How can fluorite structure exist?

From the information from Google the radius of $\ce{Ca^2+}$ cation is $100 \,\pu{pm}$ and of $\ce{F-}$ anion is $132\, \pu{pm}$, so essentially $\ce{F-}$ ion should form the Bravais lattice (FCC/CCP) as it is larger in size and $\ce{Ca^2+}$ should go to the tetrahedral voids but in reality it is just opposite.


How can smaller sized calcium cation form the Bravais lattice?


(The data has been taken form first results form Google search) 


Please do correct me if I am conceptually wrong somewhere.


