The structure of the fullerene C60F48 has been investigated in the gas phase by electron diffraction from a sample volatilized at 360 degreesC. The analysis was carried out under two assumptions: (1) the molecules have either D-3 or S-6 symmetry as suggested by NMR spectroscopy and verified by an X-ray study of the crystal, and only one of these is present in the gas; (2) all carbon-fluorine bonds have the same length. With the named symmetries, the structure of the carbon skeleton may be defined by the positions of 10 atoms forming two pentagons, one near the top of the molecule and one near the equator, and the locations of the fluorine atoms obtained as the resultant of three vectors originating from carbons not involving a double bond. Simultaneous refinement of the large number of geometrical parameters (30 for the carbon skeleton and 17 for the fluorines) either failed to converge or yielded implausible values, but successive refinements of small groups of four or five parameters were successful. Dozens of groups were tested and all of the resulting models gave satisfactory fits to the observed diffraction patterns. Although values of individual parameters in these models might differ appreciably, the values obtained as averages from the many refinements have good precision. Some of these averaged results (r(a)/Angstrom, angle/deg) for the D-3/S-6 models, with estimated standard deviations, are the following: r(C-F) = 1.368(1)/1.368(1); r(C=C) = 1.327(3)/1.326(4); r(C-sp(2)-C-sp(3)) = 1.503(15)/1.500(11); r(C-sp(3)-C-sp(3)) = 1.585(44)/1.585(41); angle(C-C=C) = 113.7(4)/113.6(4) and angle(C-C-C) = 105.5(1)/105.5(2) within pentagons; and angle(C-C=C) = 124.2(3)/124.0(4) and angle(C-C-C) = 116.6(3)/116.5(3) within hexagons. The average distances from the center of the cage (spherical radii) are quite different for the three types of carbon atoms (those in a double bond, those adjacent to a double bond, and those not adjacent to a double bond) and quite different from the C-60 value of 3.555Angstrom for all atoms. For symmetries D-3/S-6 these radii (R/Angstrom) are 3.937(23)/3.937(17) for sp(3) atoms not bonded to sp(2) ones and 3.781(18)/3.778(20) for sp(3) atoms bonded to sp(2) ones. The average radii to the sp(2) atoms are much shorter than those to the other atoms. These radii fall into two groups for each symmetry: for symmetry D3 they are 3.018(14) and 3.190(15) Angstrom, and for S-6, 3.017(11) and 3.180(15) Angstrom. The surprising length of some of the carbon-carbon bonds and other features of the structures relative to the structure of C-60 are discussed.