Crystals of the beta-form of the title compound, 1,1,3,3-tetrafluoro-5,5-(2,2,3,3-tetrafluorotetramethylenedioxy)- cyclotri(phosphazene), are triclinic, <P(1)over bar>, with lattice constants a = 12.392(2), b = 16.569(3), c = 19.257(4) Angstrom, alpha = 110.22(3), beta = 90.02(3), gamma = 97.10(3)degrees and V = 3677.9(12) Angstrom(3), with Z = 12, to yield rho(calc) = 2.010 Mg m(-3) for M(r) = 371.0 and F(000) = 2184. The structural data was refined to R = 0.0548 and wR = 0.0567 for 5536 observed reflections [\F\ greater than or equal to 3 sigma(F)] with a goodness-of-fit of 1.61 and a maximum residual of 0.47 e Angstrom(-3). The six crystallographically independent molecules are all structurally equivalent, with approximately the same orientation for each molecule. The molecules are roughly arranged in layers lying parallel to the ac plane. Two types of these layers exist within the structure. Each layer exhibits approximate noncrystallographic symmetry elements. For layers at y similar to 1/6 and 5/6, the appropriate layer-group symmetry notation is pc2a, while the layer at y similar to 1/2 has idealized p2(1)/c11 symmetry. The difference in the symmetries of the two types of layers arises from different sequencing of molecules with right- and left-handed chirality. Both layer groups require beta to be equal to 90 degrees, explaining its observed value. The structure can be described as a polytype structure, in which stacking faults occur every third layer. An ABAABA stacking pattern exists, where A corresponds to the layer at y = 1/6 and 5/6 while B corresponds to the layer at y = 1/2. In addition, successive layers are related by the following set of idealized translation vectors T-A,T-B.