• On the other hand, absence of a mirror plane or a center of inversion must not be mistaken as indicating chirality. Such a conclusion, though correct in many cases, would be wrong in the presence of an axis of rotoreflection S_n.

The following molecule is an all-trans tetra-sec-butylcyclobutane. The four sec-butyl groups are of (R)- and (S)-configuration in turn.

mirror image (hint) an all-trans tetra-sec-butylcyclobutane

This molecule does not contain a or an i, but is nevertheless identical to its mirror image, i.e. achiral. It contains a S₄. You should check all this.

Objects containing a S₄, S₈, ... have this property. Convince yourself of this fact using the diagram of S₄.

S4	The mirror image of S4 is identical to S4, as seen after a 90° rotation.

With a little experience you will not overlook a S_n (n > 2) if it is present, if you are aware of this possibility.