This article presents the results of theoretical studies of new polymorphic varieties of fluorographene, which can be formed on the basis of L4-6-12 graphene layers. The calculations of the geometrically optimized structure, band structure, and density of electronic states were performed by the density functional theory method in the generalized gradient approximation. As a result of the theoretical analysis, it was established that three basic structural types of CF layers - T1, T2, and T3 - can be formed, which differ by the order of fluorine atom attachments. In these polymorphic varieties, all carbon atoms are in equivalent structural positions. When calculating the optimized structure of CF polymorphs, it was found that only T1 and T3 varieties have a stable structure. The structure of T2 type layers collapsed during the optimization. The crystal lattices of CF-L4-6-12-T1 and CF-L4-6-12-T3 are hexagonal, with 24 atoms in each of their unit cells. The layer density of the fluorographene layers is 1.42 and 1.52 mg/m(2) for T1 and T2 types, respectively. The carbon-carbon bonds in the structure of the layers have different lengths and vary from 1.5157 to 1.6602 angstrom. The reason for this is the different number of electron pairs forming the corresponding covalent bond. The angles between bonds in CF layers vary over the wide range from 85.00 degrees to 133.47 degrees, which is caused by deformation of the layer structure in comparison with the diamond structure. The sublimation energy of the Ti type fluorographene layer is 13.84 eV/(CF), and the T3 layer is 13.80 eV/(CF). Fluorographene polymorphs are semiconductors with the band gap of 3.193 eV for the CF-L4-6-12-T1 layer and 4.150 eV for the CF-L4-6-12-T3 layer.