Structure of xenon hexafluoride
This is one of the many reasons why hybridisation including d-orbitals fails for main-group elements.

Xenon in $\ce{XeF6}$ is not hybridised at all. Instead of invoking populated core d-orbitals or energetically removed d-orbitals (remember the aufbau principle: the next shell’s s-orbital has a lower energy than the d-orbitals you are proposing to include in hybridisation!) xenon just offers its three p-orbitals $\mathrm{p}_x, \mathrm{p}_y$ and $\mathrm{p}_z$ for four-electron-three-centre bonds. These 4e3c bonds can be understood using the following two mesomeric structures:

$$\ce{F^-\bond{...}Xe^+-F &lt;-&gt; F-Xe^+\bond{...}F-}$$

Each $\ce{Xe-F}$ bond has a bond order of ½, and for each fluorine there is another with a bond angle $\angle(\ce{F-Xe-F}) \approx 180^\circ$ as part of the same 4e3c bond.

Also note that this means that xenon’s lone pair is comfortably located in the $\mathrm{5s}$ orbital.