# Chirality of spirocyclic compound

I am facing trouble with the following problem.

Is (R)-1,7-dioxaspiro[5.5]undecane chiral?

My idea is that the compound possess a plane of symmetry and thus should be achiral. However if we take its mirror image then the bond pointing below of the plane will become above the plane and thus it will not form a nonsuperimposable mirror image indicating that it is chiral. Certainly one of the approach is incorrect. I couldn't understand which one.

• This is a great example of axial chirality. – Zhe Dec 24 '16 at 20:43
• – Loong Dec 25 '16 at 20:38

The only element of symmetry I can see in the compound is a $C_2$ axis (rotation by $180^\circ$). This axis would also bisect the spiro carbon, but it would map the oxygens onto each other. Having only a $C_2$ axis allows a compound to be chiral (point group $C_2$) and thus your compound is chiral.