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Complexes of type $\ce{MA3B3}$ have two geometrical isomers, namely:
If we look closely at the mer-isomer, it has a plane of symmetry, so it is optically inactive. But the fac-isomer has no plane of symmetry. Still, it is optically inactive, why?
Being a 12th grader, I wonder where am I wrong in my understanding of optical isomerism in coordination complexes.
Orient the fac- isomer so one A atom is facing towards you and a space between two B atoms is below it. Then the left half of this view is a reflection of the right half so you are actually looking down a mirror plane.
Because you could have chosen any of three A atoms in your view there are three mirror planes, which pass through a common rotation axis. The axis passes through the face that has all A atoms at its corners and the opposite face which has all B atoms. This symmetry is called $C_{\mathrm{3v}}$ in the language of point groups.
