Permutation of Last Layer Edges
I use only two algorithms for this step, and this step requires the
application of at most two algorithms. The two algorithms, which I've
taken to liberty of making up some slightly descriptive names for, are
below. They are simply the two different types of 3-cycle of edges for
the Megaminx.
D-Cycle: [R+ L+ U++ L- U+ R-] U+ [R+ U- L+ U-- L- R-]
V-Cycle: [R U R' U' R' F R2 U' R'] U' [R U R' F']
The brackets are included as a memorization aid. In both sequences, the
first part is brackets reorders the pieces, but puts all LL pieces in
the LL. The unbracketed turn therefore only acts on LL pieces. The
turns in the second pair of brackets restore the lower layers.
About inverses, since the D-cycle is a simple conjugate (ie, an
algorithm of the form XYX'), it's inverse is simply the same sequence
with U- in the middle instead of U+. The V-cycle can be inversed by
simply U+ [normal V-Cycle] U-. Perform a V-cycle on a solved Megaminx,
then rotate the whole puzzle and perform it again to see what I mean.
The digrams below show exactly what the D-cycle, inverse D-cycle, and
V-Cycle do to the LL edges. If you have trouble reading the arrows on
my poor diagrams, just know that the non-inverse sequences permute the
pieces clockwise.
Using these algorithms, the general approach for this step involves two substeps:
1) If no two edges are in the right order, pick an edge and solve another edge relative to it, using one algorithm.
2) Fix the remaining 3 edges using one algorithm.
Of course, while you're learning, this step can be done completely with
D-cycles, although it may take a while. This was my least favorite step
while learning.
