"Antizeolite"borates are built with the positively charged porous [Ba12(BO3)6]6+ framework, hosting various guest anion groups. Resembling zeolitic structures, the porous borates ease with the control of structure-related properties by exchanging the type and amounts of those guest anion groups. Crystals of copper-doped "antizeolite"fluoride borate Ba12(BO3)6[BO3][LiF4]:Cu were grown from high-temperature solution. Using X-ray single-crystal diffraction, the structure was solved and refined in the centrosymmetric P42/mbc space group in contrast to noncentrosymmetric undoped Ba12(BO3)6[BO3][LiF4] crystals (P42bc space group). Optical and electron spin resonance spectroscopic investigations concluded the presence of copper ions in both Cu+ and Cu2+ states, which makes the Ba12(BO3)6[BO3][LiF4]:Cu crystal a potential matrix for tissue equivalent dosimeters. Intensive luminescence band at 412 nm associated with the Cu+ centers was observed under 325 nm excitation. The activation of crystals creates centers of radiative recombination which enhance the thermally stimulated luminescence intensity.