The reaction of tetraethylammonium polychlorides or polybromides in propionitrile with substoichiometric amounts of diluted fluorine at low temperatures leads to the non-classical interhalogen compounds [NEt4][F(X2)3] (X = Cl and Br). These compounds are the first examples of anions containing a central μ6 fluoride anion, which is octahedrally surrounded by Br2 or Cl2 units, respectively. Single-crystal X-ray diffraction revealed that these compounds crystallize in the cubic system with every fluoride anion bridged by halogen units, resulting in a 3D network. Furthermore, single-crystal Raman and IR spectra were measured, and investigations using solid-state calculations were carried out.