you would, wind up with inverted and swapped results of FUL and LFU.
Just look at these trends. Notice the characteristics of the oribits. This will allow you to see the correct setups for orthogonal cases. This will allow you to see the correct insertion for cyclic shifts.
This will allow you to find the correct cancelations on A9s, and Columns cases.

It's a very powerful method. Its not a list of algorithms to memorize. Its a freestyle method, that gives you a vast understanding of the cube's properties. This method goes into muscle memory. And using the techniques described here, you can actually figure out any cycle, and how to solve it by recognizing relationships.

You first recognize two pieces and their locational relationship to one another. What really sets it apart though is the 3rd piece. Just like you could recognize a lot of relationships between corner and edge pairs, but you need to reference the c/e pair to where the solved pair belongs.

Later,
DB

 

[dbeyer]

This is a freestyle method.
You can intuitively solve any cycle of three cubies.
You can optimally solve any cycle of three cubies.
You can determine optimal length of any cycle of three cubies
You can easily invert a permutation of any three cubies

You can limit the demand of thought, by limiting the number of cases by using a buffer.
By using a buffer, you can learn fewer cases and it will go into muscle memory quicker.
Using a buffer, you can correlate and cycle to an images (made of a letter pair).

You can limit parity cases.
Here is my method of approach.
I create a 2x2x1 block (The URB, UR, and UB pieces).
The UR and UB need to be switched. The URB must be permuted/switched with whatever the last corner is. This is always the final case of the parity.

Example Solve:
Buffers: UR and URB
Parity: FL and RFD

I solve all other edges and corners with commutators.
Now the URB and RFD need to be switched.
The UR and FL need to be switched.
This takes some extra moves, yes I know, but it's easier to always do a BH alg than to create difficult setups. The ease of the parity fix is reduced to 1 turn (HTM) setup and a very fast 2-cycle.

I cycle the UR -> FL -> UB. This leave now with the FL solved.
Now the UR and UB need to be switched, as well as the URB and RFD.
Simply then do a setup turn bringing the RFD (or whatever cubie it may be) to the polar opposite of the buffer. This can always be done in one turn. Since six cubies are interchangeable with every piece, the only one that isn't is the polar opposite. This means that the six cubies that are interchangeable with one turn (HTM) with the buffer are also intechangable with its polar opposite.

So, in this case,
D' y'RU'R'U'RUR'F'RUR'U'R'FRy D
Done. URB and RFD have been switched as have UR and UB. I always cycle cycle the parity edge with the UB, (using one extra commutator) to create the 2x2x1 block so that I can freely use the power of polar opposites and the fast algs that I have access to.

Here they are:

URB -> DFL; L'U'LF2R'DR'D'R2F2
URB -> LDF; L'ULUL'U'LFL'U'LULF'L'
URB -> FLD; y'RU'R'U'RUR'F'RUR'U'R'FRy

 

[byu]

Wow dbeyer, thanks for all the great information! I'll try to summarize it and put into my own words and add it to the first post.

 

[byu]

All right, I updated the first post with a bit more information about everything. I STILL can't seem to visualize when two pieces are interchangeable though...

 

[cmhardw]

This is an absolute staple of my solving, called "viewpoint shifting". If you are going to have a resource, I would say that I use this once every solve or every other solve. I find this to be a huge help in quickly seeing the interchangeability of the piece.

http://tinyurl.com/r9s92l

 

[dbeyer]

Looking at two pieces. There are three positional references at to the locations between the two cubies.
Adjacent, Opposite, or Polar Opposites.
Each cubie has 3 adjacent cubies, 3 opposite cubies, and 1 polar opposite.
Adjacent cubies are interchanged by a quarter turn.
Opposite cubies are interchanged by a half turn.
Polar Opposite cubies are interchanged by quarter turn and half turn.

Now looking at Adjacent cubies:
AsO, ApO, and AnI.
Opposite cubies:
Interchangable opposites and twisted opposites.
Polar Opposites:
Parallel polar opposites and twisted polar opposites.

Polar Opposites, twisted opposites, and AnIs are all non interchangable. The rest are. In other words. One piece such as the URB is interchangable with 9 other pieces, and the other 12 permuations are not interchangable.

Later,
DB

 

[byu]

So, I decided to look at Chris's BH edges page, and I'm REALLY confused. I'm not going to learn it until I fully understand corners.

The types I've discovered are:

Drop and Catch
SP9
SP7
Toss Up
B9
Direct Insert
Slice-Plane
A9
Half Slice-Plane

And there are also Setups and Wide Setups. Can anyone explain these? I'm still having trouble understanding A9s and Orthogonals.

 

[dbeyer]

A Wide turn setup can actually be viewed in several different ways.
We use the term Wide-turn because you are turning multiple parallel slices, to transform (setup) the case into a more finger friendly algorithm.

The cycle UR -> FD -> LB can be viewed two ways.
A nice setup for this case is M'.
You have now transformed this case into UR -> UF -> LB
Once you have done the setup, you will then proceed with RE'R' U' RER' U and undo the M' setup.

You could also transform UR -> FD -> LB into UF -> LB -> BR
This can be done by doing the setup (r).

r E' R'U'R E R'UR M

Either way you look at the transformation of the case, you will notice that M' and R merge into one move. Your viewpoint of the case could be different than mine. Chris saw it as, doing the setup and the insertion as a single move. I saw it as moving two pieces as the setup. Both are of course right. They are identities, and equivalent. The point is seeing those Wide Turn canceling effects because they are there!

 

[byu]

Some questions:

How would BH apply to big cube centers and wing edges?

Can I use BH edges and corners on big cubes and not mess up centers if they're still scrambled?

Is E in the F or B direction?

Is S in the U or D direction?

 

[Rubixcubematt]

E is in the D direction, S is in the F direction. and yes, the corners can be used on big cubes, because when you do a move, it is then reversed.

 

[Mike Hughey]

How would BH apply to big cube centers and wing edges?

They have a whole set of algorithms for those too. They'll be posted soon, I'm sure. But in the meantime, for X centers, you can actually use the corners algorithms you've already learned, just using slice moves where necessary. With just a little practice, you'll see how to do that. I've already switched to using some of them in my big cube solves, for the bad cases. There are more optimal ones than those in some cases, but the corners algorithms will generally always work for the X centers.

I've found that in general, if I was using one or two setup moves before to solve a set of X centers, I'm almost always at least as well off using the BH corners algorithm instead of my setup move. It's been a real surprise to me how well that works.

QUOTE=byu;179216]Can I use BH edges and corners on big cubes and not mess up centers if they're still scrambled?[/QUOTE]
As long as you use the proper algorithms on Chris's site (check the *'s), you'll be completely safe on big cubes. That was one of Chris and Daniel's big intentions - to make sure the algorithms are center-safe on big cubes.

 

[CT_Warrior]

Hmm, I think I may be interested in learning BH corners, since I find R2 to be a bit too inconsistent.

I have a few questions though.

1/ How often would one have to review the method? It seems like there are a lot of rules and commutators.

2/ What's the memo like? In pairs, in triplets? Or is it similar to 3OP?

3/ How many moves does it take to solve the corners on average?

Thanks.

 

[joey]

1) Not often, maybe a few of the more esoteric cases. But I think once you get them, it should be pretty much a deep understanding.

2) Pairs, or singles

3) errr, eerr, err, eerrr errr, errr, reeereeree. eerr. I dunno. I want to say like 30~ as a guess.

 

[Mike Hughey]

I did an average of 12 BH corners, in move count:
37, 42 (18T, P), 35, 28 (P), 37 (20T, P), (25 (P)), 42 (18T), 44 (18T), (54 (45T, P)), 38, 35 (P), 25 (P) = 36.3 moves

P means there was parity; I didn't bother to solve parity if it was there. So add in the moves to solve parity if you consider that part of your move count. The numbers with a "T" in parentheses mean that I had to twist corners in place, and that many moves were required to twist the corners. My bad solve in terms of move count was the one that had 4 corners twisted in place, and just 4 corners to permute - I didn't even do the parity, so it was a single 9-move BH cycle, and then 45 moves to twist all the corners. I hate cases like that.

I still just use the standard old commutator for twisting corners, so it takes me 18 moves to twist two corners. People who have bothered to learn good algorithms for it would do it in significantly fewer moves.

 

[joey]

Isn't it 16 moves to twist two like that?

 

[Mike Hughey]

Isn't it 16 moves to twist two like that?

It takes me 18. Maybe just because I'm stupid about it, but it's what Macky taught in his old BLD document, which is when I learned it. I always rotate the cube and then do something like (R' U' R U)*2 L (R' U' R U)*2 L'.

 

[Anthony]

Isn't it 16 moves to twist two like that?

It takes me 18. Maybe just because I'm stupid about it, but it's what Macky taught in his old BLD document, which is when I learned it. I always rotate the cube and then do something like (R' U' R U)*2 L (R' U' R U)*2 L'.

I do the same thing, but what's the better way to twist corners? I know some people do sune/u perm and things like that to twist a couple corners at a time, is there an even better way?

 

[Mike Hughey]

Isn't it 16 moves to twist two like that?

It takes me 18. Maybe just because I'm stupid about it, but it's what Macky taught in his old BLD document, which is when I learned it. I always rotate the cube and then do something like (R' U' R U)*2 L (R' U' R U)*2 L'.

I do the same thing, but what's the better way to twist corners? I know some people do sune/u perm and things like that to twist a couple corners at a time, is there an even better way?

There are a number of people who have learned optimal algorithms for a lot of the common cases.

Or, you could do it like Daniel Beyer does, and perform two optimal commutators to fix them in place with just 16 moves (assuming that's possible for the particular case).

 

[Anthony]

Isn't it 16 moves to twist two like that?

It takes me 18. Maybe just because I'm stupid about it, but it's what Macky taught in his old BLD document, which is when I learned it. I always rotate the cube and then do something like (R' U' R U)*2 L (R' U' R U)*2 L'.

I do the same thing, but what's the better way to twist corners? I know some people do sune/u perm and things like that to twist a couple corners at a time, is there an even better way?

There are a number of people who have learned optimal algorithms for a lot of the common cases.

Or, you could do it like Daniel Beyer does, and perform two optimal commutators to fix them in place with just 16 moves (assuming that's possible for the particular case).

Is there a list of these optimal algorithms for common cases?

I suck at commutators.