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Symmetric cube positions tend to be deeper positions than positions without symmetry. So in the search for a 21 FTM-positon it seems natural to look for positions with a higher degree of symmetry.

For the labeling of cube symmetries there does not seem to exist a really consistent procedure. Michael Reid uses a different labeling than Jaap Scherhuis which also differs from my notation. My notation uses the Schoenflies symbols, I used for example this site for a deeper understanding.

These are the distributions of the optimal solution lengths for the cosets where the edges start at the given M-symmetric position, using the quarter turn metric. The first run took longer than the other three combined; not sure why. Only a handful of positions at length 24; none at 26 or higher. I'm currently running the coset where the edges begin in the known length-26 position. It's interesting to note that with the edges superflipped and reflected across the center, all solutions took either 18, 20, or 22 moves.