AHornbaker
Regular
- Joined
- Oct 9, 2012
- Messages
- 64
Hello All,
I wanted to present an idea I had to the forum for using phasing with Winter Variation algs. This achieves the same thing as zz-d in solving LL corners and permuting LL edges.
To help understand this concept better, we must take a look at how phasing works. In short, you use the simple set of moves R U R' U' to permute the edges for the last pair insertion. Considering the last slot on FR, three things happen when you use this alg:
1. Edge Permutation (or Phasing)
-The edge permutation cycles three times in which the edges move from FR -> UR -> UB
-This doesn't account for the parity case
2. Corner Permutation
-The four edges swap position UBL/UBR and FLU/FLD
3. Corner Orientation (or Winter Variation)
-The corner orientation cycles 6 times, and can be illustrated through WV cases. For the 27 WV cases, there are four 6-cycle groups and one 3-cycle group that are as follows:
-The WV cases must preserve the permuted 2x2x1 block on ULB and doesn't have to be 2-gen (which would call for a completely new set of algs)
To use phasing with WV, (assuming no parity case) you use RUR'U' until you have created a permuted 2x2x1 block on ULB, then use a special WV case to orient the corners while preserving the permutation.
This method requires only 27 algorithms in the situation that there is no parity error during phasing. During phasing, because there are 6 distinct RUR'U' cycles, the farthest away a case can be is three cycles. With this in mind, on average you will only spend 6 moves on phasing to create the permuted 2x2x1 block. Taking the parity into account, there is a 1/12 chance you will not have to do any phasing.
Looking back on this, I see the only new thing this thread has posed is influencing the corner permutation as well as edge perm during phasing, taking away those pesky U, H and Z perms after all that hard work doing CP.
I feel that this has a lot of potential because it makes recognition fast (although in two parts, you can look ahead easier) with fast phasing and a very low alg count. Hopefully I haven't left anything out in my explanation.
I wanted to present an idea I had to the forum for using phasing with Winter Variation algs. This achieves the same thing as zz-d in solving LL corners and permuting LL edges.
To help understand this concept better, we must take a look at how phasing works. In short, you use the simple set of moves R U R' U' to permute the edges for the last pair insertion. Considering the last slot on FR, three things happen when you use this alg:
1. Edge Permutation (or Phasing)
-The edge permutation cycles three times in which the edges move from FR -> UR -> UB
-This doesn't account for the parity case
2. Corner Permutation
-The four edges swap position UBL/UBR and FLU/FLD
3. Corner Orientation (or Winter Variation)
-The corner orientation cycles 6 times, and can be illustrated through WV cases. For the 27 WV cases, there are four 6-cycle groups and one 3-cycle group that are as follows:
RUR'U' and WV Case
000 -> 020 -> 221 -> 211 -> 112 -> 102
001 -> 022 -> 222 -> 210 -> 110 -> 101
002 -> 021 -> 220 -> 212 -> 111 -> 100
010 -> 122 -> 201
011 -> 121 -> 202 -> 012 -> 120 -> 200
To understand my notation (pretty simple), here is a page I made about WV:
http://www.speedsolving.com/forum/showthread.php?11594-Winter-Variation-Resources/page2
000 -> 020 -> 221 -> 211 -> 112 -> 102
001 -> 022 -> 222 -> 210 -> 110 -> 101
002 -> 021 -> 220 -> 212 -> 111 -> 100
010 -> 122 -> 201
011 -> 121 -> 202 -> 012 -> 120 -> 200
To understand my notation (pretty simple), here is a page I made about WV:
http://www.speedsolving.com/forum/showthread.php?11594-Winter-Variation-Resources/page2
To use phasing with WV, (assuming no parity case) you use RUR'U' until you have created a permuted 2x2x1 block on ULB, then use a special WV case to orient the corners while preserving the permutation.
This method requires only 27 algorithms in the situation that there is no parity error during phasing. During phasing, because there are 6 distinct RUR'U' cycles, the farthest away a case can be is three cycles. With this in mind, on average you will only spend 6 moves on phasing to create the permuted 2x2x1 block. Taking the parity into account, there is a 1/12 chance you will not have to do any phasing.
Looking back on this, I see the only new thing this thread has posed is influencing the corner permutation as well as edge perm during phasing, taking away those pesky U, H and Z perms after all that hard work doing CP.
I feel that this has a lot of potential because it makes recognition fast (although in two parts, you can look ahead easier) with fast phasing and a very low alg count. Hopefully I haven't left anything out in my explanation.
Other notes:
-Recognition and WV algs may be faster by making a different pattern than the 2x2x1 block, such as looking at the pieces on F and R
Try this:
Solve F2L with EO, CP, and last pair on top, then use RUR'U' (assuming no parity) to phase with the 2x2x1 block, then insert the pair. The whole last layer should be permuted at this point.
-Recognition and WV algs may be faster by making a different pattern than the 2x2x1 block, such as looking at the pieces on F and R
Try this:
Solve F2L with EO, CP, and last pair on top, then use RUR'U' (assuming no parity) to phase with the 2x2x1 block, then insert the pair. The whole last layer should be permuted at this point.
