The central atom has a hybridization of $\mathrm{sp^3d^3}$. Thus, its structure should be pentagonal bipyramidal.
Why is it not that but a distorted octahedron?
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2$\begingroup$ related chemistry.stackexchange.com/questions/34073/… $\endgroup$– MithoronDec 15 '16 at 17:52
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4$\begingroup$ Possible duplicate of What is hybridisation of XeF6 in solid state? $\endgroup$– MithoronDec 15 '16 at 22:30
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$\begingroup$ NOT a duplicate of @Mithoron's second comment. The answers may be similar, but this question asks about the structure due to an assumed hybridization, whereas the linked "duplicate" asks about the hybridization itself. $\endgroup$– hBy2PyDec 16 '16 at 4:57
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$\begingroup$ While the question linked in @Mithoron's first comment does provide the symmetry group of $\ce{XeF6}$, it does not indicate the actual structure of the molecule. Further, it's closed. $\endgroup$– hBy2PyDec 16 '16 at 4:59
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$\begingroup$ >Why is it not that but a distorted octahedron? || It actually is, though for different reasons. $\endgroup$– permeakraApr 22 '18 at 19:07
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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:
$$\ce{F^-\bond{...}Xe^+-F <-> F-Xe^+\bond{...}F-}$$
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.
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$\begingroup$ So, the molecules of $XeF_6$ are arranged in a lattice with a structure that has more similarity with transition metal halide salts with bridge-bonding, right? $\endgroup$ Dec 15 '16 at 18:27
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$\begingroup$ @EashaanGodbole Erm … what? I’m sorry, I don’t understand what you’re asking … $\endgroup$– JanDec 15 '16 at 18:28
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$\begingroup$ @ Jan The bonding between xenon and the fluorides is 3c-4e like the titanium chloride salts...? $\endgroup$ Dec 17 '16 at 16:54
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$\begingroup$ @EashaanGodbole I’m not familiar with solid state ionic structures too much, but $\ce{TiCl3}$ is a typical ionic structure with closest packing of anions and cations in the octahedral voids. This doesn’t compare well to molecular structures as are present in xenon compounds which feature distinct $\ce{XeF_{2n}}$ molecules. $\endgroup$– JanDec 17 '16 at 17:47
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1$\begingroup$ Correct to a first approximation; the 3c4e model doesn't fully explain XeF6, though, as it is not a static octahedral molecule. [Of course, as you said, there is no (or at most, little) d-orbital involvement.] $\endgroup$– orthocresol ♦Sep 8 '17 at 14:35