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This message addresses both the Non-Trivial Identities thread and the Generalizing Dan Hoey's Syllables thread.  I thought that I had a good handle on the relationship between Non-Trivial Identities and Duplicate Positions, but I find a confusing discrepancy.

Consider the following four positions.

     w = F  R' F' R  U  F'    w' = F  U' R' F  R  F'
     x = U  F' L' U  L  U'    x' = U  L' U' L  F  U'
     y = U' R  U  R' F' U     y' = U' F  R  U' R' U
     z = F' U  L  F' L' F     z' = F' L  F  L' U' F

It is the case that w=x=y=z, what I call a duplicate position.  This duplicate position is obviously related to the list of 1440 non-trivial identities from the Non-Trivial Identity Thread.  Therefore, I was thinking that (for example) we would find wx', wy', and wz' in the list of 1440 non-trivial identities.  But we don't, or at least not exactly.  We find wx' and wy', but not wz'.  Why not?