In the gas phase ${\mathrm{PCl}}_5$ exists as individual molecules but in the solid it takes on the ionic structure ${\mathrm{PCl}}_4^{+}{\mathrm{PCl}}_6^{-}$. What are the geometries of these three species?

It is an ionic solid called $\left[\mathrm{PC}14{]}^{+}\right[\mathrm{PCl}16{]}^{-}$ in the solid state.$[\mathrm{PCl}4{]}^{+}$ is a tetrahedral, ${\mathrm{sp}}^3$ hybridised cation. Octahedral and ${\mathrm{sp}}^3{\mathrm{d}}^2$ hybridised, ${\left[{\mathrm{PCl}}^{-}\right]}^{-}$is an anion.