#### Cride5

##### Premium Member

After solving COLL, the edges may be in 12 possible positions relative to the corners (assuming you don't allow AUF). This means that if you wanted to solve COLL, while simultaneously solving the edges you would need to know 12 algs for each COLL case (this is what ZBLL is)*....It seems like there would be a lot more than 4 though. (retain edges, swap F/B edges, swap L/R, rotate all clockwise, rotate all counterclockwise, rotate all 180, 2 different adjacent swaps) Or would the oriented edges (or something else) eliminate some of these situations?

Now if you imagine doing phasing and then solving COLL without permuting the edges. The resulting EPLL cases would only include those possibilities in which edges are phased. There are four: H-perm, Solved, and Z-perm from two angles. Solving phased edges during COLL (ZZLL) involves using an algorithm which permutes the edges in one of those four ways.

The theoretical reason that some of the cases you mentioned don't exist (e.g. 4 edges rotated by 90°) is because they form a permutation of the pieces with an odd parity, which is not possible on a Rubik's cube.

*This number is slightly lower than 12 for symmetric COLL cases.