When a ring flips, how do we calculate RMSD?

This surprisingly simple question leads to a very interesting problem! If we take a benzene molecule, say, and rotate it 180 degrees, then we have the exact same molecule, but if we have a data structure in which our atoms are labelled, and we apply the same transformation to the atomic positions, the numbering does not reflect that symmetry. If we were then naively to calculate the RMSD it would be huge, despite the fact that the molecule is, chemically speaking, identical.

How can we make our RMSD calculations reflect these symmetries?

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