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Does an axis of symmetry determine chiralty?

Is axis of symmetry considered a true symmetry?

From the above two links, I read that a compound having axis /alternating axis of symmetry is NOT necessarily achiral. For example, trans-1,3-dimethyl cyclopentane has an axis of symmetry but it is still chiral and hence optically active.

My doubt is, then why would we look for alternating axis of symmetry in the first place? Where/How is it useful?

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    $\begingroup$ "I call any geometrical figure, or any group of points chiral, and say that it has chirality, if its image in a plane mirror, ideally realized, cannot be brought to coincide with itself." Lord Kelvin, Baltimore Lectures, 1904. $\endgroup$
    – user55119
    Commented Feb 26, 2019 at 19:53

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Alternating axes are not axes, much like a Guinea pig is not a pig.

Having axes of symmetry is irrelevant to chirality.

Having alternating axes is a necessary and sufficient condition of non-chirality, that's why we look for them.

So it goes.

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    $\begingroup$ Some users may be more familiar with the term "improper axis of rotation" versus "alternating axis." $\endgroup$
    – Zhe
    Commented Nov 16, 2018 at 13:56

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