Difference between revisions of "Beyer-Hardwick Method"

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== BH Edges ==
 
== BH Edges ==
 
- these are the type of edges you'll "see" while learning BH.
 
- these are the type of edges you'll "see" while learning BH.
 
+
I'll edit soon. ;)
'''Half Slice or Slice Plane Moves (4,5,7,9 moves)'''
 
- These guys are the Per Specials of edge comms. Due to the properties of edges on a odd size cube a double interchange om the same layer is allowed making the smallest # of moves to solve edge comms is 4 (Note: Alongside with Pure Comms all commutators comes from them). The commutator [M, U2] is the basis of all slice/half slice plane moves. A 5 mover is a conjugated 4 mover with a cancellation, a 7 mover is a conjugated 5 mover, and a 9 mover is a conjugated 7 mover. Formula: [A, B](4) [S: [A,B]](5,7,9)
 
 
 
'''Pure Commutators (8 moves)'''
 
- alongside with 4 movers all other commutators comes from them. Everything else is a conjugated Pure/4movers commutator. Read BH Pure Comms for more info. Formula: [A, B].
 
 
 
''' A9/B9 (9 moves)'''
 
- same as BH A9s except B9s exist. S9(Slice/Half Slice 9 movers) are a different way of solving 9 moves cases. Formula: [S: [A, B]]
 
 
 
''' Orthogonals (10 moves)'''
 
- Read BH Corners for more info. I don't how to recognize them so good luck. All I know from Chris's post is that this is their formula. Formula: [S: [A, B]]
 
 
 
I'll update this once I know how to recognize them. Byu fucked up and never made a BH edges tutorial. But doing conjugated Pure Comms will still get you far. Besides move optimal is not always fast unless you're good at rotating. No one on SS Forums answered how to recognize BH edges so fuck you guys. :)
 
  
 
== External links ==
 
== External links ==

Revision as of 15:12, 22 May 2017

Beyer-Hardwick Method. An advanced blindsolving method based on the use of 3-cycle algorithms. The fundamental idea behind the BH method is to use pre-memorized, move optimal, commutator 3-cycles for all possible 3-cycles starting from a fixed buffer location. For pieces where orientation is defined, the position and orientation of pieces are solved simultaneously. The use of commutators allows the BH method to be used for solving any sized cube blindfolded.

BH Corners

These are the different types of commutators you will "see" while learning BH.

Pure Commutators (8 moves) - are the purest and smallest form of commutators and all other commutators are just setups into them hence called Pure Commutators (except Cyclic Shifts and Per Specials). They follow this formula: ABA'B' or [A, B] for short.

A is always a 3 move insert B is the interchange move and always 1 move and opposite from the middle move of A. Ex [R U R', D] U is the middle move of the A move that means the B move must be some form of D move

To recognize 1 corner is in 1 layer and the remaining 2 are in a different layer. The 2 corners in one layer must be interchangeable and there must be a 3 move insert between 1 corner in 1 layer and 1 corner in the different layer.

There are only 3 A moves: R U R' R U' R' R U2 R' All Pure Comms are composed from these 3 A moves meaning there's only 18 algs and everything else is just mirror/inverse/rotation from the 18 algs.

A9 (9 moves) - are conjugated Pure Comms with a cancellation resulting in 9 moves instead of 10. They follow this formula: SABA'B'S' or [S: [A, B] ]where S is the setup move.

Ex. [R: RUR', D] becomes R R U R' D R U' R' D' R' or simply R2 U R' D R U' R' D' R'.

All setup moves or S moves must cancel with A. There are no B9s or a corner commutator with a S move that cancels with the B move. If you find 1 then that just means it's a Pure Comm. Edge commutators though have B9s.

To recognize them they're the same as Pure Comms but they don't have a 3 move insert. But that's not always the case so just use elimination to figure it out. The first rule always applies so if you see that then it's a A9.

Orthogonals (10 moves) - are conjugated Pure Comms with no cancellations resulting in 10 moves instead of 9. They follow the same formula [S: [A, B]] as well but the S move doesn't cancel with A nor B.

To recognize them you must know 2 terms:

Opposites - when 2 corners can't go to each other's places with 1 quarter turn. Ex. UBL is opposite to DBR Note: We're only talking permutation-wise. Meaning UBL being opposite to BDR is as the same as saying UBL is opposite to DBR.

AnI or nI (Adj Non-interchangeable or Non-interchangeable - nI is a better term since saying AnI sometimes doesn't make sense. Put it simply a sticker is not interchangeable with another if you can't do it 1 move.

To recognize all 3 corners are opposites and nI to each other. (See what I mean? Saying AnI here doesn't make sense when alll the corners are opposite)

To do them just do ANY quarter turn S move and it will setup into a Pure Comm and undo the S move.

Cyclic Shifts (11 moves) - they don't come from Pure Comms and follow a different formula: [A: B] [C: B] or A B A' C B C'

A is always 2 moves which are comprised of 2 adjacent layers (Ex. F and R) and one is going clockwise and another going counterclockwise

B is always a half turn and is not a opposite layer to either A or C Ex. A is R F so B must not be any form of B or L move

C is the reverse of A(not inverse) Ex. A is R F so C must be F R

Ex. [R F: U2] [F R: U2]

To recognize all 3 corners are on the same layer and are nI.

To do them figure out the middle piece of the cycle. Ex. UBL -> LFU -> BRU The middle piece is UBL and must go to LFU. Do [R F: U2] to swap them and now the next piece must go to BRU so do [F R: U2] to swap them and then you're done.

If you don't understand any of these it's all right since all Cyclic Shifts are the same meaning just by learning the one alg above you just need to mirror/inverse/rotate to solve any Cyclic Shift.

Column Cases (11 moves) - they're just 11 movers that can be done in 2 ways: a setup into an A9 with no cancellation or a setup into a Cyclic Shift with a cancellation.

To recognize there are 2 corners interchangeable by a half turn and the remaining corner is nI to them.

Per Specials (12 moves) - a special type of commutators that follow the same [A, B] formula but the A part is a 5 move insert and B is just a half turn. There's 6 of them and they're all the same meaning you just need to learn 1 alg and just mirror/inverse/rotate it.

Ex. [L U2 R' U2 L, U2]

To recognize all 3 corners are opposite and mutually interchangeable. Ex. UBL -> DFL -> DBR

BH Edges

- these are the type of edges you'll "see" while learning BH. I'll edit soon. ;)

External links

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