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Let X be an object that has exactly three symmetries, so its symmetry group Sym(X) has...

Let X be an object that has exactly three symmetries, so its symmetry group Sym(X) has exactly three elements. Show that X is chiral.

Please show detailed prove!!! Thanks!

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The simple test for chirality is to see whether the mirror image of an object is superimposable (identical): if it is, the object is not chiral (we call this achiral); if the mirror image is different (non-superimposable), then the object is chiral. The two mirror images have a handed relationship to each other.

The object having 3 symmetries doesnot superimpose to its mirror image. Therefore the object having 3 symmetries is not achiral, it is chiral.

Therefore we say that the object X is chiral since the object X is not superimposable to its mirror image.

Hence the above given relation is proved.

I hope it is clear. Thank you.

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